Relevant bibliographies by topics / Discrete Fourier transform (DFT)

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  1. Journal articles
  2. Dissertations / Theses
  3. Books
  4. Book chapters
  5. Conference papers
  6. Reports

Academic literature on the topic 'Discrete Fourier transform (DFT)'

Author: Grafiati
Published: 4 June 2021
Last updated: 6 September 2023

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Journal articles on the topic "Discrete Fourier transform (DFT)"

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Mukhammad Solikhin, Yohanssen Pratama, Purnama Pasaribu, Josua Rumahorbo, and Bona Simanullang. "Analisis Watermarking Menggunakan Metode Discrete Cosine Transform (DCT) dan Discrete Fourier Transform (DFT)." Jurnal Sistem Cerdas 5, no. 3 (December 11, 2022): 155–70. http://dx.doi.org/10.37396/jsc.v5i3.192.

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Digital image watermarking is the insertion of watermarks into digital image media. Several types of watermarking methods used are Discrete Cosine Transform (DCT) and Discrete Fourier Transform (DFT). Both of these watermarking methods work in the frequency domain (transform). Digital image watermarking using the frequency domain is carried out on the frequency coefficient. This study used 30 digital image data as material for digital image watermaking analysis with 10 data each in binary, grayscale and color digital images in jpg, png and bmp formats. Digital images in the binary and grayscale domains are conversions from digital images in the true color (RGB) domain. Digital image watermarking includes three main processes, namely embedding the watermarked image on the original digital image, extracting the watermarked image and measuring the correlation between the two digital images. Correlation aims to measure two variables that have the same relationship. The technology used in this research work is MATLAB (Matrix Laboratory) as a high-performance programming language for computing in solving problems with solutions expressed in mathematical notation. The results of the discussion prove that the watermarking process in terms of color, for DCT, RGB is better and binary is better for DFT. And the watermaking process, in terms of the type of watermark inserted, for both DCT and DFT, a good watermark is an invisible watermark.
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Balsa, Jose. "Comparison of Image Compressions: Analog Transformations." Proceedings 54, no. 1 (August 21, 2020): 37. http://dx.doi.org/10.3390/proceedings2020054037.

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A comparison between the four most used transforms, the discrete Fourier transform (DFT), discrete cosine transform (DCT), the Walsh–Hadamard transform (WHT) and the Haar-wavelet transform (DWT), for the transmission of analog images, varying their compression and comparing their quality, is presented. Additionally, performance tests are done for different levels of white Gaussian additive noise.
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Somasekhar, B., Ch Mohana Krishna, and Y. Murty. "Investigations on wavelet and Fourier transform based channel estimation in MIMO-OFDM system." International Journal of Engineering & Technology 7, no. 2.21 (April 20, 2018): 228. http://dx.doi.org/10.14419/ijet.v7i2.21.12178.

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In this paper channel estimation methods for MIMO-OFDM system are investigated based on Fourier Transform and Wavelet Transform. The channel estimation algorithm based on Discrete Fourier Transform (DFT) cause energy leakage in multipath channel with non-sample-spaced time delays. Discrete Cosine Transform (DCT) based channel estimator can mitigate the drawback of Discrete Fourier Transform based channel estimator, when the non-sample spaced path delays are available in multipath fading channels. Wavelet based systems provide better spectral efficiency because of no cyclic prefix requirement, with narrow side lobes and also exhibit improved BER performance. Simulation results reveal that the DWT based transform outperforms the conventional DFT and DCT based channel estimator in terms of bit error rate and mean square error.
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Ito, Izumi. "A New Pseudo-Spectral Method Using the Discrete Cosine Transform." Journal of Imaging 6, no. 4 (March 28, 2020): 15. http://dx.doi.org/10.3390/jimaging6040015.

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The pseudo-spectral (PS) method on the basis of the Fourier transform is a numerical method for estimating derivatives. Generally, the discrete Fourier transform (DFT) is used when implementing the PS method. However, when the values on both sides of the sequences differ significantly, oscillatory approximations around both sides appear due to the periodicity resulting from the DFT. To address this problem, we propose a new PS method based on symmetric extension. We mathematically derive the proposed method using the discrete cosine transform (DCT) in the forward transform from the relation between DFT and DCT. DCT allows a sequence to function as a symmetrically extended sequence and estimates derivatives in the transformed domain. The superior performance of the proposed method is demonstrated through image interpolation. Potential applications of the proposed method are numerical simulations using the Fourier based PS method in many fields such as fluid dynamics, meteorology, and geophysics.
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Ramadhyagita, Irsya Luthfiah, Annisa Annisa, Faishal Kamindra, and Farhan Muhammad Rizky. "Kajian Discrete Fourier Transform untuk Menganalisis Sinyal Arbitrer." Mitra Pilar: Jurnal Pendidikan, Inovasi, dan Terapan Teknologi 1, no. 1 (June 30, 2022): 7–16. http://dx.doi.org/10.58797/pilar.0101.02.

