Time-Frequency Processing

2021 ◽  
pp. 156-203
Author(s):  
Victor Lazzarini
Keyword(s):  
Frequency Estimation ◽  
Spectral Processing ◽  
Instantaneous Frequency Estimation ◽  
Processing Application ◽  
Time Frequency ◽  
Analysis And Synthesis ◽  
Time Varying Frequency ◽  
The Hilbert Transform ◽  
Short Time ◽  
Frequency Domain Approach

The idea of dynamic spectral processing, introduced at the end of the previous chapter is fully developed here. The principle of sub-band analysis and synthesis is shown as the basis for a time-varying frequency-domain approach. The short-time Fourier transform (STFT) is introduced as a sequence of time-ordered DFT frames from which amplitude and phase data can be obtained. Different methods for instantaneous frequency estimation are discussed. A streaming system for dynamic spectral processing is introduced, and various modification techniques are explored. The latter part of the chapter presents the Hilbert transform as yet another streaming spectral processing application. The chapter concludes with further additions to the notions of spectrum developed earlier in the volume.

scholarly journals Widely Linear Adaptive Instantaneous Frequency Estimation in Vector Hydrophones

Sensors ◽  
2018 ◽  
Vol 18 (10) ◽  
pp. 3348 ◽  
Author(s):  
Panpan Peng ◽  
Liang An
Keyword(s):  
Instantaneous Frequency ◽  
Frequency Estimation ◽  
Linear Method ◽  
Estimation Method ◽  
Frequency Resolution ◽  
Linear Filter ◽  
Instantaneous Frequency Estimation ◽  
Time Frequency ◽  
Short Time ◽  
Widely Linear

To solve the problem that the time-frequency resolution of Short-Time Fourier Transform (STFT) is constrained by the window length and the moving step of the short time window, and to utilize the merits of a widely linear method, a novel instantaneous frequency estimation method in vector hydrophone was proposed. In this paper, a complex variable was constructed. It is composed of sound pressure and particle velocity as its real part and imaginary part, respectively. The constructed variable was approved to be second order noncircular (improper). For the modelling of noncircular signals, the standard linear estimation is not adequate and the pseudo-covariance matrix should also be taken into consideration. As a result, a widely linear adaptive instantaneous frequency estimation algorithm and its three solutions based on the augmented complex least mean square (ACLMS) method are presented to estimate the instantaneous frequency in vector hydrophones. The results of simulations and laboratory experiments prove that this approach based on a widely linear model performs better compared to STFT and strict linear filter methods.

scholarly journals Analysis of adaptive short-time Fourier transform-based synchrosqueezing transform

2020 ◽  
Vol 19 (01) ◽  
pp. 71-105 ◽  
Author(s):  
Haiyan Cai ◽  
Qingtang Jiang ◽  
Lin Li ◽  
Bruce W. Suter
Keyword(s):  
Fourier Transform ◽  
Theoretical Analysis ◽  
Instantaneous Frequency ◽  
Frequency Estimation ◽  
Short Time Fourier Transform ◽  
Instantaneous Frequency Estimation ◽  
Time Frequency ◽  
Synchrosqueezing Transform ◽  
Non Stationary Signal ◽  
Short Time

Recently, the study of modeling a non-stationary signal as a superposition of amplitude and frequency-modulated Fourier-like oscillatory modes has been a very active research area. The synchrosqueezing transform (SST) is a powerful method for instantaneous frequency estimation and component separation of non-stationary multicomponent signals. The short-time Fourier transform-based SST (FSST) reassigns the frequency variable to sharpen the time-frequency representation and to separate the components of a multicomponent non-stationary signal. Very recently the FSST with a time-varying parameter, called the adaptive FSST, was introduced. The simulation experiments show that the adaptive FSST is very promising in instantaneous frequency estimation of the component of a multicomponent signal, and in accurate component recovery. However, the theoretical analysis of the adaptive FSST has not been carried out. In this paper, we study the theoretical analysis of the adaptive FSST and obtain the error bounds for the instantaneous frequency estimation and component recovery with the adaptive FSST and the second-order adaptive FSST.

scholarly journals RANSAC algorithm for instantaneous frequency estimation and reconstruction of frequency-modulated undersampled signals

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Igor Djurović
Keyword(s):  
Instantaneous Frequency ◽  
Matching Pursuit ◽  
Frequency Estimation ◽  
Consensus Algorithm ◽  
Multidimensional Space ◽  
Instantaneous Frequency Estimation ◽  
Time Frequency ◽  
Polynomial Phase ◽  
Fm Signals ◽  
Fifth Order

AbstractFrequency modulated (FM) signals sampled below the Nyquist rate or with missing samples (nowadays part of wider compressive sensing (CS) framework) are considered. Recently proposed matching pursuit and greedy techniques are inefficient for signals with several phase parameters since they require a search over multidimensional space. An alternative is proposed here based on the random samples consensus algorithm (RANSAC) applied to the instantaneous frequency (IF) estimates obtained from the time-frequency (TF) representation of recordings (undersampled or signal with missing samples). The O’Shea refinement strategy is employed to refine results. The proposed technique is tested against third- and fifth-order polynomial phase signals (PPS) and also for signals corrupted by noise.

