Signal Processing, Filtering & Fourier Transform Page

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Signal Processing, Filtering & Fourier Transform Page

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Thank you for your support.

Sincerely, Tom Irvine
Email: tomirvine@aol.com

Tutorials

An Introduction to Digital Filtering: This tutorial focuses on the Butterworth filter. filter.pdf

Notes on Refiltering for Phase Correction: REFILT.pdf

Introduction to the Spectral Functions. The Fourier Transform and Power Spectral Density Function: spectral.pdf

Fast Fourier Transform: The FFT transform is based on the butterfly algorithm.
fft.pdf

Shock and Vibration Signal Analysis: Shock_and_Vibration_Signal_Analysis.pdf

Power Spectral Density Calculation via Matlab: Guest tutorial submitted by Bob Light. psd_mat.pdf

Sine Function Identification and Removal. sinefind.pdf

Statistical Degrees of Freedom: statdof.pdf

Frederic J. Harris, Trigonometric Transforms: trig_harris.pdf

Scientific Atlanta, Random Vibration Testing:
SA_VibrationTesting.pdf

The Fourier Series of a Rectangular Wave: fourier_series_rectangular.pdf

The autocorrelation function autocorrelation.pdf

Kurtosis in Vibration Analysis: kurtosis.pdf

A Method for Generating White Noise Time Histories with Skewness > 0 and Kurtosis >0

Matlab script: witch.m

white_kurtosis.pdf

See Also Random Vibration Page -

ZOOM FFT
-

Bruel & Kjaer, Zoom FFT: zoom_fft.pdf

Zoom FFT of a time series, Matlab: zoomFFT.m
zoomFFT_plot.m

Example tutorial: zoomFFT_example.pdf

Sample input file: d9p5.txt

ALIASING
-

Notes on sample rate and aliasing: aliasing_notes.pdf

The Need for Analog Anti-aliasing Filters in the Pyrotechnic Shock Testing of Avionics Components: AA_Filter_Pyro.pdf

Signal Identification from Aliased Data:

Matlab Scripts

sinefind_alias.m & sfa_engine.m
alias_synthesis.pdf

Excel application for demonstrating bit resolution and aliasing effects. This file was submitted by Robert Davis of NASA/Wallops. It may be freely downloaded. BitResolutionandAliasingG.zip

Ceiling fan, optical aliasing video: fan_aliased.avi

WEIGHTING FUNCTIONS
-

Bruel & Kjaer, Use of Weighting Functions in DFT/FFT Analysis (Part I): weight1.pdf

Bruel & Kjaer, Use of Weighting Functions in DFT/FFT Analysis (Part II): weight2.pdf

Aude, A Tutorial in Coherent and Windowed Sampling with A/D Converters: AN9675.pdf

Hanning Window Compensation Factor: Hanning_compensation.pdf

Bingham Window Compensation Factor: Bingham_compensation.pdf

Starting Engines 3 & 4 and taxiing of EAA's B-17 at Felts field:
B-17_engine_aliasing.avi

Recommend viewing this with RealPlayer with DivX.

This video clip shows an example of optical aliasing. Each of the propellers for the 3 & 4 engines seem to switch rotational direction during start-up because the frame samping rate is too low.

A similar error can occur with measured accelerometer data if the sampling rate is too low. Spectral components in the Fourier transform can become aliased about the Nyquist frequency, which is one-half of the sampling rate. The sample rate should be as high as possible to adequate capture the highest frequency of interest. Also, analog anti-aliasing filters should be used to minimize the potential for aliasing errors.