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Abstract This study aims to examine the Discrete Fourier Transform using arbitrary signals. Signal processing is a mathematical operation performed on a signal to obtain the required information. In this case, a transformation occurs. The Fourier transform is a popular method often used to change the time form to the frequency form intended to facilitate analysis. The Fourier transform is divided into two parts: the Continuous Fourier and the Discrete Fourier. The program developed by the researcher, DFT, analyzes arbitrary signals created in two programs. The first program is a function of the DFT and the second is the main program used to generate DFT graphs. In this project, researchers will analyze arbitrary signals decomposed into sine waves. This program uses two main libraries, namely matplotlib, and NumPy. In this case, we have used the DFT method and plotted the results of the calculations performed. Now the researcher will analyze the process that the researcher did while using the DFT method and plot the results. Using DFT, arbitrary signals can be arranged into a series of sinusoids, each with a different frequency. The DFT method can arrange signals into a series of sinusoids with different frequencies. In the DFT amplitude spectrum, the signal frequency is shown as a vertical bar, with the height being the signal amplitude in the time domain. DFT can convert a sequence of equally spaced signals into information about the frequencies of all sine waves needed to sum the time domain signals. Abstrak Penelitian ini bertujuan untuk mengkaji Discrete Fourier Transform dengan menggunakan sinyal arbitrer. Pengolahan sinyal adalah suatu operasi matematik yang dilakukan terhadap suatu sinyal sehingga diperoleh suatu informasi yang dibutuhkan. Dalam hal ini terjadi suatu transformasi. Transformasi Fourier merupakan salah satu metode popular yang sering digunakan untuk mengubah bentuk waktu bentuk frekuensi yang ditujukan untuk mempermudah analisis. Transformasi Fourier dibagi menjadi 2 bagian yaitu Fourier Kontinu dan Fourier Diskret. Program yang dikembangkan oleh peneliti yaitu, DFT untuk menganalisis sinyal arbitrer yang dibuat dalam dua program. Program pertama adalah fungsi dari DFT dan program kedua adalah program utama yang digunakan untuk memunculkan grafik DFT. Dalam project ini peneliti akan menganalisis sinyal arbitrer yang sudah diuraikan menjadi gelombang sinus. Program ini menggunakan dua library utama, yaitu matplotlib dan numpy. Pada case kali ini, telah menggunakan metode DFT dan membuat hasil plot dari perhitungan yang dilakukan. Sekarang peneliti akan menganalisis proses yang peneliti lakukan selama menggunakan metode DFT dan membuat hasil plot. Sebelum membahas hasil perhitungan, mari kembali membahas metode DFT itu sendiri. Dengan menggunakan DFT, dapat disusun sinyal arbitrer menjadi serangkaian sinusoid dan masing-masing akan memiliki frekuensi yang berbeda.Metode DFT dapat menyusun sinyal menjadi serangkaian sinusoid yang memiliki frekuensi yang berbeda-beda. Dalam spektrum amplitude DFT, frekuensi sinyal ditampilkan sebagai batang vertikal dengan ketinggiannya adalah amplitude sinyal dalam domain waktu. DFT dapat mengubah urutan sinyal dengan jarak yang sama menjadi informasi tentang frekuensi semua gelombang sinus yang diperlukan untuk menjumlahkan sinyal domain waktu.
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Shi, Zhiping, Yupeng Zhang, Yong Guan, Liming Li, and Jie Zhang. "The Formalization of Discrete Fourier Transform in HOL." Mathematical Problems in Engineering 2015 (2015): 1–8. http://dx.doi.org/10.1155/2015/687152.

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Traditionally, Discrete Fourier Transform (DFT) is performed with numerical or symbolic computation, which cannot guarantee 100% accurate analysis which may be necessary for safety-critical applications. Machine theorem proving is one of the formal methods that perform accurate analysis with completeness to some extent. This paper proposes the formalization of DFT in a higher-order logic theorem prover named HOL. We propose the formal definition of DFT and verify the fundamental properties of DFT. Two case studies are presented to illustrate usefulness and correctness of the formalized DFT, including formal verifications of Fast Fourier Transform (FFT) and cosine frequency shift.
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Reed, Michael J., Hung V. Nguyen, and Ronald E. Chambers. "Computing the Fourier transform in geophysics with the transform decomposition DFT." GEOPHYSICS 58, no. 11 (November 1993): 1707–9. http://dx.doi.org/10.1190/1.1443386.

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The Fourier transform and its computationally efficient discrete implementation, the fast Fourier transform (FFT), are omnipresent in geophysical processing. While a general implementation of the discrete Fourier transform (DFT) will take on the order [Formula: see text] operations to compute the transform of an N point sequence, the FFT algorithm accomplishes the DFT with an operation count proportional to [Formula: see text] When a large percentage of the output coefficients of the transform are not desired, or a majority of the inputs to the transform are zero, it is possible to further reduce the computation required to perform the DFT. Here, we review one possible approach to accomplishing this reduction and indicate its application to phase‐shift migration.
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Yao, Xueyang, and Natalie Baddour. "Discrete two dimensional Fourier transform in polar coordinates part II: numerical computation and approximation of the continuous transform." PeerJ Computer Science 6 (March 2, 2020): e257. http://dx.doi.org/10.7717/peerj-cs.257.

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The theory of the continuous two-dimensional (2D) Fourier Transform in polar coordinates has been recently developed but no discrete counterpart exists to date. In the first part of this two-paper series, we proposed and evaluated the theory of the 2D Discrete Fourier Transform (DFT) in polar coordinates. The theory of the actual manipulated quantities was shown, including the standard set of shift, modulation, multiplication, and convolution rules. In this second part of the series, we address the computational aspects of the 2D DFT in polar coordinates. Specifically, we demonstrate how the decomposition of the 2D DFT as a DFT, Discrete Hankel Transform and inverse DFT sequence can be exploited for coding. We also demonstrate how the proposed 2D DFT can be used to approximate the continuous forward and inverse Fourier transform in polar coordinates in the same manner that the 1D DFT can be used to approximate its continuous counterpart.
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Ariyanto, Yuri, Rizky Ardiansyah, and Bias Paris. "STEGANOGRAFI MENGGUNAKAN METODE DISCRETE FOURIER TRANSFORM (DFT)." Jurnal Informatika Polinema 4, no. 2 (February 1, 2018): 87. http://dx.doi.org/10.33795/jip.v4i2.151.

