Gaussian filter is commonly used in image processing, and in Matlab it is by: h = fspecial('gaussian', hsize, sigma), where the values of sigma and hsize need to be determined by the user. For a low-pass filter, the direct parameter is the cut-off frequency, then, my questions are: for a given normailzed cut-off frequency value, how to determine the sigma, the sampling range, and the sampling interval value (and thus the length/size).
There are related questions, such as
https://stackoverflow.com/questions/16165666/how-to-determine-the-window-size-of-a-gaussian-filter
https://stackoverflow.com/questions/2773606/gaussian-filter-in-matlab
https://stackoverflow.com/questions/23832852/by-which-measures-should-i-set-the-size-of-my-gaussian-filter-in-matlab
https://stackoverflow.com/questions/23832852/by-which-measures-should-i-set-the-size-of-my-gaussian-filter-in-matlab
https://stackoverflow.com/questions/2773606/gaussian-filter-in-matlab
https://stackoverflow.com/questions/16165666/how-to-determine-the-window-size-of-a-gaussian-filter
The cut-off frequency of the Gaussian filter is proportional to the standard deviation of the filter in the frequency domain: https://en.wikipedia.org/wiki/Gaussian_filter
The Gaussian filter impulse response is expressed by the relation in space domain:
h(x)= (1/sqroot 2 sigma) exp - (x^2/2 sigma^2),
and its frequency response is H(f) is expressed by
H(f)= exp^- (f^2/2 sigmaf^2)
and sigma* sigmaf = 1/2 pi,
The cut off frequency is considered= sigmaf, then one can determine sigma from the last equation. The range of the filter is from -sigma to +sigma in the space x,
The range is equal to double the standard deviation. Then it remains to determine the sampling frequency where h(x) must be sampled with a sampling frequency fs which must be greater than 2 the cut off frequency sigmaf. Say we choose the sampling frequency N times sigmaf, Then the the sampling interval xs=delta x sampling= 1/(N sigmaf),
The order of the filter which is the number of taps in it= 2sgma/ xs= 2 sigma* Nsigmaf= 2N/2pi
Best wishes
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