Dissertations / Theses on the topic 'Instantaneous frequency estimation'

Any periodic signal can be decomposed into a sum of oscillating functions. Traditionally, cosine and sine segments have been used to represent a single period of the periodic signal (Fourier Series). In more general cases, each of these functions can be represented by a set of spectral parameters such as its amplitude, frequency, phase, and the variability of its instantaneous spectral components. The accuracy of these parameters depends on several processing variables such as resolution, noise level, and bias of the algorithm used. This thesis presents some background of existing frequency estimation techniques and proposes a new technique for estimating the instantaneous frequency of signals using short sinusoid-like basis functions. Furthermore, it also shows that the proposed algorithm can be implemented in a popular embedded DSPmicroprocessor for practical use. This algorithm can also be implemented using more complex features on more resourceful processing processors in order to improve estimation accuracy

Most of the human-made and physical signals have nonstationary spectra that evolve rapidly with time. To study and characterize such signals, the classic time-domain and frequency-domain representations are inadequate, since they do not provide joint time and frequency information; meaning that, they are signal representations in which the time and frequency variables are mutually exclusive. Time-frequency (TF) signal analysis (TFSA) concerns the processing of signals with time-varying spectral content. It allows for the construction of a signal representation in which the time and frequency variables are not averaged with respect to each other, but rather present together. This doctoral thesis has two main points of focus: TFSA based on a linear TF transform with progressive frequency-dependent resolution in the TF domain, known in the literature as the S-transform (ST), and designing adaptive methods for instantaneous frequency (IF) estimation, which is a fundamental concept in TFSA with numerous practical applications. The main original contributions are: 1- Modifications in the existing discrete definitions for implementing and inverting the ST to ensure exact invertibility and eliminate artifacts in the synthesized signal. 2- Derivation of an algorithm for least-squares signal synthesis form a modified discrete ST. 3- Formulation of a computationally efficient, fully discrete, and exactly invertible ST with a controllable TF sampling scheme, providing frequency resolution that can be varied and made as high as required. 4- Accuracy analysis of IF estimation based on a family of linear TF transforms that use Gaussian observation windows to localize the Fourier oscillatory kernel with arbitrarily defined standard deviations, and derivation of closed-form easily interpreted expressions for the bias and the variance of the estimation error. 5- Design of adaptive methods for IF estimation based on linear and quadratic TF representations.