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Seiring dengan kemajuan teknologi, serangan terjadi pada industri photography di mana banyak penyalahgunaan foto yang memiliki hak cipta tanpa seijin pemilik foto tersebut. Karena itulah dibuat sebuah aplikasi yang berfungsi untuk menyisipkan watermark dengan menggunakan metode DFT (Discrete Fourier Transform). Metode tersebut adalah metode matematika yang sering digunakan dalam bidang elektronika dan komputer. Metode ini secara khusus digunakan untuk menyelesaikan masalah yang berhubungan dengan frekuensi, sehingga metode ini dapat digunakan dalam bidang citra digital. Metode ini diterapkan untuk melakukan penyisipan dan ekstraksi watermark pada citra penampung. Watermark tersebut disisipkan kedalam frekuensi domain pada gambar dan akan menghasilkan output citra ber-watermark atau embeded image. Hal ini adalah untuk mencegah penyalahgunaan hak cipta, namun watermark tersebut tidak nampak secara fisik. Hal ini dilakukan selain memberikan jaminan keamanan terhadap gambar, tapi juga tidak mengurangi estetika pada gambar tersebut. Analisa yang dilakukan adalah tingkat keberhasilan proses insertion dan extraction, serangan pada citra, uji kemiripan dengan pengujian NPCR (Number of Pixel of Change Rate), UACI (Unified Averaged Changed Intensity), dan PSNR (Peak Signal-to-Noise Ratio) pada proses insertion dan extraction. DFT disimpulkan aman terhadap serangan berupa cropping, resize, dan editing. Selain itu, dihasilkan nilai presentase perubahan yang rendah pada pengujian NPCR & UACI dan nilai yang tinggi pada pengujian PSNR.
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Fischer, Jens. "Four Particular Cases of the Fourier Transform." Mathematics 6, no. 12 (December 18, 2018): 335. http://dx.doi.org/10.3390/math6120335.

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In previous studies we used Laurent Schwartz’ theory of distributions to rigorously introduce discretizations and periodizations on tempered distributions. These results are now used in this study to derive a validity statement for four interlinking formulas. They are variants of Poisson’s Summation Formula and connect four commonly defined Fourier transforms to one another, the integral Fourier transform, the Discrete-Time Fourier Transform (DTFT), the Discrete Fourier Transform (DFT) and the integral Fourier transform for periodic functions—used to analyze Fourier series. We prove that under certain conditions, these four Fourier transforms become particular cases of the Fourier transform in the tempered distributions sense. We first derive four interlinking formulas from four definitions of the Fourier transform pure symbolically. Then, using our previous results, we specify three conditions for the validity of these formulas in the tempered distributions sense.
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Dissertations / Theses on the topic "Discrete Fourier transform (DFT)"

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Sayyah, Jahromi Mohammad Reza Information Technology &amp Electrical Engineering Australian Defence Force Academy UNSW. "Efficient broadband antenna array processing using the discrete fourier form transform." Awarded by:University of New South Wales - Australian Defence Force Academy. School of Information Technology and Electrical Engineering, 2005. http://handle.unsw.edu.au/1959.4/38690.

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Processing of broadband signals induced on an antenna array using a tapped delay line filter and a set of steering delays has two problems. Firstly one needs to manipulate large matrices to estimate the filter coefficients. Secondly the use of steering delays is not only cumbersome but implementation errors cause loss of system performance. This thesis looks at both of these problems and presents elegant solutions by developing and studying a design method referred to as the DFT method, which does not require steering delays and is computationally less demanding compared to existing methods. Specifically the thesis studies and compares the performance of a time domain element space beamformer using the proposed method and that using an existing method, and develops the DFT method when the processor is implemented in partitioned form. The study presented in the thesis shows that the processors using the DFT method are robust to look direction errors and require less computation than that using the existing method for comparable performance. The thesis further introduces a broadband beamformer design which does not require any steering delays between the sensors and the tapped delay line section as is presently the case. It has the capability of steering the array in an arbitrary direction with a specified frequency response in the look direction while canceling unwanted uncorrelated interferences. The thesis presents and compares the performance of a number of techniques to synthesize an antenna pattern of a broadband array. These techniques are designed to produce isolated point nulls as well as broad sector nulls and to eliminate the need for the steering delays. Two of the pattern synthesis techniques presented in the thesis allow optimization against unwanted interferences in unknown directions. The techniques allow formulation of a beamforming problem such that the processor is not only able to place nulls in specified directions but also able to cancel directional interferences in unknown directions along with a specified frequency response in the look direction over a band of interest. The thesis also presents a set of directional constraints such that one does not need steering delays and an array can be constrained in an arbitrary direction with a specified frequency response. The constraints presented in the thesis are simple to implement. Based on these constraints a pattern synthesis technique for broadband antenna array is also presented.
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Ganesh, Murthy C. N. S. "A Study On Bandpassed Speech From The Point Of Intelligibility." Thesis, Indian Institute of Science, 1989. http://hdl.handle.net/2005/93.