Filtering Software
Executable
Source

Digital filtering using a Butterworth 6th order filter. The user must supply an input time history file. Both lowpass and highpass options are available. filter.exe filter.cpp

Mean filter. This is a type of lowpass filter. mean_filter.exe mean_filter.cpp

Median filter. This is a type of lowpass filter. It is useful for noise spike removal.
median_filter.exe median_filter.cpp

Transfer function magnitude for analog Butterworth and Bessel lowpass filters.
Butterworth_transfer.exe
Butterworth_transfer.cpp

Decimation with filtering.
decimate.exe
decimate.cpp

Decimation with no filtering.
decimate_nf.exe decimate_nf.cpp

Calculate a PSD via successive bandpass filtering.
filter_psd.exe
filter_psd.cpp

Bessel two-pole lowpass filter Bessel_lowpass_filter.exe Bessel_lowpass_filter.cpp

Other Software Programs

Executable

Source

Fast Fourier transform (FFT) of a time history. The transform operates on a time series with 2^n points, where n is an integer.

Also, corresponding inverse FFT.

fft.exe

invfft.exe

fft.cpp

invfft.cpp

Conventional Fourier transform of a time series with an arbitrary number of points.

Also, corresponding inverse Fourier transform.

fourier.exe

inv_fourier.exe

fourier.cpp

inv_fourier.cpp

Zoom FFT of a time series.

zoomFFT.exe

zoomFFT.cpp

This program converts a Fourier transform magnitude with constant bandwidth to an octave or one-third octave format.

FFToct.exe

  FFToct.cpp

This program converts a Fourier transform magnitude with constant bandwidth to a wider resolution.

FFT_smooth.exe

FFT_smooth.cpp

Cross-spectrum of two time histories. The output files may be used for modal test data analysis.

cross_spectrum.exe

cross_spectrum.cpp

Cross-spectrum of two time histories. The program generates H1 and H2 frequency response functions (FRFs), the coherence function, and the corresponding impulse response functions.

cross_spectrum_modal.exe

cross_spectrum_modal.cpp

Energy Spectral Density

espec.exe

espec.cpp

Generation of time history signals:
1. sine
2. damped sine
3. sine sweep
4. white noise
5. pink noise

generate.exe

_

Beat frequency time history generation

beat_generate.exe

beat_generate.cpp

Cubic Spline Curve-fit:

spline.exe

spline.cpp

Integrate a time history via the trapezoidal rule.

integ.exe

integ.cpp

This script corrects an acceelration signal so that is corresponding velocity and displacement time histories are stable and oscillate about the zero baseline. displacement_correction.exe displacement_correction.cpp

Differentiate a time history.

differ.exe

differ.cpp

Autocorrelation

autocor.exe

autocor.cpp

Cross-correlation

cross_correlation.exe

cross_correlation.cpp

Correlation Coefficient of two time histories

correlation_coefficient.exe

correlation_coefficient.cpp

This program multiplies the Fourier transform of a base input function by the transfer function of a single-degree-of-freedom system.

transfer_fft.exe

transfer_fft.cpp

This program divides a response function by an excitation function. Each function must be in complex format. The functions may be Fourier transforms.

comp_div.exe

  comp_div.cpp

This program divides a response function by an excitation function. Each function must be in real format.

real_div.exe

real_div.cpp

This program multiplies a function by another function. Each function must be in real format.

real_mult.exe

real_mult.cpp

This program adds a function to another function. Each function must be in real format.
real_add.exe real_add.cpp

Convolution integral for two time histories.

convolution.exe

convolution.cpp

This program calculates a response time history from an input time history and a transfer function where the transfer function is a complex Fourier transform. It uses the convolution method.

blast.exe

blast.cpp

Multiply an input Fourier transform by a transfer function.

fourier_mult.exe

  fourier_mult.cpp

Signal scaling with adjustment options.

signal.exe

signal.cpp

Multipurpose frequency response function processing.

frequency_function.exe

frequency_function.cpp

Histogram, probability density function, and peak distribution of a time history.

histogram.exe

histogram.cpp

Cumulative RMS of a time history. Used as an alternate tool for shock severity evaluation.