This thesis deals with the problem of the instantaneous frequency (IF) estimation of sinusoidal signals. This topic plays significant role in signal processing and communications. Depending on the type of the signal, two major approaches are considered. For IF estimation of single-tone or digitally-modulated sinusoidal signals (like frequency shift keying signals) the approach of digital phase-locked loops (DPLLs) is considered, and this is Part-I of this thesis. For FM signals the approach of time-frequency analysis is considered, and this is Part-II of the thesis. In part-I we have utilized sinusoidal DPLLs with non-uniform sampling scheme as this type is widely used in communication systems. The digital tanlock loop (DTL) has introduced significant advantages over other existing DPLLs. In the last 10 years many efforts have been made to improve DTL performance. However, this loop and all of its modifications utilizes Hilbert transformer (HT) to produce a signal-independent 90-degree phase-shifted version of the input signal. Hilbert transformer can be realized approximately using a finite impulse response (FIR) digital filter. This realization introduces further complexity in the loop in addition to approximations and frequency limitations on the input signal. We have tried to avoid practical difficulties associated with the conventional tanlock scheme while keeping its advantages. A time-delay is utilized in the tanlock scheme of DTL to produce a signal-dependent phase shift. This gave rise to the time-delay digital tanlock loop (TDTL). Fixed point theorems are used to analyze the behavior of the new loop. As such TDTL combines the two major approaches in DPLLs: the non-linear approach of sinusoidal DPLL based on fixed point analysis, and the linear tanlock approach based on the arctan phase detection. TDTL preserves the main advantages of the DTL despite its reduced structure. An application of TDTL in FSK demodulation is also considered. This idea of replacing HT by a time-delay may be of interest in other signal processing systems. Hence we have analyzed and compared the behaviors of the HT and the time-delay in the presence of additive Gaussian noise. Based on the above analysis, the behavior of the first and second-order TDTLs has been analyzed in additive Gaussian noise. Since DPLLs need time for locking, they are normally not efficient in tracking the continuously changing frequencies of non-stationary signals, i.e. signals with time-varying spectra. Nonstationary signals are of importance in synthetic and real life applications. An example is the frequency-modulated (FM) signals widely used in communication systems. Part-II of this thesis is dedicated for the IF estimation of non-stationary signals. For such signals the classical spectral techniques break down, due to the time-varying nature of their spectra, and more advanced techniques should be utilized. For the purpose of instantaneous frequency estimation of non-stationary signals there are two major approaches: parametric and non-parametric. We chose the non-parametric approach which is based on time-frequency analysis. This approach is computationally less expensive and more effective in dealing with multicomponent signals, which are the main aim of this part of the thesis. A time-frequency distribution (TFD) of a signal is a two-dimensional transformation of the signal to the time-frequency domain. Multicomponent signals can be identified by multiple energy peaks in the time-frequency domain. Many real life and synthetic signals are of multicomponent nature and there is little in the literature concerning IF estimation of such signals. This is why we have concentrated on multicomponent signals in Part-H. An adaptive algorithm for IF estimation using the quadratic time-frequency distributions has been analyzed. A class of time-frequency distributions that are more suitable for this purpose has been proposed. The kernels of this class are time-only or one-dimensional, rather than the time-lag (two-dimensional) kernels. Hence this class has been named as the T -class. If the parameters of these TFDs are properly chosen, they are more efficient than the existing fixed-kernel TFDs in terms of resolution (energy concentration around the IF) and artifacts reduction. The T-distributions has been used in the IF adaptive algorithm and proved to be efficient in tracking rapidly changing frequencies. They also enables direct amplitude estimation for the components of a multicomponent

Instantaneous Frequency (IF) estimation based on time-varying autoregressive (TVAR) modeling has been shown to perform well in practical scenarios when the IF variation is rapid and/or non-linear and only short data records are available for modeling. A challenging aspect of implementing IF estimation based on TVAR modeling is the efficient computation of the time-varying coefficients by solving a set of linear equations referred to as the generalized covariance equations. Conventional approaches such as Gaussian elimination or direct matrix inversion are computationally inefficient for solving such a system of equations especially when the covariance matrix has a high order. We implement two recursive algorithms for efficiently inverting the covariance matrix. First, we implement the Akaike algorithm which exploits the block-Toeplitz structure of the covariance matrix for its recursive inversion. In the second approach, we implement the Wax-Kailath algorithm that achieves a factor of 2 reduction over the Akaike algorithm in the number of recursions involved and the computational effort required to form the inverse matrix. Although a TVAR model works well for IF estimation of frequency modulated (FM) components in white noise, when the model is applied to a signal containing a finitely correlated signal in addition to the white noise, estimation performance degrades; especially when the correlated signal is not weak relative to the FM components. We propose a decorrelating TVAR (DTVAR) model based IF estimation and a DTVAR model based linear prediction error filter for FM interference rejection in a finitely correlated environment. Simulations show notable performance gains for a DTVAR model over the TVAR model for moderate to high SIRs.
Master of Science

International Telemetering Conference Proceedings / October 13-16, 1986 / Riviera Hotel, Las Vegas, Nevada
A digital frequency discriminator (DFD) of the delay-correlator type is described. The device is shown to have an instantaneous frequency measurement capability on very short pulses. The theoretical performance of the DFD in a noisy background is derived and shown to compare favorably with measured results.

