TVF: Theoretical Basis The Time Variable Filtering (TVF) is a filtering technique that does not give a dispersion curve but a smooth signal (a signal time-variable.

Slides:



Advertisements
Similar presentations
11 paths & 21 events registered. 11 paths & 15 events registered.
Advertisements

Frequency analysis.
DCSP-13 Jianfeng Feng Department of Computer Science Warwick Univ., UK
ECE 8443 – Pattern Recognition ECE 8423 – Adaptive Signal Processing Objectives: Periodograms Bartlett Windows Data Windowing Blackman-Tukey Resources:
ACHIZITIA IN TIMP REAL A SEMNALELOR. Three frames of a sampled time domain signal. The Fast Fourier Transform (FFT) is the heart of the real-time spectrum.
FilteringComputational Geophysics and Data Analysis 1 Filtering Geophysical Data: Be careful!  Filtering: basic concepts  Seismogram examples, high-low-bandpass.
1 Chapter 16 Fourier Analysis with MATLAB Fourier analysis is the process of representing a function in terms of sinusoidal components. It is widely employed.
DFT/FFT and Wavelets ● Additive Synthesis demonstration (wave addition) ● Standard Definitions ● Computing the DFT and FFT ● Sine and cosine wave multiplication.
Fourier series With coefficients:. Complex Fourier series Fourier transform (transforms series from time to frequency domain) Discrete Fourier transform.
AES 120 th Convention Paris, France, 2006 Adaptive Time-Frequency Resolution for Analysis and Processing of Audio Alexey Lukin AES Student Member Moscow.
Page 0 of 34 MBE Vocoder. Page 1 of 34 Outline Introduction to vocoders MBE vocoder –MBE Parameters –Parameter estimation –Analysis and synthesis algorithm.
1 Hough transform Some Fourier basics: –Nyquist frequency: 1/2 , with  the difference between time samples. If signal is bandwidth limited below Nyquist.
Basic Filters: Basic Concepts Filtering is an important computation process in Geophysics that can be divided in two principal categories: Natural filtering.
Wavelet method determination of long period tidal waves and polar motion in superconducting gravity data X.-G.. Hu 1,2,*, L.T. Liu 1, Ducarme. B. 3, H.T.
1 Speech Parametrisation Compact encoding of information in speech Accentuates important info –Attempts to eliminate irrelevant information Accentuates.
MFT: Theoretical Basis
Time-Frequency and Time-Scale Analysis of Doppler Ultrasound Signals
System Microphone Keyboard Output. Cross Synthesis: Two Implementations.
Image Fourier Transform Faisal Farooq Q: How many signal processing engineers does it take to change a light bulb? A: Three. One to Fourier transform the.
Problem: Ground Clutter Clutter: There is always clutter in signals and it distorts the purposeful component of the signal. Getting rid of clutter, or.
Wiener Deconvolution: Theoretical Basis The Wiener Deconvolution is a technique used to obtain the phase-velocity dispersion curve and the attenuation.
Spectra: ApplicationsComputational Geophysics and Data Analysis 1 Fourier Transform: Applications in seismology Estimation of spectra –windowing –resampling.
Spectral Analysis Spectral analysis is concerned with the determination of the energy or power spectrum of a continuous-time signal It is assumed that.
What are the dominant frequencies? Fourier transforms decompose a data sequence into a set of discrete spectral estimates – separate the variance of a.
Multiresolution STFT for Analysis and Processing of Audio
1 CS 551/651: Structure of Spoken Language Lecture 8: Mathematical Descriptions of the Speech Signal John-Paul Hosom Fall 2008.
6.2 - The power Spectrum of a Digital PAM Signal A digtal PAM signal at the input to a communication channl scale factor (where 2d is the “Euclidean.
Acoustic Analysis of Speech Robert A. Prosek, Ph.D. CSD 301 Robert A. Prosek, Ph.D. CSD 301.
The Story of Wavelets.
Deconvolution Bryce Hutchinson Sumit Verma Objectives: -Understand the difference between exponential and surface consistent gain -Identify power line.
The Wavelet Tutorial Dr. Charturong Tantibundhit.
Ping Zhang, Zhen Li,Jianmin Zhou, Quan Chen, Bangsen Tian
1 Chapter 5 Image Transforms. 2 Image Processing for Pattern Recognition Feature Extraction Acquisition Preprocessing Classification Post Processing Scaling.
Time Series Data Analysis - I Yaji Sripada. Dept. of Computing Science, University of Aberdeen2 In this lecture you learn What are Time Series? How to.
EEE 503 Digital Signal Processing Lecture #1 : Introduction Dr. Panuthat Boonpramuk Department of Control System & Instrumentation Engineering KMUTT.
Deconvolution in Reaction Kinetics Ernő Keszei Eötvös University Budapest, Hungary.
Lecture#10 Spectrum Estimation
02/05/2002 (C) University of Wisconsin 2002, CS 559 Last Time Color Quantization Mach Banding –Humans exaggerate sharp boundaries, but not fuzzy ones.
Surface-wave Derived Focal Mechanisms in Mid-America R. B. Herrmann 1, C. J. Ammon 2 and H. M. Benz 3 1 Saint Louis University, 2 Pennsylvania State University,
Fourier Transform.
Multiscale Geometric Signal Processing in High Dimensions
Time/frequency analysis of some MOST data F. Baudin (IAS) & J. Matthews (UBC)
The Analysis of Non-Stationary Time Series with Time Varying Frequencies using Time Deformation The Analysis of Non-Stationary Time Series with Time Varying.
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Areas in the Plane Section 7.2.
Analysis of Traction System Time-Varying Signals using ESPRIT Subspace Spectrum Estimation Method Z. Leonowicz, T. Lobos
The Story of Wavelets Theory and Engineering Applications
4.A Fourier Series & Fourier Transform Many slides are from Taiwen Yu.
Signal Analyzers. Introduction In the first 14 chapters we discussed measurement techniques in the time domain, that is, measurement of parameters that.
Parametric Equations Lesson Movement of an Object Consider the position of an object as a function of time  The x coordinate is a function of.
Fourier Analyses Time series Sampling interval Total period Question: How perturbations with different frequencies contribute to the turbulent kinetic.
Learning from the Past, Looking to the Future James R. (Jim) Beaty, PhD - NASA Langley Research Center Vehicle Analysis Branch, Systems Analysis & Concepts.
FFT corrections for tune measurements
Fourier series With coefficients:.
Discrete Fourier Transform (DFT)
Susan L. Beck George Zandt Kevin M. Ward Jonathan R. Delph.
Spectral Analysis Spectral analysis is concerned with the determination of the energy or power spectrum of a continuous-time signal It is assumed that.
MECH 373 Instrumentation and Measurements
Fourier Analyses Time series Sampling interval Total period
Basic Filters: Basic Concepts
Filtering Geophysical Data: Be careful!
HARMONICS AND FILTERS.
Quiz: Fast Fourier Transforms (FFTs) and Windowing TIPL 4302 TI Precision Labs – ADCs Created by Art Kay.
Neurons Skip a Beat during Fast Ripples
Advanced Digital Signal Processing
Shear-wave splitting measurements for Asia
Fourier Analyses Time series Sampling interval Total period
8.1 Circuit Parameters definition of decibels using decibels
Neurons Skip a Beat during Fast Ripples
9.4 Enhancing the SNR of Digitized Signals
8.6 Autocorrelation instrument, mathematical definition, and properties autocorrelation and Fourier transforms cosine and sine waves sum of cosines Johnson.
Presentation transcript:

TVF: Theoretical Basis The Time Variable Filtering (TVF) is a filtering technique that does not give a dispersion curve but a smooth signal (a signal time-variable filtered), in which all effects of noise, higher modes and other undesirable perturbations have been removed (Cara, 1973). For it, a Fourier synthesis of the observed signal is performed (Brigham, 1988), in which only are considered the Fourier harmonics in the neighboring of the group time t g (f), given by the formula: where F(f) is the Fourier spectrum of f(t), computed applying the FFT forward to the observed signal f(t). The expression for time-frequency window w(t,f) is presented in the following slide (Bath, 1974).

TVF: Theoretical Basis The parameters  and  are constant during the filtering process (Cara, 1973). Usually, the values for these constant parameters are  = 5 and  = 0. This filtering technique requires a starting dispersion curve t g (f), to perform the Fourier synthesis. This dispersion curve can be provided by the application of the MFT to the observed signal f(t), previously to the computation of the TVF. where t w is given by

Filtered signal g(t) f(t) F(f) FFT Selection of an initial dispersion curve tg(f) =  /Ug(f) Time-variable filtering Time window w(t,f) Preprocessed signal f(t) (observed seismogram with instrumental correction) TVF: Flow Chart

TVF: An Example The above-described filtering process, as an example, has been applied to the trace shown below, which has been instrumentally corrected. The starting dispersion curve t g (f) necessary to perform the TVF, has been obtained from this observed trace by application of the MFT, as it is shown in the PPT presentation: MFT.MFT

TVF: An Example A Fourier synthesis of the observed signal shown in (a) is performed, considering only the Fourier harmonics in the neighboring of the dispersion curve shown in (b), to obtain the time-variable filtered signal shown in (c).

TVF: References Bath M. (1974). Spectral Analysis in Geophysics. Elsevier, Amsterdam. Brigham E. O. (1988). The Fast Fourier Transform and Its Applications. Prentice Hall, New Jersey. Cara M. (1973). Filtering dispersed wavetrains. Geophys. J. R. astr. Soc., 33, TVF: Web Page