Frequency Characteristics of Convolution Filters
Convolution maps to multiplication in the Fourier co-domain. The discrete Fourier transform of a convolution filter is a real-valued function which can be represented as
z run from 0 to π radians, after which the function merely repeats itself. FT(0)=1. This shows that the convolution filter can be described as a low-pass filter: the noise that is removed is primarily high-frequency noise and low-frequency noise passes through the filter.
Read more about this topic: Numerical Smoothing And Differentiation
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