This thesis deals with the problem of estimating the velocity of a mobile station (MS)in a mobile communication system using the instantaneous frequency (IF) of the received signal at the MS antenna. This estimate is essential for satisfactory handover performance, effective dynamic channel assignment, and optimisation of adaptive multiple access wireless receivers. Conventional methods for estimating the MS velocity are based either on the statistics of the envelope or quadrature components of the received signal. In chapter 4 of the thesis, we show that their performance deteriorates in the presence of shadowing. Other velocity estimators have also been proposed which require prior estimation of the channel or the average received power. These are generally difficult to obtain due to the non-stationary nature of the received signal. An appropriate window which depends on the unknown MS velocity must first be applied in order to accurately estimate the required quantities. Using the statistics of the IF of the received signal at the MS antenna given in chapter 3, new velocity estimators are proposed in chapter 4 of this thesis. The proposed estimators are based on the moments, zero-crossing rate, and covariance of the received IF. Since the IF of the received signal is not affected by any amplitude distortion, the proposed IF-based estimators are robust to shadowing and propagation path-loss. The estimators for the MS velocity in a macro- and micro-cellular system are presented separately. A macro-cell system can be considered as a special case of a micro-cell in which there is no line-of-sight component at the receiver antenna. It follows that those estimators which are derived for micro-cells can be used in a macro-cell as well. In chapter 4, we analyse the performance of the proposed velocity estimators in the presence of additive noise, non-isotropic scattering, and shadowing. We also prove analytically that the proposed velocity estimators outperform the existing methods in the presence of shadowing and additive noise. The proposed IF-based estimators need prior estimation of both the IF of the received signal and Ricean K-factor. The IF estimation in a typical wireless environment, can be considered as a special case of a general problem of IF estimation in the presence of multiplicative and additive noise. In chapter 5, we show that current time-frequency approaches to this problem which are based on the peak of a time-frequency distribution (TFD) of the signal, fail because of the special shape of the power spectral density of the multiplicative noise in a wireless environment. To overcome this drawback, the use of the first-order moment of a TFD is studied in chapter 5. Theoretical analysis and simulations show that the IF estimator based on the first-order moment of a TFD exhibits negligible bias when the signal-to-additive noise ratio is more than 10 dB. The Ricean K-factor is not only necessary for velocity estimation in micro-cells, but also is a measure of the severity of fading and a good indicator of the channel quality. Two new methods for estimating the Ricean K-factor based on the first two moments of the envelope of the received signal, are proposed in chapter 6. Performance analysis presented in chapter 6, prove that the proposed K estimators are robust to non-isotropic scattering. Theoretical analysis and simulations which are presented in chapters 4 and 7 of this thesis, prove that the proposed velocity and K estimators outperform existing estimators in the presence of shadowing and additive noise.

This thesis deals with the problem of estimating the velocity of a mobile station (MS)in a mobile communication system using the instantaneous frequency (IF) of the received signal at the MS antenna. This estimate is essential for satisfactory handover performance, effective dynamic channel assignment, and optimisation of adaptive multiple access wireless receivers. Conventional methods for estimating the MS velocity are based either on the statistics of the envelope or quadrature components of the received signal. In chapter 4 of the thesis, we show that their performance deteriorates in the presence of shadowing. Other velocity estimators have also been proposed which require prior estimation of the channel or the average received power. These are generally difficult to obtain due to the non-stationary nature of the received signal. An appropriate window which depends on the unknown MS velocity must first be applied in order to accurately estimate the required quantities. Using the statistics of the IF of the received signal at the MS antenna given in chapter 3, new velocity estimators are proposed in chapter 4 of this thesis. The proposed estimators are based on the moments, zero-crossing rate, and covariance of the received IF. Since the IF of the received signal is not affected by any amplitude distortion, the proposed IF-based estimators are robust to shadowing and propagation path-loss. The estimators for the MS velocity in a macro- and micro-cellular system are presented separately. A macro-cell system can be considered as a special case of a micro-cell in which there is no line-of-sight component at the receiver antenna. It follows that those estimators which are derived for micro-cells can be used in a macro-cell as well. In chapter 4, we analyse the performance of the proposed velocity estimators in the presence of additive noise, non-isotropic scattering, and shadowing. We also prove analytically that the proposed velocity estimators outperform the existing methods in the presence of shadowing and additive noise. The proposed IF-based estimators need prior estimation of both the IF of the received signal and Ricean K-factor. The IF estimation in a typical wireless environment, can be considered as a special case of a general problem of IF estimation in the presence of multiplicative and additive noise. In chapter 5, we show that current time-frequency approaches to this problem which are based on the peak of a time-frequency distribution (TFD) of the signal, fail because of the special shape of the power spectral density of the multiplicative noise in a wireless environment. To overcome this drawback, the use of the first-order moment of a TFD is studied in chapter 5. Theoretical analysis and simulations show that the IF estimator based on the first-order moment of a TFD exhibits negligible bias when the signal-to-additive noise ratio is more than 10 dB. The Ricean K-factor is not only necessary for velocity estimation in micro-cells, but also is a measure of the severity of fading and a good indicator of the channel quality. Two new methods for estimating the Ricean K-factor based on the first two moments of the envelope of the received signal, are proposed in chapter 6. Performance analysis presented in chapter 6, prove that the proposed K estimators are robust to non-isotropic scattering. Theoretical analysis and simulations which are presented in chapters 4 and 7 of this thesis, prove that the proposed velocity and K estimators outperform existing estimators in the presence of shadowing and additive noise.

