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Convolution

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How to smooth data with convolution
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In linear systems convolution is used to describe the relationship between three signals of interest:
 the input signal Y[i],
 the impulse response F[i] (filter kernel),
 the output signal W[i].
Convolution is defined by the convolution sum: Convolution formula Smooth data with convolution

FindGraph includes several filter kernels F(u):
 Common filter kernels (Delta function, Amplification, Attenuation, Inverting, Shift, Echo, First derivative, Integral).
 Low-pass filter kernels to provide an averaging (smoothing) of the signal (exponential, rectangular, Gauss function, sinc function with Hamming or with Blackman windows).
 High-pass filter kernels.

You can draw your own signal or to modify a selected signal. Simple click on left chart and use the mouse to draw your own signal.

Select filter kernel

Useful link: The Scientist and Engineer's Guide to Digital Signal Processing by Steven W. Smith, Ph.D.

Read more about:

Digitizing Digitizing
Graphing Graphing
Curve fitting Curve fitting
Linear regression Linear regression
Best-fit Best-fit equation
Closed curves Closed curves
Rationals Empirical models
Library Library
Analysis Analysis
Filters Filters
Extract of periodic signals Periodic signals
Procrustes analysis Procrustes analysis
Multi-peak fitting Multi-peak fitting
SSA forecasting SSA forecasting

 

 

 

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