TRMS.exe

TRMS.cpp

Generation of a "white noise" time history.

white.exe

white.cpp

Add white noise to a signal.

add_white.exe

add_white.cpp

Generation of a "white noise" time history with kurtosis control.

white_kurtosis.exe

white_kurtosis.cpp

Aliasing frequency calculator.

aliasing.exe

aliasing.cpp

This program calculates the peak frequency vs. time of a time history, using the Fourier transform method.

freq_peak.exe

freq_peak.cpp

This program calculates the peak frequency vs. time of a time history, using the FFT transform method.

fft_peak.exe

fft_peak.cpp

Additional software is given at: Matlab & Java

Book Recommendations

Web

www.vibrationdata.com

____________

Please recommend this site by clicking on the Google +1 Button.

Other Vibrationdata Pages: Home | Tutorials

Tutorials
An Introduction to Digital Filtering: This tutorial focuses on the Butterworth filter.	filter.pdf
Notes on Refiltering for Phase Correction:	REFILT.pdf
Introduction to the Spectral Functions. The Fourier Transform and Power Spectral Density Function:	spectral.pdf
Fast Fourier Transform: The FFT transform is based on the butterfly algorithm.	fft.pdf
Shock and Vibration Signal Analysis:	Shock_and_Vibration_Signal_Analysis.pdf
Power Spectral Density Calculation via Matlab: Guest tutorial submitted by Bob Light.	psd_mat.pdf
Sine Function Identification and Removal.	sinefind.pdf
Statistical Degrees of Freedom:	statdof.pdf
Frederic J. Harris, Trigonometric Transforms:	trig_harris.pdf
Scientific Atlanta, Random Vibration Testing:	SA_VibrationTesting.pdf
The Fourier Series of a Rectangular Wave:	fourier_series_rectangular.pdf
The autocorrelation function	autocorrelation.pdf
Kurtosis in Vibration Analysis:	kurtosis.pdf
A Method for Generating White Noise Time Histories with Skewness > 0 and Kurtosis >0 Matlab script: witch.m	white_kurtosis.pdf
See Also Random Vibration Page	-
ZOOM FFT	-
Bruel & Kjaer, Zoom FFT:	zoom_fft.pdf
Zoom FFT of a time series, Matlab:	zoomFFT.m zoomFFT_plot.m
Example tutorial:	zoomFFT_example.pdf
Sample input file:	d9p5.txt
ALIASING	-
Notes on sample rate and aliasing:	aliasing_notes.pdf
The Need for Analog Anti-aliasing Filters in the Pyrotechnic Shock Testing of Avionics Components:	AA_Filter_Pyro.pdf
Signal Identification from Aliased Data: Matlab Scripts sinefind_alias.m & sfa_engine.m	alias_synthesis.pdf
Excel application for demonstrating bit resolution and aliasing effects. This file was submitted by Robert Davis of NASA/Wallops. It may be freely downloaded.	BitResolutionandAliasingG.zip
Ceiling fan, optical aliasing video:	fan_aliased.avi
WEIGHTING FUNCTIONS	-
Bruel & Kjaer, Use of Weighting Functions in DFT/FFT Analysis (Part I):	weight1.pdf
Bruel & Kjaer, Use of Weighting Functions in DFT/FFT Analysis (Part II):	weight2.pdf
Aude, A Tutorial in Coherent and Windowed Sampling with A/D Converters:	AN9675.pdf
Hanning Window Compensation Factor:	Hanning_compensation.pdf
Bingham Window Compensation Factor:	Bingham_compensation.pdf