Signal processing has been playing a key role in providing solutions to key problems encountered in communications, in general, and in wireless communications, in particular. Time-Frequency Signal Processing (TFSP) provides eective tools for analyzing nonstationary signals where the frequency content of signals varies in time as well as for analyzing linear time-varying systems. This research aimed at exploiting the advantages of TFSP, in dealing with nonstationary signals, into the fundamental issues of signal processing, namely the signal estimation and signal separation. In particular, it has investigated the problems of (i) the Instantaneous Frequency (IF) estimation of Linear Frequency-Modulated (LFM) signals corrupted in complex-valued zero-mean Multiplicative Noise (MN), and (ii) the Underdetermined Blind Source Separation (UBSS) of LFM signals, while focusing onto the fast-growing area of Wireless Communications (WCom). A common problem in the issue of signal estimation is the estimation of the frequency of Frequency-Modulated signals which are seen in many engineering and real-life applications. Accurate frequency estimation leads to accurate recovery of the true information. In some applications, the random amplitude modulation shows up when the medium is dispersive and/or when the assumption of point target is not valid; the original signal is considered to be corrupted by an MN process thus seriously aecting the recovery of the information-bearing frequency. The IF estimation of nonstationary signals corrupted by complex-valued zero-mean MN was investigated in this research. We have proposed a Second-Order Statistics approach, rather than a Higher-Order Statistics approach, for IF estimation using Time-Frequency Distributions (TFDs). The main assumption was that the autocorrelation function of the MN is real-valued but not necessarily positive (i.e. the spectrum of the MN is symmetric but does not necessary has the highest peak at zero frequency). The estimation performance was analyzed in terms of bias and variance, and compared between four dierent TFDs: Wigner-Ville Distribution, Spectrogram, Choi-Williams Distribution and Modified B Distribution. To further improve the estimation, we proposed to use the Multiple Signal Classification algorithm and showed its better performance. It was shown that the Modified B Distribution performance was the best for Signal-to-Noise Ratio less than 10dB. In the issue of signal separation, a new research direction called Blind Source Separation (BSS) has emerged over the last decade. BSS is a fundamental technique in array signal processing aiming at recovering unobserved signals or sources from observed mixtures exploiting only the assumption of mutual independence between the signals. The term "blind" indicates that neither the structure of the mixtures nor the source signals are known to the receivers. Applications of BSS are seen in, for example, radar and sonar, communications, speech processing, biomedical signal processing. In the case of nonstationary signals, a TF structure forcing approach was introduced by Belouchrani and Amin by defining the Spatial Time- Frequency Distribution (STFD), which combines both TF diversity and spatial diversity. The benefit of STFD in an environment of nonstationary signals is the direct exploitation of the information brought by the nonstationarity of the signals. A drawback of most BSS algorithms is that they fail to separate sources in situations where there are more sources than sensors, referred to as UBSS. The UBSS of nonstationary signals was investigated in this research. We have presented a new approach for blind separation of nonstationary sources using their TFDs. The separation algorithm is based on a vector clustering procedure that estimates the source TFDs by grouping together the TF points corresponding to "closely spaced" spatial directions. Simulations illustrate the performances of the proposed method for the underdetermined blind separation of FM signals. The method developed in this research represents a new research direction for solving the UBSS problem. The successful results obtained in the research development of the above two problems has led to a conclusion that TFSP is useful for WCom. Future research directions were also proposed.