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Speech has been the subject of interest for a very long time. Even with so much advancement in the processing techniques and in the understanding of the source of speech, it is, even today, rather difficult to generate speech in the laboratory in all its aspects. A simple aspect like how the speech can retain its intelligibility even if it is distorted or band passed is not really understood. This thesis deals with one small feature of speech viz., the intelligibility of speech is retained even when it is bandpassed with a minimum bandwidth of around 1 KHz located any where on the speech spectrum of 0-4 KHz. Several experiments have been conducted by the earlier workers by passing speech through various distortors like differentiators, integrators and infinite peak clippers and it is found that the intelligibility is retained to a very large extent in the distorted speech. The integrator and the differentiator remove essentially a certain portion of the spectrum. Therefore, it is thought that the intelligibility of the speech is spread over the entire speech spectrum and that, the intelligibility of speech may not be impaired even when it is bandpassed with a minimum bandwidth and the band may be located any where in the speech spectrum. To test this idea and establish this feature if it exists, preliminary experiments have been conducted by passing the speech through different filters and it is found that the conjecture seems to be on the right line. To carry out systematic experiments on this an experimental set up has been designed and fabricated which consists of a microprocessor controlled speech recording, storing and speech playback system. Also, a personal computer is coupled to the microprocessor system to enable the storage and processing of the data. Thirty persons drawn from different walks of life like teachers, mechanics and students have been involved for collecting the samples and for recognition of the information of the processed speech. Even though the sentences like 'This is devices lab' are used to ascertain the effect of bandwidth on the intelligibility, for the purpose of analysis, vowels are used as the speech samples. The experiments essentially consist of recording words and sentences spoken by the 30 participants and these recorded speech samples are passed through different filters with different bandwidths and central frequencies. The filtered output is played back to the various listeners and observations regarding the intelligibility of the speech are noted. The listeners do not have any prior information about the content of the speech. It has been found that in almost all (95%) cases, the messages or words are intelligible for most of the listeners when the band width of the filter is about 1 KHz and this is independent of the location of the pass band in the spectrum of 0-4 KHz. To understand how this feature of speech arises, spectrums of vowels spoken by 30 people have using FFT algorithms on the digitized samples of the speech. It is felt that there is a cyclic behavior of the spectrum in all the samples. To make sure that the periodicity is present and also to arrive at the periodicity, a moving average procedure is employed to smoothen the spectrum. The smoothened spectrums of all the vowels indeed show a periodicity of about 1 KHz. When the periodicities are analysed the average value of the periodicities has been found to be 1038 Hz with a standard deviation of 19 Hz. In view of this it is thought that the acoustic source responsible for speech must have generated this periodic spectrum, which might have been modified periodically to imprint the intelligibility. If this is true, one can perhaps easily understand this feature of the speech viz., the intelligibility is retained in a bandpassed speech of bandwidth 1 K H z . the pass band located any where in the speech spectrum of 0-4 KHz. This thesis describing the experiments and the analysis of the speech has been presented in 5 chapters. Chapter 1 deals with the basics of speech and the processing tools used to analyse the speech signal. Chapter 2 presents the literature survey from where the present problem is tracked down. Chapter 3 describes the details of the structure and the fabrication of the experimental setup that has been used. In chapter 4, the detailed account of the way in which the experiments are conducted and the way in which the speech is analysed is given. In conclusion in chapter 5, the work is summarised and the future work needed to establish the mechanism of speech responsible for the feature of speech described in this thesis is suggested.
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Miar, Yasin. "Improved Wideband Spectrum Sensing Methods for Cognitive Radio." Thèse, Université d'Ottawa / University of Ottawa, 2012. http://hdl.handle.net/10393/23333.

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Abstract Cognitive Radio (CR) improves the efficiency of spectrum utilization by allowing non- licensed users to utilize bands when not occupied by licensed users. In this thesis, we address several challenges currently limiting the wide use of cognitive radios. These challenges include identification of unoccupied bands, energy consumption and other technical challenges. Improved accuracy edge detection techniques are developed for CR to mitigate both noise and estimation error variance effects. Next, a reduced complexity Simplified DFT (SDFT) is proposed for use in CR. Then, a sub-Nyquist rate A to D converter is introduced to reduce energy consumption. Finally, a novel multi-resolution PSD estimation based on expectation-maximization algorithm is introduced that can obtain a more accurate PSD within a specified sensing time.
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Heiskanen, Andreas, and Erik Johansson. "Analysing Memory Performance when computing DFTs using FFTW." Thesis, KTH, Skolan för elektroteknik och datavetenskap (EECS), 2018. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-230225.