Robust estimation of instantaneous phase using a time-frequency adaptive filter

Geophysics ◽  
2013 ◽  
Vol 78 (1) ◽  
pp. O1-O7 ◽  
Author(s):  
Wen-kai Lu ◽  
Chang-Kai Zhang
Keyword(s):  
Adaptive Filter ◽  
Signal To Noise Ratio ◽  
Amplitude Spectrum ◽  
Estimation Method ◽  
Frequency Component ◽  
Data Sets ◽  
Time Frequency ◽  
Instantaneous Phase ◽  
The Hilbert Transform ◽  
Short Time

The instantaneous phase estimated by the Hilbert transform (HT) is susceptible to noise; we propose a robust approach for the estimation of instantaneous phase in noisy situations. The main procedure of the proposed method is applying an adaptive filter in time-frequency domain and calculating the analytic signal. By supposing that one frequency component with higher amplitude has higher signal-to-noise ratio, a zero-phase adaptive filter, which is constructed by using the time-frequency amplitude spectrum, enhances the frequency components with higher amplitudes and suppresses those with lower amplitudes. The estimation of instantaneous frequency, which is defined as the derivative of instantaneous phase, is also improved by the proposed robust instantaneous phase estimation method. Synthetic and field data sets are used to demonstrate the performance of the proposed method for the estimation of instantaneous phase and frequency, compared by the HT and short-time-Fourier-transform methods.

Instantaneous Frequency Estimation of Ultrasonic Testing Signal Based on Matching Pursuits

2013 ◽  
Vol 631-632 ◽  
pp. 1367-1372 ◽  
Author(s):  
Xiu Li Du
Keyword(s):  
Instantaneous Frequency ◽  
Ultrasonic Testing ◽  
Frequency Estimation ◽  
Signal To Noise Ratio ◽  
Instantaneous Frequency Estimation ◽  
Time Frequency ◽  
Frequency Representation ◽  
Matching Pursuits ◽  
Testing Signal ◽  
Suppress Noise

The differences of instantaneous frequency (IF) characteristics between the defect echo and the noise can be used to detect defect and suppress noise for ultrasonic testing signal. Therefore, the IF is one of the important instantaneous parameters of ultrasonic testing signal. To estimate the IF of ultrasonic testing signals more effectively, the peak of time-frequency representation (TFR) from matching pursuits (MP) decomposition is proposed. The performances of IF estimators are compared on the simulated signals at different signal-to-noise ratio (SNR) and the real ultrasonic testing signal. The simulation results present that the proposed method can estimate accurate IF at different SNR.

Approach to Extraction of Incipient Fault Features on Unstable Rotating Rolling Bearings Based on Time-Frequency Order Tracking and SPWVD

2013 ◽  
Vol 819 ◽  
pp. 266-270 ◽  
Author(s):  
Long Long Song ◽  
De Gang Song ◽  
Wei Dong Cheng ◽  
Tai Yong Wang ◽  
Kai Kai Su
Keyword(s):  
Frequency Estimation ◽  
Rolling Bearing ◽  
Instantaneous Frequency Estimation ◽  
Rotating Speed ◽  
Time Frequency ◽  
Speed Variation ◽  
Order Tracking ◽  
Fault Features ◽  
Incipient Fault ◽  
Non Stationary Signal

Frequency-smear phenomenon caused by fierce rotating speed variation made it difficult to extract the fault features of the rolling bearing. An approach based on time-frequency order tracking and SPWVD was proposed in this paper. The influence of speed variation was reduced by resampling the time-domain non-stationary signal at constant angle increments with order tracking analysis. The precision of instantaneous frequency estimation (IFE) in time-frequency order tracking was improved by the use of Smoothed Pseudo Wigner-Ville Distribution (SPWVD). The simulation signal and experiment on test-rig revealed that the proposed method was more effective than the traditional order tracking in clarifying incipient fault.

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