Signal processing has been playing a key role in providing solutions to key problems encountered in communications, in general, and in wireless communications, in particular. Time-Frequency Signal Processing (TFSP) provides eective tools for analyzing nonstationary signals where the frequency content of signals varies in time as well as for analyzing linear time-varying systems. This research aimed at exploiting the advantages of TFSP, in dealing with nonstationary signals, into the fundamental issues of signal processing, namely the signal estimation and signal separation. In particular, it has investigated the problems of (i) the Instantaneous Frequency (IF) estimation of Linear Frequency-Modulated (LFM) signals corrupted in complex-valued zero-mean Multiplicative Noise (MN), and (ii) the Underdetermined Blind Source Separation (UBSS) of LFM signals, while focusing onto the fast-growing area of Wireless Communications (WCom). A common problem in the issue of signal estimation is the estimation of the frequency of Frequency-Modulated signals which are seen in many engineering and real-life applications. Accurate frequency estimation leads to accurate recovery of the true information. In some applications, the random amplitude modulation shows up when the medium is dispersive and/or when the assumption of point target is not valid; the original signal is considered to be corrupted by an MN process thus seriously aecting the recovery of the information-bearing frequency. The IF estimation of nonstationary signals corrupted by complex-valued zero-mean MN was investigated in this research. We have proposed a Second-Order Statistics approach, rather than a Higher-Order Statistics approach, for IF estimation using Time-Frequency Distributions (TFDs). The main assumption was that the autocorrelation function of the MN is real-valued but not necessarily positive (i.e. the spectrum of the MN is symmetric but does not necessary has the highest peak at zero frequency). The estimation performance was analyzed in terms of bias and variance, and compared between four dierent TFDs: Wigner-Ville Distribution, Spectrogram, Choi-Williams Distribution and Modified B Distribution. To further improve the estimation, we proposed to use the Multiple Signal Classification algorithm and showed its better performance. It was shown that the Modified B Distribution performance was the best for Signal-to-Noise Ratio less than 10dB. In the issue of signal separation, a new research direction called Blind Source Separation (BSS) has emerged over the last decade. BSS is a fundamental technique in array signal processing aiming at recovering unobserved signals or sources from observed mixtures exploiting only the assumption of mutual independence between the signals. The term "blind" indicates that neither the structure of the mixtures nor the source signals are known to the receivers. Applications of BSS are seen in, for example, radar and sonar, communications, speech processing, biomedical signal processing. In the case of nonstationary signals, a TF structure forcing approach was introduced by Belouchrani and Amin by defining the Spatial Time- Frequency Distribution (STFD), which combines both TF diversity and spatial diversity. The benefit of STFD in an environment of nonstationary signals is the direct exploitation of the information brought by the nonstationarity of the signals. A drawback of most BSS algorithms is that they fail to separate sources in situations where there are more sources than sensors, referred to as UBSS. The UBSS of nonstationary signals was investigated in this research. We have presented a new approach for blind separation of nonstationary sources using their TFDs. The separation algorithm is based on a vector clustering procedure that estimates the source TFDs by grouping together the TF points corresponding to "closely spaced" spatial directions. Simulations illustrate the performances of the proposed method for the underdetermined blind separation of FM signals. The method developed in this research represents a new research direction for solving the UBSS problem. The successful results obtained in the research development of the above two problems has led to a conclusion that TFSP is useful for WCom. Future research directions were also proposed.