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Discrete Fourier Transforms (DFTs) are used in a wide variety of dif-ferent scientific areas. In addition, there is an ever increasing demand on fast and effective ways of computing DFT problems with large data sets. The FFTW library is one of the most common used libraries when computing DFTs. It adapts to the system architecture and predicts the most effective way of solving the input problem. Previous studies have proved the FFTW library to be superior to other DFT solving libraries. However, not many have specifically examined the cache memory performance, which is a key factor for overall performance. In this study, we examined the cache memory utilization when computing 1-D complex DFTs using the FFTW library. Testing was done using bench FFT, Linux Perf and testing scripts. The results from this study show that cache miss ratio increases with problem size when the input size is smaller than the theoretical input size matching the cache capacity. This is also verified by the results from the L2 prefetcher miss ratio. However, the study show that cache miss ratio stabilizes when exceeding the cache capacity. In conclusion, it is possible to use bench FFT and Linux Perf to measure cache memory utilization. Also, the analysis shows that cache memory performance is good when computing 1-D complex DFTS using the FFTW library, since the miss ratios stabilizes at low values. However, we suggest further examination ofthe memory behaviour for DFT computations using FFTW with larger input sizes and a more in-depth testing method.
Diskret Fouriertransform (DFT) används inom många olika vetenskapliga områden. Det finns en ökande efterfrågan på snabba och effektiva sätt att beräkna DFT-problem med stora mängder data. FFTW-biblioteket är ett av de mest använda biblioteken vid beräkning av DFT-problem. FFTW-biblioteket anpassar sig till systemarkitekturen och försöker generera det mest effektiva sättet att lösa ett givet DFT-problem. Tidigare studier har visat att FFTW-biblioteket är effektivare än andra bibliotek som kan användas för att lösa DFT-problem. Däremot har studierna inte fokuserat på minneshanteringen, vilket är en nyckelfaktor för den generella prestandan. I den här studien undersökte vi FFTW-bibliotekets cache-minneshanteringen vid beräkning av 1-D komplexa DFT-problem. Tester utfördes med hjälp av bench FFT, Linux Perf och testskript. Resultaten från denna studie visar att cache-missförhållandet ökar med problemstorleken när problemstorleken ärmindre än den teoretiska problemstorleken som matchar cachekapaciteten. Detta bekräftas av resultat från L2-prefetcher-missförhållandet. Studien visar samtidigt att cache-missförhållandet stabiliseras när problemstorleken överskrider cachekapaciteten. Sammanfattningsvis går det att argumentera för att det är möjligt att använda bench FFT och Linux Perf för att mäta cache-minneshanteringen. Analysen visar också att cache-minneshanteringen är bra vid beräkning av 1-D komplexa DFTs med hjälp av FFTW-biblioteket eftersom missförhållandena stabiliseras vid låga värden. Vi föreslår dock ytterligare undersökning av minnesbeteendet för DFT-beräkningar med hjälp av FFTW där problemstorlekarna är större och en mer genomgående testmetod används.
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baktir, selcuk. "Frequency Domain Finite Field Arithmetic for Elliptic Curve Cryptography." Digital WPI, 2008. https://digitalcommons.wpi.edu/etd-dissertations/272.

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Efficient implementation of the number theoretic transform(NTT), also known as the discrete Fourier transform(DFT) over a finite field, has been studied actively for decades and found many applications in digital signal processing. In 1971 Schonhage and Strassen proposed an NTT based asymptotically fast multiplication method with the asymptotic complexity O(m log m log log m) for multiplication of $m$-bit integers or (m-1)st degree polynomials. Schonhage and Strassen's algorithm was known to be the asymptotically fastest multiplication algorithm until Furer improved upon it in 2007. However, unfortunately, both algorithms bear significant overhead due to the conversions between the time and frequency domains which makes them impractical for small operands, e.g. less than 1000 bits in length as used in many applications. With this work we investigate for the first time the practical application of the NTT, which found applications in digital signal processing, to finite field multiplication with an emphasis on elliptic curve cryptography(ECC). We present efficient parameters for practical application of NTT based finite field multiplication to ECC which requires key and operand sizes as short as 160 bits in length. With this work, for the first time, the use of NTT based finite field arithmetic is proposed for ECC and shown to be efficient. We introduce an efficient algorithm, named DFT modular multiplication, for computing Montgomery products of polynomials in the frequency domain which facilitates efficient multiplication in GF(p^m). Our algorithm performs the entire modular multiplication, including modular reduction, in the frequency domain, and thus eliminates costly back and forth conversions between the frequency and time domains. We show that, especially in computationally constrained platforms, multiplication of finite field elements may be achieved more efficiently in the frequency domain than in the time domain for operand sizes relevant to ECC. This work presents the first hardware implementation of a frequency domain multiplier suitable for ECC and the first hardware implementation of ECC in the frequency domain. We introduce a novel area/time efficient ECC processor architecture which performs all finite field arithmetic operations in the frequency domain utilizing DFT modular multiplication over a class of Optimal Extension Fields(OEF). The proposed architecture achieves extension field modular multiplication in the frequency domain with only a linear number of base field GF(p) multiplications in addition to a quadratic number of simpler operations such as addition and bitwise rotation. With its low area and high speed, the proposed architecture is well suited for ECC in small device environments such as smart cards and wireless sensor networks nodes. Finally, we propose an adaptation of the Itoh-Tsujii algorithm to the frequency domain which can achieve efficient inversion in a class of OEFs relevant to ECC. This is the first time a frequency domain finite field inversion algorithm is proposed for ECC and we believe our algorithm will be well suited for efficient constrained hardware implementations of ECC in affine coordinates.
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Martins, Carlos Henrique Nascimento. "Estudo e implementação de um analisador de harmônicos variantes no tempo." Universidade Federal de Juiz de Fora (UFJF), 2015. https://repositorio.ufjf.br/jspui/handle/ufjf/4176.