Filtering Software	Executable	Source
Digital filtering using a Butterworth 6th order filter. The user must supply an input time history file. Both lowpass and highpass options are available.	filter.exe	filter.cpp
Mean filter. This is a type of lowpass filter.	mean_filter.exe	mean_filter.cpp
Median filter. This is a type of lowpass filter. It is useful for noise spike removal.	median_filter.exe	median_filter.cpp
Transfer function magnitude for analog Butterworth and Bessel lowpass filters.	Butterworth_transfer.exe	Butterworth_transfer.cpp
Decimation with filtering.	decimate.exe	decimate.cpp
Decimation with no filtering.	decimate_nf.exe	decimate_nf.cpp
Calculate a PSD via successive bandpass filtering.	filter_psd.exe	filter_psd.cpp
Bessel two-pole lowpass filter	Bessel_lowpass_filter.exe	Bessel_lowpass_filter.cpp

Other Software Programs	Executable	Source
Fast Fourier transform (FFT) of a time history. The transform operates on a time series with 2^n points, where n is an integer. Also, corresponding inverse FFT.	fft.exe invfft.exe	fft.cpp invfft.cpp
Conventional Fourier transform of a time series with an arbitrary number of points. Also, corresponding inverse Fourier transform.	fourier.exe inv_fourier.exe	fourier.cpp inv_fourier.cpp
Zoom FFT of a time series.	zoomFFT.exe	zoomFFT.cpp
This program converts a Fourier transform magnitude with constant bandwidth to an octave or one-third octave format.	FFToct.exe	FFToct.cpp
This program converts a Fourier transform magnitude with constant bandwidth to a wider resolution.	FFT_smooth.exe	FFT_smooth.cpp
Cross-spectrum of two time histories. The output files may be used for modal test data analysis.	cross_spectrum.exe	cross_spectrum.cpp
Cross-spectrum of two time histories. The program generates H1 and H2 frequency response functions (FRFs), the coherence function, and the corresponding impulse response functions.	cross_spectrum_modal.exe	cross_spectrum_modal.cpp
Energy Spectral Density	espec.exe	espec.cpp
Generation of time history signals: 1. sine 2. damped sine 3. sine sweep 4. white noise 5. pink noise	generate.exe	_
Beat frequency time history generation	beat_generate.exe	beat_generate.cpp
Cubic Spline Curve-fit:	spline.exe	spline.cpp
Integrate a time history via the trapezoidal rule.	integ.exe	integ.cpp
This script corrects an acceelration signal so that is corresponding velocity and displacement time histories are stable and oscillate about the zero baseline.	displacement_correction.exe	displacement_correction.cpp
Differentiate a time history.	differ.exe	differ.cpp
Autocorrelation	autocor.exe	autocor.cpp
Cross-correlation	cross_correlation.exe	cross_correlation.cpp
Correlation Coefficient of two time histories	correlation_coefficient.exe	correlation_coefficient.cpp
This program multiplies the Fourier transform of a base input function by the transfer function of a single-degree-of-freedom system.	transfer_fft.exe	transfer_fft.cpp
This program divides a response function by an excitation function. Each function must be in complex format. The functions may be Fourier transforms.	comp_div.exe	comp_div.cpp
This program divides a response function by an excitation function. Each function must be in real format.	real_div.exe	real_div.cpp
This program multiplies a function by another function. Each function must be in real format.	real_mult.exe	real_mult.cpp
This program adds a function to another function. Each function must be in real format.	real_add.exe	real_add.cpp
Convolution integral for two time histories.	convolution.exe	convolution.cpp
This program calculates a response time history from an input time history and a transfer function where the transfer function is a complex Fourier transform. It uses the convolution method.	blast.exe	blast.cpp
Multiply an input Fourier transform by a transfer function.	fourier_mult.exe	fourier_mult.cpp
Signal scaling with adjustment options.	signal.exe	signal.cpp
Multipurpose frequency response function processing.	frequency_function.exe	frequency_function.cpp
Histogram, probability density function, and peak distribution of a time history.	histogram.exe	histogram.cpp
Cumulative RMS of a time history. Used as an alternate tool for shock severity evaluation.	TRMS.exe	TRMS.cpp
Generation of a "white noise" time history.	white.exe	white.cpp
Add white noise to a signal.	add_white.exe	add_white.cpp
Generation of a "white noise" time history with kurtosis control.	white_kurtosis.exe	white_kurtosis.cpp
Aliasing frequency calculator.	aliasing.exe	aliasing.cpp
This program calculates the peak frequency vs. time of a time history, using the Fourier transform method.	freq_peak.exe	freq_peak.cpp
This program calculates the peak frequency vs. time of a time history, using the FFT transform method.	fft_peak.exe	fft_peak.cpp