The performance of an adaptive filter may be studied through the behaviour of the optimal and adaptive coefficients in a given environment. This thesis investigates the performance of finite impulse response adaptive lattice filters for two classes of input signals: (a) frequency modulated signals with polynomial phases of order p in complex Gaussian white noise (as nonstationary signals), and (b) the impulsive autoregressive processes with alpha-stable distributions (as non-Gaussian signals). Initially, an overview is given for linear prediction and adaptive filtering. The convergence and tracking properties of the stochastic gradient algorithms are discussed for stationary and nonstationary input signals. It is explained that the stochastic gradient lattice algorithm has many advantages over the least-mean square algorithm. Some of these advantages are having a modular structure, easy-guaranteed stability, less sensitivity to the eigenvalue spread of the input autocorrelation matrix, and easy quantization of filter coefficients (normally called reflection coefficients). We then characterize the performance of the stochastic gradient lattice algorithm for the frequency modulated signals through the optimal and adaptive lattice reflection coefficients. This is a difficult task due to the nonlinear dependence of the adaptive reflection coefficients on the preceding stages and the input signal. To ease the derivations, we assume that reflection coefficients of each stage are independent of the inputs to that stage. Then the optimal lattice filter is derived for the frequency modulated signals. This is performed by computing the optimal values of residual errors, reflection coefficients, and recovery errors. Next, we show the tracking behaviour of adaptive reflection coefficients for frequency modulated signals. This is carried out by computing the tracking model of these coefficients for the stochastic gradient lattice algorithm in average. The second-order convergence of the adaptive coefficients is investigated by modeling the theoretical asymptotic variance of the gradient noise at each stage. The accuracy of the analytical results is verified by computer simulations. Using the previous analytical results, we show a new property, the polynomial order reducing property of adaptive lattice filters. This property may be used to reduce the order of the polynomial phase of input frequency modulated signals. Considering two examples, we show how this property may be used in processing frequency modulated signals. In the first example, a detection procedure in carried out on a frequency modulated signal with a second-order polynomial phase in complex Gaussian white noise. We showed that using this technique a better probability of detection is obtained for the reduced-order phase signals compared to that of the traditional energy detector. Also, it is empirically shown that the distribution of the gradient noise in the first adaptive reflection coefficients approximates the Gaussian law. In the second example, the instantaneous frequency of the same observed signal is estimated. We show that by using this technique a lower mean square error is achieved for the estimated frequencies at high signal-to-noise ratios in comparison to that of the adaptive line enhancer. The performance of adaptive lattice filters is then investigated for the second type of input signals, i.e., impulsive autoregressive processes with alpha-stable distributions . The concept of alpha-stable distributions is first introduced. We discuss that the stochastic gradient algorithm which performs desirable results for finite variance input signals (like frequency modulated signals in noise) does not perform a fast convergence for infinite variance stable processes (due to using the minimum mean-square error criterion). To deal with such problems, the concept of minimum dispersion criterion, fractional lower order moments, and recently-developed algorithms for stable processes are introduced. We then study the possibility of using the lattice structure for impulsive stable processes. Accordingly, two new algorithms including the least-mean P-norm lattice algorithm and its normalized version are proposed for lattice filters based on the fractional lower order moments. Simulation results show that using the proposed algorithms, faster convergence speeds are achieved for parameters estimation of autoregressive stable processes with low to moderate degrees of impulsiveness in comparison to many other algorithms. Also, we discuss the effect of impulsiveness of stable processes on generating some misalignment between the estimated parameters and the true values. Due to the infinite variance of stable processes, the performance of the proposed algorithms is only investigated using extensive computer simulations.

碩士
國立中山大學
電機工程研究所
82
The problem of estimating the frequency content of signals is very important in many digital signal processing applications. In this thesis, we are concerned with the problem of estimat- ing and tracking the instantaneous frequency of the sinusoidal signal together with additive white noise. Its solution has im- portant applications in the fields of vibration measurements, Doppler radar returns, passive sonar systems, and formant frequency estimation of speech signals. In this thesis, a new algorithm for IFE is developed. To do so, the forward linear prediction filter is employed. In consequence, the modified Trench's method along with the Bauer-Fike theorem is proposed for solving the principal eigenvalues of the Hermitian Toepli- tz autocorrelation matrix for instantaneous frequency estima- tion (IFE).In fact,three kinds of eigenvalue searching schemes can be employed in the modified Trench's method. In the new algorithm for IFE, the modified Trench's method is first used for solving the principal eigenvalues for initial block of data with length N. When a new data is received,the Bauer-Fike theorem is applied to search the new eigenvalues based on the previous obtained eigenvalues.Such that the computational cost can be reduced. The performance of the IFE using the presented methodis compared with the conventional LMS adaptive method as well as the QR based method. From the simulation results, we found that the presented method can perform as good as the QR based method, in terms of multiple frequencies estimation where the frequencies are closer.But in the same situation the conventional LMS adaptive method may not perform satisfacto- rily. Moreover, the computational complexity of the presented method is much less than QR based method, especially when the presented method is implemented by the parallelized structure.