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Esta tese apresenta as etapas de desenvolvimento de um sistema de monitoramento de parâmentos de qualidade de energia dedicado a análise de harmônicos variantes no tempo através do equipamento denominado AHVT (Analisador de Harmônicos Variantes no Tempo). O desenvolvimento do trabalho é composto por: (i) estudo e implementação MATLAB de algoritmos para processamento em tempo real, com capacidade de sintonização dos componentes harmônicos; (ii) análise e desenvolvimento de estratégias para detecção e validação da presença de interharmônicos próximos à frequência fundamental e suas consequência na estimação de parâmetros como fase, amplitude e frequência para o componente fundamental, (iii) proposta de implementação do dispositivo, sistema de aquisição/ condicionamento de sinais/ filtragem, sistema de conversão analógico digital e plataforma de processamentoDSP/FPGA, sistema de transmissão de dados e plataformas de análise online/offline dos eventos de harmônicos variantes no tempo; (iv) plataforma de simulação do Analisador de Harmônicos Variantes no Tempo (AHVT) para estudo dos métodos de trigger para detecção e captura dos eventos.
In this work is presented the steps of development and implementation of a Power Quality paramaters monitoring system with main goal events denomined ”time arying harmonics”named of Time Varying Harmonic Analyzer. The development is comprises:(i) research and implementation of real time algorithms with capable to tuning harmonic waves,(ii) Analyze and research/development of strategies for detect and validation of interharmonics with frequencies near of fundamental, and conseguencies and challenges to phase, magnitude and frequency estimation with presence interharmonic waveform (iii) The proposal of a hardware design including analog to digital conversion and digital signal processing plataform, broadcast data link and IHM(Interface Human Machine) for online and offline analyzes to time varying harmonic analyzer;(iiii)off-line simulation plataform of Analisador de Harmônicos Variantes no Tempo Time Varying Harmonic Analyzer (TVHA) to trigger detect methods to detection and capture of waveforms.
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Barnhart, Samuel. "Design and Development of a Coherent Detection Rayleigh Doppler Lidar System for Use as an Alternative Velocimetry Technique in Wind Tunnels." University of Dayton / OhioLINK, 2020. http://rave.ohiolink.edu/etdc/view?acc_num=dayton1595276402371536.

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Madishetty, Suresh. "Design of Multi-Beam Hybrid Digital Beamforming Receivers." University of Akron / OhioLINK, 2018. http://rave.ohiolink.edu/etdc/view?acc_num=akron1545178805415923.

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Dvořák, Vojtěch. "Implementace výpočtu FFT v obvodech FPGA a ASIC." Master's thesis, Vysoké učení technické v Brně. Fakulta elektrotechniky a komunikačních technologií, 2013. http://www.nusl.cz/ntk/nusl-220087.

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The aim of this thesis is to design the implementation of fast Fourier transform algorithm, which can be used in FPGA or ASIC circuits. Implementation will be done in Matlab and then this form of implementation will be used as a reference model for implementation of fast Fourier transform algorithm in VHDL. To verify the correctness ofdesign verification enviroment will be created and verification process wil be done. Program that will generate source code for various parameters of the module performing a fast Fourier transform will be created in the last part of this thesis.
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Yu, Sungwook. "VLSI implementation of multidimensional discrete Fourier transform and discrete cosine transform /." Digital version accessible at:, 2000. http://wwwlib.umi.com/cr/utexas/main.

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Books on the topic "Discrete Fourier transform (DFT)"

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Henson, Van Emden. DFTS on irregular grids: The anterpolated DFT. Monterey, Calif: Naval Postgraduate School, 1992.

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Briggs, William L. The DFT: An owner's manual for the discrete Fourier transform. Philadelphia: Society for Industrial and Applied Mathematics, 1995.

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Mathematics of the discrete Fourier transform (DFT): With music and audio applicaitons. [S.l.]: W3K Pub., 2003.

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Tolimieri, R., Myoung An, and Chao Lu. Algorithms for Discrete Fourier Transform and Convolution. Edited by C. S. Burrus. New York, NY: Springer New York, 1989. http://dx.doi.org/10.1007/978-1-4757-3854-4.

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Tolimieri, Richard, Chao Lu, and Myoung An. Algorithms for Discrete Fourier Transform and Convolution. New York, NY: Springer New York, 1997. http://dx.doi.org/10.1007/978-1-4757-2767-8.

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Myoung, An, and Lu Chao 1959-, eds. Algorithms for discrete fourier transform and convolution. New York: Springer-Verlag, 1989.

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Myoung, An, and Lu Chao 1959-, eds. Algorithms for discrete Fourier transform and convolution. 2nd ed. New York: Springer, 1997.

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Center, Ames Research, ed. A discrete Fourier transform for virtual memory machines. Moffett Field, Calif: National Aeronautics and Space Administration, Ames Research Center, 1992.

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The discrete fourier transform: Theory, algorithms and applications. Singapore: World Scientific, 2001.

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Bagchi, Sonali, and Sanjit K. Mitra. The Nonuniform Discrete Fourier Transform and Its Applications in Signal Processing. Boston, MA: Springer US, 1999. http://dx.doi.org/10.1007/978-1-4615-4925-3.

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Book chapters on the topic "Discrete Fourier transform (DFT)"

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Keydana, Sigrid. "Exploring the Discrete Fourier Transform (DFT)." In Deep Learning and Scientific Computing with R torch, 319–42. Boca Raton: Chapman and Hall/CRC, 2023. http://dx.doi.org/10.1201/9781003275923-26.

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Heideman, Michael T. "Multiplicative Complexity of Discrete Fourier Transform." In Multiplicative Complexity, Convolution, and the DFT, 76–107. New York, NY: Springer New York, 1988. http://dx.doi.org/10.1007/978-1-4612-3912-3_5.

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Zieliński, Tomasz P. "Discrete Fourier Transforms: DtFT and DFT." In Starting Digital Signal Processing in Telecommunication Engineering, 65–92. Cham: Springer International Publishing, 2021. http://dx.doi.org/10.1007/978-3-030-49256-4_4.

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Palani, S. "Discrete and Fast Fourier Transforms (DFT and FFT)." In Principles of Digital Signal Processing, 81–248. Cham: Springer International Publishing, 2022. http://dx.doi.org/10.1007/978-3-030-96322-4_2.

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Kubota, Atsushi, Tomohiro Matsushita, and Naohisa Happo. "Parallelization of Atomic Image Reconstruction from X-ray Fluorescence Holograms with XcalableMP." In XcalableMP PGAS Programming Language, 205–18. Singapore: Springer Singapore, 2020. http://dx.doi.org/10.1007/978-981-15-7683-6_8.

