GENERALIZED INSTANTANEOUS AMPLITUDE AND FREQUENCY FUNCTIONS AND THEIR APPLICATION FOR PITCH FREQUENCY DETERMINATION

1995 ◽  
Vol 05 (02) ◽  
pp. 145-165 ◽  
Author(s):  
RUDOLF FÖLDVÁRI
Keyword(s):  
Instantaneous Frequency ◽  
Signal To Noise Ratio ◽  
Frequency Function ◽  
Instantaneous Amplitude ◽  
Time Frequency ◽  
Frequency Representation ◽  
Pitch Frequency ◽  
True Time ◽  
Human Hearing ◽  
Frequency Detector

By defining an instantaneous frequency function it could be shown that if a signal is analytic, instantaneous frequency is analytic, too. A generalized instantaneous amplitude function could then be introduced which is also analytic in character. These functions — apart from an arbitrary constant phase — uniquely define the analytic time function. It could be proved that the transformation gives a true time-frequency representation which fulfills all the necessary requirements. Moreover, the application of instantaneous parameters in connection with a Zwicker's filter bank makes it possible even to model human hearing. By applying a simplified hearing model, an efficient pitch-frequency detector able to decide between voiced-unvoiced signals with the same reliability as visual detection even at a 0 dB signal-to-noise ratio could be developed.

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.

Simulation of Real-Time Frequency Estimators for Pulsed Doppler Systems

1986 ◽  
Vol 8 (4) ◽  
pp. 252-271 ◽  
Author(s):  
G.H. van Leeuwen ◽  
A.P.G. Hoeks ◽  
R.S. Reneman
Keyword(s):  
Real Time ◽  
Instantaneous Frequency ◽  
Wide Frequency Range ◽  
Frequency Range ◽  
Zero Crossings ◽  
Time Frequency ◽  
Doppler Signals ◽  
Extended Frequency Range ◽  
Extended Frequency ◽  
Frequency Detector

Four time-domain oriented, real-time frequency estimators, based on the detection of phase, zero-crossings, instantaneous frequency or autocorrelation, were simulated on a digital computer and subjected to computer generated Doppler signals, enabling the investigation of the influence of spectral shape, filtering, frequency shift, noise and quantization. Three estimators, the autocorrelator as well as the instantaneous frequency detector and the autocorrelator, both with extended frequency range, appeared to be very accurate. They exhibit a bias in the estimator output of less than 2 percent over a wide frequency range, the former up to nearly the Nyquist frequency, the latter two beyond, even for skew spectra and under poor signal conditions regarding bandwidth and noise.

Random denoising and signal nonlinearity approach by time-frequency peak filtering using weighted frequency reassignment

Geophysics ◽  
2013 ◽  
Vol 78 (6) ◽  
pp. V229-V237 ◽  
Author(s):  
Hongbo Lin ◽  
Yue Li ◽  
Baojun Yang ◽  
Haitao Ma
Keyword(s):  
Weight Function ◽  
Instantaneous Frequency ◽  
Seismic Data ◽  
Signal To Noise Ratio ◽  
Random Noise ◽  
Signal To Noise ◽  
Transform Method ◽  
Time Frequency ◽  
Frequency Peak ◽  
Noise Ratio

Time-frequency peak filtering (TFPF) may efficiently suppress random noise and hence improve the signal-to-noise ratio. However, the errors are not always satisfactory when applying the TFPF to fast-varying seismic signals. We begin with an error analysis for the TFPF by using the spread factor of the phase and cumulants of noise. This analysis shows that the nonlinear signal component and non-Gaussian random noise lead to the deviation of the pseudo-Wigner-Ville distribution (PWVD) peaks from the instantaneous frequency. The deviation introduces the signal distortion and random oscillations in the result of the TFPF. We propose a weighted reassigned smoothed PWVD with less deviation than PWVD. The proposed method adopts a frequency window to smooth away the residual oscillations in the PWVD, and incorporates a weight function in the reassignment which sharpens the time-frequency distribution for reducing the deviation. Because the weight function is determined by the lateral coherence of seismic data, the smoothed PWVD is assigned to the accurate instantaneous frequency for desired signal components by weighted frequency reassignment. As a result, the TFPF based on the weighted reassigned PWVD (TFPF_WR) can be more effective in suppressing random noise and preserving signal as compared with the TFPF using the PWVD. We test the proposed method on synthetic and field seismic data, and compare it with a wavelet-transform method and [Formula: see text] prediction filter. The results show that the proposed method provides better performance over the other methods in signal preserving under low signal-to-noise ratio.

scholarly journals NOISE CORRUPTION OF EMPIRICAL MODE DECOMPOSITION AND ITS EFFECT ON INSTANTANEOUS FREQUENCY

2010 ◽  
Vol 02 (03) ◽  
pp. 373-396 ◽  
Author(s):  
DANIEL N. KASLOVSKY ◽  
FRANÇOIS G. MEYER
Keyword(s):  
Empirical Mode Decomposition ◽  
Instantaneous Frequency ◽  
Poor Performance ◽  
Specific Mechanism ◽  
Time Frequency ◽  
Seismic Waveform ◽  
Mode Decomposition ◽  
Frequency Representation ◽  
Transition Modes ◽  
Nonstationary Data

