Spectral Estimation of Noisy Seismogram using Time-Frequency Analyses

2016 ◽  
Vol 7 (1) ◽  
pp. 19-32 ◽  
Author(s):  
Vaneeta Devi ◽  
M. L. Sharma
Keyword(s):  
Fourier Transform ◽  
Wavelet Transform ◽  
Frequency Domain ◽  
Spectral Estimation ◽  
Window Size ◽  
Frequency Component ◽  
Maximum Energy ◽  
Gabor Transform ◽  
Time Frequency ◽  
Signal Features

Time–Frequency analyses have the advantage of explaining the signal features in both time domain and frequency domain. This paper explores the performance of Time–Frequency analyses on noisy seismograms acquired from seismically active region in NW Himalayan. The Short Term Fourier Transform, Gabor Transform, Wavelet Transform and Wigner-Ville Distribution have been used in the present study to carry out Time-Frequency analyses. Parametric study has been carried out by varying basic parameters viz. sampling, window size and types. Wavelet analysis (Continuous Wavelet Transform) has been studied with different type of wavelets. The seismograms have been stacked in time-frequency domain using Gabor Transform and have been converted using Discrete Gabor Expansion techniques. The Spectrograms reveals better spectral estimation in time-frequency domain than Fourier Transform and hence recommended to estimate dominate frequency components, phase marking and timings of phase. The time of occurrence of frequency component corresponding to maximum energy burst can be identified on seismograms

scholarly journals Time Frequency Analysis of Wavelet and Fourier Transform

2020 ◽  
Author(s):  
Karlton Wirsing
Keyword(s):  
Signal Processing ◽  
Fourier Transform ◽  
Wavelet Transform ◽  
Frequency Domain ◽  
Frequency Analysis ◽  
Discrete Wavelet ◽  
Continuous Wavelet ◽  
Time Frequency ◽  
Efficient Access ◽  
The Fourier Transform

Signal processing has long been dominated by the Fourier transform. However, there is an alternate transform that has gained popularity recently and that is the wavelet transform. The wavelet transform has a long history starting in 1910 when Alfred Haar created it as an alternative to the Fourier transform. In 1940 Norman Ricker created the first continuous wavelet and proposed the term wavelet. Work in the field has proceeded in fits and starts across many different disciplines, until the 1990’s when the discrete wavelet transform was developed by Ingrid Daubechies. While the Fourier transform creates a representation of the signal in the frequency domain, the wavelet transform creates a representation of the signal in both the time and frequency domain, thereby allowing efficient access of localized information about the signal.

Analysis of Vibration Signals in Monitoring Titanium End Milling Process Using Triaxial Accelerometer

2021 ◽  
Author(s):  
John Henry Navarro-Devia ◽  
Dzung Viet Dao ◽  
Yun Chen ◽  
Huaizhong Li
Keyword(s):  
Titanium Alloys ◽  
Frequency Domain ◽  
Single Channel ◽  
End Milling ◽  
Cutting Parameters ◽  
Frequency Component ◽  
Spindle Speed ◽  
Triaxial Accelerometer ◽  
Vibration Signals ◽  
Time Frequency

Abstract Vibrations during milling of hard-to-cut materials can cause low productivity, inferior quality and short tool life. It is one of the common issues in the machining of hard-to-cut materials employed in aerospace applications, such as titanium alloys. This paper presents an analysis of the vibration signals in the 3 axes of movement during titanium end milling, under diverse cutting parameters, manipulating spindle speed and feed rate. Signals were obtained using a triaxial accelerometer and processed in MATLAB. The analysis was conducted in the frequency-domain and the time-frequency domain. The results show that high-frequency vibration could occur in any direction with different amplitudes. Response on each axis depends on spindle speed, feed, and type of milling. A frequency component continually appeared in each axis regardless of cutting conditions and is located near the natural frequencies. Finally, the triaxial accelerations were compared for the milling cases with a new and a worn tool. Results highlight the importance and need for continuous monitoring of vibration in the 3 axes, instead of only using a single-channel signal, providing experimental data which could expand knowledge relating to the milling of titanium alloys.

scholarly journals An Efficient Adaptive Window Size Selection Method for Improving Spectrogram Visualization

2016 ◽  
Vol 2016 ◽  
pp. 1-13 ◽  
Author(s):  
Shibli Nisar ◽  
Omar Usman Khan ◽  
Muhammad Tariq
Keyword(s):  
Fourier Transform ◽  
Filter Bank ◽  
Window Size ◽  
Fixed Time ◽  
Frequency Resolution ◽  
High Spectral Resolution ◽  
Background Information ◽  
High Temporal Resolution ◽  
Low Frequencies ◽  
Time Frequency

Short Time Fourier Transform (STFT) is an important technique for the time-frequency analysis of a time varying signal. The basic approach behind it involves the application of a Fast Fourier Transform (FFT) to a signal multiplied with an appropriate window function with fixed resolution. The selection of an appropriate window size is difficult when no background information about the input signal is known. In this paper, a novel empirical model is proposed that adaptively adjusts the window size for a narrow band-signal using spectrum sensing technique. For wide-band signals, where a fixed time-frequency resolution is undesirable, the approach adapts the constant Q transform (CQT). Unlike the STFT, the CQT provides a varying time-frequency resolution. This results in a high spectral resolution at low frequencies and high temporal resolution at high frequencies. In this paper, a simple but effective switching framework is provided between both STFT and CQT. The proposed method also allows for the dynamic construction of a filter bank according to user-defined parameters. This helps in reducing redundant entries in the filter bank. Results obtained from the proposed method not only improve the spectrogram visualization but also reduce the computation cost and achieves 87.71% of the appropriate window length selection.

Spectral decomposition of seismic data with continuous-wavelet transform

Geophysics ◽  
2005 ◽  
Vol 70 (6) ◽  
pp. P19-P25 ◽  
Author(s):  
Satish Sinha ◽  
Partha S. Routh ◽  
Phil D. Anno ◽  
John P. Castagna
Keyword(s):  
Fourier Transform ◽  
Wavelet Transform ◽  
Continuous Wavelet Transform ◽  
Time Scale ◽  
Fixed Time ◽  
Frequency Resolution ◽  
Continuous Wavelet ◽  
Window Length ◽  
Time Frequency ◽  
Frequency Map

This paper presents a new methodology for computing a time-frequency map for nonstationary signals using the continuous-wavelet transform (CWT). The conventional method of producing a time-frequency map using the short time Fourier transform (STFT) limits time-frequency resolution by a predefined window length. In contrast, the CWT method does not require preselecting a window length and does not have a fixed time-frequency resolution over the time-frequency space. CWT uses dilation and translation of a wavelet to produce a time-scale map. A single scale encompasses a frequency band and is inversely proportional to the time support of the dilated wavelet. Previous workers have converted a time-scale map into a time-frequency map by taking the center frequencies of each scale. We transform the time-scale map by taking the Fourier transform of the inverse CWT to produce a time-frequency map. Thus, a time-scale map is converted into a time-frequency map in which the amplitudes of individual frequencies rather than frequency bands are represented. We refer to such a map as the time-frequency CWT (TFCWT). We validate our approach with a nonstationary synthetic example and compare the results with the STFT and a typical CWT spectrum. Two field examples illustrate that the TFCWT potentially can be used to detect frequency shadows caused by hydrocarbons and to identify subtle stratigraphic features for reservoir characterization.

Sign in / Sign up

Export Citation Format

Share Document