碩士
國立臺灣大學
電機工程學研究所
93
This thesis deals with two applications of instantaneous frequency to signal analysis and estimation. The first application is the analysis of aircraft longitudinal long-period oscillation named phugoid phenomenon. A Hilbert-Huang Transform (HHT) is proposed here to analyze the physical measurements in time domain. It is based on the empirical mode decomposition (EMD), which generate a set of intrinsic mode functions (IMF). The HHT is applicable to non-stationary and nonlinear data analysis, and finding out the instantaneous characteristics including frequency of the data is its main part. Besides, combining Fast Fourier Transform (FFT) with EMD shows the different results with HHT. In the phugoid analysis, we present the comparison between the non-stationary signal analysis, HHT, and the conventional Fourier based method from the real-time flight test data measured by kinematic GPS. In the second part of this thesis, an application of adaptive all-pass based notch filter (ANFA) with Gaussian-Newton adaptive algorithm in a GPS narrowband anti-jamming system was presented. In the simulations, there are several stationary and non-stationary interferences considered. The ANFA can estimate the instantaneous frequency of the jamming in real-time, and it achieves a better performance than the conventional time-domain adaptive predictors in terms of mean squared prediction error (MSPE) and signal-to-noise ratio (SNR) improvement.

碩士
國立中山大學
電機工程研究所
81
A new adaptive scheme based on the second-order statistics of the received signal is devised, in this thesis, for estimating the digital instantaneous frequency of the narrowband input buried in additive white noise. Since the desired signal (the sinusoidal signal) and the additive noise are independent, the correlation between both will be null, ideally. Due to the reason described above, the adaptive second-order statistics method for estimating the parameters of the autoregressive (AR) model can be derived. That is, the second-order statistics of the received signal samples is used instead of the received signal samples of the input sequence in the conventional method. To estimate the AR parameters, a gradient-type algorithm is employed to approximate the optimum solution. The estimated AR parameters can be then applied to obtain the spectrum via the modified maximum entropy method. In consequence, the instantaneous frequency can be identified by searching the peak of the spectrum. 　　To reduce the computation effort and make the hardware implementation more easier, the sign algorithm is adopted instead of the gradient-type algorithm in the second-order moment method. From the simulation result, we found that the performance of the presented methods, viz., the gradient-type algorithm and the sign algorithm, are performed very similar very similar but superior to the conventional first-order moment method.

碩士
國立中山大學
電機工程研究所
83
In this thesis, the optimal step-size of the adaptive second- order moment (SOM) algorithm for tracking a complex chirped sinusoid buried in additive white Gaussian noise is derived. To do so, the misadjustment of adaptive filter output which is defined as the excess mean-square error (MSE) as compared to the optimal filter is developed. Since in the SOM algorithm the autocorrelation functions are involved in the adaptation process. Also, in the chirped signal problem, the forgetting factor is an important parameters for estimating the autocorrelation functions. To obtain the optimal step-size and forgetting factor, we can simply minimize the misadjustment. Finally, the closed form expressions of optimal values of the step-size, the forgetting factor, the misadjustment and the time constant are obtained for further investigation of the characteristics of the adaptive SOM algorithm. In fact, these closed form expressions are functions of chirped rate of the chirped signal, the length of predictor, the noise power, and the signal-to-noise ratio. Based on the closed form expressions of the misadjustment and the time constant, we are able to investigate the performance and the statistical property of the adaptive SOM algorithm. The accuracy of the theoretical expressions of the MSE, the optimal step-size and the optimal forgetting factor is shown to be very close to the simulation results. Moreover, from computer simulation results, we learn that the adaptive SOM algotithm has a superior tracking capability in the residual fluctuation compared to the adaptive LMS and RLS algorithms for tracking a chirped signal. Finally, we conclude that the adaptive SOM algorithm is more robust than the conventional LMS and RLS algorithms.