Huang's Empirical Mode Decomposition (EMD) is an algorithm for analyzing nonstationary data that provides a localized time-frequency representation by decomposing the data into adaptively defined modes. EMD can be used to estimate a signal's instantaneous frequency (IF) but suffers from poor performance in the presence of noise. To produce a meaningful IF, each mode of the decomposition must be nearly monochromatic, a condition that is not guaranteed by the algorithm and fails to be met when the signal is corrupted by noise. In this work, the extraction of modes containing both signal and noise is identified as the cause of poor IF estimation. The specific mechanism by which such "transition" modes are extracted is detailed and builds on the observation of Flandrin and Goncalves that EMD acts in a filter bank manner when analyzing pure noise. The mechanism is shown to be dependent on spectral leak between modes and the phase of the underlying signal. These ideas are developed through the use of simple signals and are tested on a synthetic seismic waveform.

scholarly journals An Improved Time-Frequency Analysis Method for Instantaneous Frequency Estimation of Rolling Bearing

2018 ◽  
Vol 2018 ◽  
pp. 1-18 ◽  
Author(s):  
Zengqiang Ma ◽  
Wanying Ruan ◽  
Mingyi Chen ◽  
Xiang Li
Keyword(s):  
Frequency Analysis ◽  
Instantaneous Frequency ◽  
Frequency Estimation ◽  
Rolling Bearing ◽  
Analysis Method ◽  
Instantaneous Frequency Estimation ◽  
Time Frequency Analysis ◽  
Noise Interference ◽  
Time Frequency ◽  
Frequency Representation

Instantaneous frequency estimation of rolling bearing is a key step in order tracking without tachometers, and time-frequency analysis method is an effective solution. In this paper, a new method applying the variational mode decomposition (VMD) in association with the synchroextracting transform (SET), named VMD-SET, is proposed as an improved time-frequency analysis method for instantaneous frequency estimation of rolling bearing. The SET is a new time-frequency analysis method which belongs to a postprocessing procedure of the short-time Fourier transform (STFT) and has excellent performance in energy concentration. Considering nonstationary broadband fault vibration signals of rolling bearing under variable speed conditions, the time-frequency characteristics cannot be obtained accurately by SET alone. Thus, VMD-SET method is proposed. Firstly, the signal is decomposed into several intrinsic mode functions (IMFs) with different center frequency by VMD. Then, effective IMFs are selected by mutual information and kurtosis criteria and are reconstructed. Next, the SET method is applied to the reconstructed signal to generate the time-frequency representation with high resolution. Finally, instantaneous frequency trajectory can be accurately extracted by peak search from the time-frequency representation. The proposed method is free from time-varying sidebands and is robust to noise interference. It is proved by numerical simulated signal analysis and is further validated by lab experimental rolling bearing vibration signal analysis. The results show this method can estimate the instantaneous frequency with high precision without noise interference.

HHT-Based Selection of Optimal Time-Frequency Patterns for Motor Imagery

2013 ◽  
Vol 380-384 ◽  
pp. 3522-3525 ◽  
Author(s):  
Ping Gong ◽  
Min You Chen ◽  
Li Zhang ◽  
Wen Juan Jian
Keyword(s):  
Motor Imagery ◽  
Instantaneous Frequency ◽  
Optimal Time ◽  
Instantaneous Amplitude ◽  
Hilbert Huang Transform ◽  
Time Frequency ◽  
Mode Decomposition ◽  
Frequency Components ◽  
Novel Method ◽  
Selection Of

In this paper, a novel method based on Hilbert-Huang transform (HHT) is presented to select optimal timefrequency patterns for single-trial motor imagery electroencephalograph (EEG). The method comprises three progressive steps: 1) employ Empirical Mode Decomposition (EMD) method to decompose EEG signal into a superposition of components or functions called IMFs, and then apply Hilbert transform to the IMFs to calculate the instantaneous frequency and instantaneous amplitude; 2) select the IMFs including the most useful frequency components 3) the optimal timefrequency patterns can be selected according to the instantaneous frequency and instantaneous amplitude of the selected IMFs. After selecting the optimal timefrequency patterns, the features extracted by different methods are classified by Fisher linear discriminator. The results showed that the proposed method could improve the classification accuracy.

Automatic waveform-based source-location imaging using deep learning extracted microseismic signals

Geophysics ◽  
2020 ◽  
Vol 85 (6) ◽  
pp. KS171-KS183 ◽  
Author(s):  
Omar M. Saad ◽  
Yangkang Chen
Keyword(s):  
Clustering Algorithm ◽  
Signal To Noise Ratio ◽  
Reverse Time ◽  
Reverse Time Migration ◽  
Time Frequency ◽  
Time Migration ◽  
Frequency Representation ◽  
Convolutional Autoencoder ◽  
Migration Method

We have used an automatic unsupervised technique to extract waveform signals from continuous microseismic data. First, the time-frequency representation (scalogram) is obtained for the input microseismic trace. Second, the convolutional autoencoder (CAE) is used to extract the significant scalogram features related to the waveform signals and discard the rest. Third, the extracted features from the CAE encoder are considered as the input for the k-means clustering algorithm, in which the input samples are classified into waveform and nonwaveform components. The proposed algorithm is evaluated using several synthetic and field examples. We find that the proposed algorithm successfully extracts the waveform signals even in a noisy environment with a signal-to-noise-ratio as low as −10 dB. We compared the proposed algorithm to benchmark algorithms, for example, simple k-means and short-term and long-term average ratio methods, and find that the proposed algorithm performs best. We find that the detected waveform signals can enhance the resolution of microseismic imaging using a waveform-based reverse time migration method.

Sign in / Sign up

Export Citation Format

Share Document