scholarly journals Method of estimation of frequency variation relying on estimation of shift of spectral peaks

2021 ◽  
pp. 53-61
Author(s):  
D. A. Kechik ◽  
Yu. P. Aslamov ◽  
I. G. Davydov
Keyword(s):  
Fundamental Frequency ◽  
Instantaneous Frequency ◽  
Three Dimensional ◽  
Frequency Variation ◽  
Frequency Tracking ◽  
Variation Reduction ◽  
Time Frequency ◽  
Frequency Representation ◽  
Spectral Peaks ◽  
Current Window

Problem of estimation of variated frequency of components of polyharmonic signals has been arose. Three-dimensional time-frequency representation of signals is usually used to resolve this problem. But simple and reliable method of instantaneous frequency tracking is needed. Frequency tracking method based on estimation of shifts of peaks of spectrogram has been proposed in this paper. It is assumed that shift of spectral peaks of components of signal is proportional to variation of fundamental frequency. Logarithmic scaling of time-frequency representation is used to make spectral peaks equidistant. Temporal dependence of shift of spectral maximums is obtained using correlation of windowed spectrum at the first frame and spectrum of signal in the current window. Then obtained track is translated in linear scale. Proposed method does not estimate values of instantaneous frequency or central frequency of signal component but estimates its variation. Advantage of the method is that it can estimate frequency track even if range of frequency variation and its central value are known roughly or unknown at all. Multiple components do not interfere to estimate fundamental frequency variation. Reduction of bandwidth is recommended to increase accuracy of frequency track estimation, but analysis of time-frequency representation containing a few components is also possible. Dependency of performance of analysis of synthetic signals using the method on various signal to noise ratios under different conditions was estimated. Applicability of the method for vibrational diagnosing of rotary equipment was checked out using spectral interference method.

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.

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.

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.

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.

Influence of input data representations for time-dependent instrument recognition

2021 ◽  
Vol 88 (5) ◽  
pp. 274-281
Author(s):  
Markus Schwabe ◽  
Michael Heizmann
Keyword(s):  
Signal Processing ◽  
Three Dimensional ◽  
Time Dependent ◽  
Frequency Error ◽  
Additional Time ◽  
Time Frequency ◽  
Music Signal ◽  
Frequency Representation ◽  
Instrument Recognition ◽  
Signal Processing Algorithms

Abstract An important preprocessing step for several music signal processing algorithms is the estimation of playing instruments in music recordings. To this aim, time-dependent instrument recognition is realized by a neural network with residual blocks in this approach. Since music signal processing tasks use diverse time-frequency representations as input matrices, the influence of different input representations for instrument recognition is analyzed in this work. Three-dimensional inputs of short-time Fourier transform (STFT) magnitudes and an additional time-frequency representation based on phase information are investigated as well as two-dimensional STFT or constant-Q transform (CQT) magnitudes. As additional phase representations, the product spectrum (PS), based on the modified group delay, and the frequency error (FE) matrix, related to the instantaneous frequency, are used. Training and evaluation processes are executed based on the MusicNet dataset, which enables the estimation of seven instruments. With a higher number of frequency bins in the input representations, an improved instrument recognition of about 2 % in F1-score can be achieved. Compared to the literature, frame-level instrument recognition can be improved for different input representations.

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