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AbstractX-ray fluorescence holography is a three-dimensional middle range local structure analysis method, which can provide three-dimensional atomic images around specific elements within a radius of a few nanometers. Three-dimensional atomic images are reconstructed by applying discrete Fourier transform (DFT) to hologram data. Presently, it takes long time to process this DFT. In this study, the DFT program is parallelized by using a parallel programming language XcalableMP. The DFT process, whose input is 21 holograms data of 179 × 360 points and output is a three-dimensional atomic image of 1923 points, is executed on PC cluster which consists of 8 nodes of Intel Xeon X5660 processors and 96 cores in total and we confirmed that the parallelized DFT execution is 94 times faster than the sequential execution.
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Palani, S. "Fourier Transform Analysis of Discrete Time Signals and Systems—DTFT, DFT and FFT." In Signals and Systems, 651–736. Cham: Springer International Publishing, 2021. http://dx.doi.org/10.1007/978-3-030-75742-7_7.

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Khan, Muhammad N., Syed K. Hasnain, and Mohsin Jamil. "Discrete-Time Fourier Transform Discrete Fourier Transform." In Digital Signal Processing, 239–303. New York: River Publishers, 2022. http://dx.doi.org/10.1201/9781003337935-6.

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Kido, Ken’iti. "Discrete Fourier Transform." In Undergraduate Lecture Notes in Physics, 77–105. New York, NY: Springer New York, 2014. http://dx.doi.org/10.1007/978-1-4614-9260-3_4.

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Jackson, Leland B. "Discrete Fourier Transform." In Digital Filters and Signal Processing, 189–248. Boston, MA: Springer US, 1996. http://dx.doi.org/10.1007/978-1-4757-2458-5_7.

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Gan, Woon Siong. "Discrete Fourier Transform." In Signal Processing and Image Processing for Acoustical Imaging, 13–16. Singapore: Springer Singapore, 2020. http://dx.doi.org/10.1007/978-981-10-5550-8_4.

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Conference papers on the topic "Discrete Fourier transform (DFT)"

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L. Fontaine, Fred. "Multi Resolution Lattice Discrete Fourier Transform (MRL-DFT)." In 4th International Conference on Information Technology, Control, Chaos, Modeling and Applications. Academy & Industry Research Collaboration Center (AIRCC), 2017. http://dx.doi.org/10.5121/csit.2017.70706.

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Yao, Xueyang, and Natalie Baddour. "Numerical Computation of the Discrete 2D Fourier Transform in Polar Coordinates." In ASME 2018 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 2018. http://dx.doi.org/10.1115/detc2018-85616.

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The discrete Fourier transform in Cartesian coordinates has proven to be invaluable in many disciplines. However, in application such as photoacoustics and tomography, a discrete 2D-Fourier transform in polar coordinates is needed. In this paper, a discrete 2D-Fourier transform in polar coordinates is presented. It is shown that numerical implementation is best achieved by interpreting the transform as a 1D-discrete Fourier transform (DFT), a 1D-discrete Hankel transform (DHT) and a 1D-discrete inverse transform (IDFT) in sequence. The transform is tested by numerical simulations with respect to accuracy and precision for computation of the continuous 2D transform at specific discrete points. It was found that both the forward and inverse transform showed good accuracy to approximate the continuous Fourier transform. Moreover, good precision results were obtained, which indicate that the proposed transform itself does not add much error.
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Talwalkar, Sumit A., and S. Lawrence Marple. "Time-frequency scaling property of Discrete Fourier Transform (DFT)." In 2010 IEEE International Conference on Acoustics, Speech and Signal Processing. IEEE, 2010. http://dx.doi.org/10.1109/icassp.2010.5495902.

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Khalil, Ethar H. "EHK Index Method for Calculating Discrete Fourier Transform." In ASME 2009 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2009. http://dx.doi.org/10.1115/detc2009-86442.

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A new mathematical model has been achieved, for the calculation of DFT and its inversion depending on the indices which represent the shortest way for referring to the elements, pixels or pixels in each slide dealing with 1-D, 2-D, and 3-D digital signals respectively. This method indicates clearly the contribution factor of each input signal element in each output signal element.
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Reihani, Kamran, Wiley E. Thompson, and Yiping Fan. "Flexible systolic design with asynchronous communication protocols for discrete Fourier transform (DFT) and inverse discrete Fourier transform (IDFT)." In SPIE's International Symposium on Optical Engineering and Photonics in Aerospace Sensing, edited by Dennis R. Pape. SPIE, 1994. http://dx.doi.org/10.1117/12.179115.

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Ersoy, O. K., and D. Y. Kim. "Image recognition with the discrete rectangular wave transform." In OSA Annual Meeting. Washington, D.C.: Optica Publishing Group, 1986. http://dx.doi.org/10.1364/oam.1986.md1.