Dear Guest,

The subscription entitles the user to download all of the items on this page, as well as other Vibrationdata pages.

Thank you for your support.

Sincerely, Tom Irvine Email: tomirvine@aol.com

Fast Fourier Transform: The FFT transform is based on the butterfly algorithm.

Scientific Atlanta, Random Vibration Testing:

Recommend viewing this with RealPlayer with DivX.

This video clip shows an example of optical aliasing. Each of the propellers for the 3 & 4 engines seem to switch rotational direction during start-up because the frame samping rate is too low.

Executable

Median filter. This is a type of lowpass filter. It is useful for noise spike removal.

Transfer function magnitude for analog Butterworth and Bessel lowpass filters.

Decimation with filtering.

Decimation with no filtering.

Calculate a PSD via successive bandpass filtering.

Other Software Programs

Executable

Source

Fast Fourier transform (FFT) of a time history. The transform operates on a time series with 2^n points, where n is an integer.

Also, corresponding inverse FFT.

Conventional Fourier transform of a time series with an arbitrary number of points.

Also, corresponding inverse Fourier transform.

Zoom FFT of a time series.

This program converts a Fourier transform magnitude with constant bandwidth to an octave or one-third octave format.

This program converts a Fourier transform magnitude with constant bandwidth to a wider resolution.

Cross-spectrum of two time histories. The output files may be used for modal test data analysis.

Cross-spectrum of two time histories. The program generates H1 and H2 frequency response functions (FRFs), the coherence function, and the corresponding impulse response functions.

Energy Spectral Density

Generation of time history signals: 1. sine 2. damped sine 3. sine sweep 4. white noise 5. pink noise

Beat frequency time history generation

Cubic Spline Curve-fit:

Integrate a time history via the trapezoidal rule.

Differentiate a time history.

Autocorrelation

Cross-correlation

Correlation Coefficient of two time histories

This program multiplies the Fourier transform of a base input function by the transfer function of a single-degree-of-freedom system.

This program divides a response function by an excitation function. Each function must be in complex format. The functions may be Fourier transforms.

This program divides a response function by an excitation function. Each function must be in real format.

This program multiplies a function by another function. Each function must be in real format.

This program adds a function to another function. Each function must be in real format.

Convolution integral for two time histories.

This program calculates a response time history from an input time history and a transfer function where the transfer function is a complex Fourier transform. It uses the convolution method.

Multiply an input Fourier transform by a transfer function.

Signal scaling with adjustment options.

Multipurpose frequency response function processing.

Histogram, probability density function, and peak distribution of a time history.

Cumulative RMS of a time history. Used as an alternate tool for shock severity evaluation.

Generation of a "white noise" time history.

Add white noise to a signal.

Generation of a "white noise" time history with kurtosis control.

Aliasing frequency calculator.

This program calculates the peak frequency vs. time of a time history, using the Fourier transform method.

This program calculates the peak frequency vs. time of a time history, using the FFT transform method.

Additional software is given at: Matlab & Java

Additional software is given at: Matlab & Java

Book Recommendations

______________________________________________________________________________________________

Please recommend this site by clicking on the Google +1 Button.

Other Vibrationdata Pages: Home | Tutorials

Sincerely, Tom Irvine
Email: tomirvine@aol.com

Generation of time history signals:
1. sine
2. damped sine
3. sine sweep
4. white noise
5. pink noise