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
Famous quotes containing the words frequency and/or filters:
“One is apt to be discouraged by the frequency with which Mr. Hardy has persuaded himself that a macabre subject is a poem in itself; that, if there be enough of death and the tomb in ones theme, it needs no translation into art, the bold statement of it being sufficient.”
—Rebecca West (18921983)
“Raise a million filters and the rain will not be clean, until the longing for it be refined in deep confession. And still we hear, If only this nation had a soul, or, Let us change the way we trade, or, Let us be proud of our region.”
—Leonard Cohen (b. 1934)