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The discrete rectangular wave transform (DRWT) is obtained by replacing sines and cosines in the discrete Fourier transform (DFT) by the bipolar rectangular wave function. Thus, DRWT of size N is defined as follows: where x(·) is the input data, and μ(t) is the bipolar rectangular wave function which is 1 for 0 < t mod 1 < 0.5, −1 for 0.5 < t mod 1 < 1, and 0 for t mod 1 = 0 or 0.5. The DRWT matrix contains no numbers other than ±1, ±j, and their combinations. There are also data structures for its fast computation. Since there are add operations only, its electrooptical as well as VLSI implementations are very attractive. DRWT is not an orthogonal transform, but its inverse is well defined, consisting of the complex conjugate transpose of the DRWT matrix followed by a matrix which is the direct sum of blocks of circular correlations. There are no general multiplications in the inverse transform either for N ≤ 32, when N is a power of 2. Since DRWT is both much faster and easier to implement than DFT, it is very attractive to use in applications if it also performs well in terms of various criteria such as accuracy and resolution. Our computer simulations with the method of Fourier descriptors for shape recognition indicate that DRWT performs considerably better than DFT in image recognition where the transform is used for the purpose of feature extraction. The new method using DRWT is obtained by simply replacing DFT with DRWT in the method of Fourier descriptors. In both methods, the same number of largest transform coefficients was kept, and the recognition was based on the Euclidian distances to the set of library features belonging to different reference images. Especially in the presence of white Gaussian noise, the new method is found to be considerably more accurate than the DFT method. We have also developed normalization procedures such that the new transform is invariant under translation, rotation, and scaling of the signal.
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Aghagolzadeh, Sabzali, and Okan K. Ersoy. "Transform image enhancement." In OSA Annual Meeting. Washington, D.C.: Optica Publishing Group, 1991. http://dx.doi.org/10.1364/oam.1991.ml3.

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Blockwise transform image enhancement techniques are discussed. Previously, transform image enhancement has usually been based on the discrete Fourier transform (DFT) applied to the whole image. Two major drawbacks with the DFT are high complexity of implementation involving complex multiplications and additions, with intermediate results being complex numbers, and the creation of severe block effects if image enhancement is done blockwise. In addition, the quality of enhancement is not very satisfactory. In this paper, it is shown that the best transforms for transform image coding, namely, the scrambled real discrete Fourier transform, the discrete cosine transform, and the discrete cosine-III transform, are also the best for image enhancement. Three enhancement techniques discussed in detail are alpha-rooting, modified unsharp masking, and filtering based on the human visual system response (HVS). With proper modifications, it is observed that unsharp making and HVS filtering are basically equivalent. Block effects are completely removed by using an overlap-save technique in addition to the best transform. In conclusion, transform image enhancement yields highly satisfactory performance, it is biologically sound, provides parallel models for implementation, and can be performed simultaneously with transform image coding.
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Serbes, Ahmet, and Lutfiye Durak Ata. "Eigenvectors of the DFT and discrete fractional fourier transform based on the bilinear transform." In 2010 IEEE 18th Signal Processing and Communications Applications Conference (SIU). IEEE, 2010. http://dx.doi.org/10.1109/siu.2010.5650245.

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Fan Jiang, Z. Bo, and Zhe Chen. "A novel algorithm for digital overcurrent relay using discrete Fourier transform (DFT)." In 7th IET International Conference on Advances in Power System Control, Operation and Management (APSCOM 2006). IEE, 2006. http://dx.doi.org/10.1049/cp:20061983.

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Rocha, Rafael L., Cleison D. Silva, Ana Claudia S. Gomes, Bruno V. Ferreira, Eduardo C. Carvalho, Ana Carolina Q. Siravenha, and Schubert R. Carvalho. "Image Inspection of Railcar Structural Components: An approach through Deep Learning and Discrete Fourier Transform." In VII Symposium on Knowledge Discovery, Mining and Learning. Sociedade Brasileira de Computação - SBC, 2019. http://dx.doi.org/10.5753/kdmile.2019.8786.

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Railcar components inspection is one of the most critical tasks in railway maintenance. The use of image processing, coupled with machine learning, has emerged as a solution for replacing current standard methodologies. The spectral analysis gives the frequency representation of a signal and has been largely used in signal processing tasks. In this sense, this work proposes the evaluation of the use of the Discrete Fourier Transform (DFT) in addition to the spatial representation image of railcar components for an automatic detector of defective parts performed by Convolutional Neural Network (CNN) classi cation. The results are given in measures of accuracy, precision, recall, and F1-score metrics in addition to the accuracy boxplot, and showed that the use of the DFT increase in 1.04% the CNN classi cation accuracy.
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Reports on the topic "Discrete Fourier transform (DFT)"

1

Gabriel, William F. Adaptive Digital Processing Investigation of DFT (Discrete Fourier Transform) Subbanding vs. Transversal Filter Canceler. Fort Belvoir, VA: Defense Technical Information Center, July 1986. http://dx.doi.org/10.21236/ada171894.

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Lucke, Robert L. A Local Interpolator Derived From the Discrete Fourier Transform. Fort Belvoir, VA: Defense Technical Information Center, April 1992. http://dx.doi.org/10.21236/ada251066.

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Nuttall, Albert H. Weighted Least Squares Fit of a Real Tone to Discrete Data, by Means of an Efficient Fast Fourier Transform Search. Fort Belvoir, VA: Defense Technical Information Center, August 1986. http://dx.doi.org/10.21236/ada185910.

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Collier, Wiehrs L. VLSI (Very Large Scale Integrated Circuits) Implementation of a Quantized Sinusoid Filter Algorithm and Its Use to Compute the Discrete Fourier Transform. Fort Belvoir, VA: Defense Technical Information Center, March 1986. http://dx.doi.org/10.21236/ada168605.

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Geist, Jon, and M. Yaqub Afridi. Simulated Sinewave Testing of Data Acquisition Systems using Sine Fitting and Discrete Fourier Transform Methods Part 1: Frequency Offset, Random, Quantization, and Jitter Noise. National Institute of Standards and Technology, July 2015. http://dx.doi.org/10.6028/nist.ir.8073.

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