Welcome to Vibrationdata
Signal Processing, Filtering, & Fourier Transform Page

TUTORIALS An Introduction to Digital Filtering: filter.pdf This tutorial focuses on the Butterworth filter. 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: fft.pdf   The FFT transform is based on the butterfly algorithm. Shock and Vibration Signal Analysis: Shock_and_Vibration_Signal_Analysis.pdf Power Spectral Density Calculation via Matlab: psd_mat.pdf Guest tutorial submitted by Bob Light. 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 Kurtosis in Vibration Analysis: kurtosis.pdf See Also Random Vibration Page

WINDOWS & 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

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: alias_synthesis.pdf Matlab Scripts: sinefind_alias.m & sfa_engine.m 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 Starting Engines 3&4 and taxiing of EAA's B-17 Aluminum Overcast 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.

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
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
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