[music-dsp] Gaussian FIR filter

[Massimiliano Tonelli]

Dear All

Is there any expression to calculate the variance 'alfa' of a Gaussian
filter, given a desired 3dB frequency cut off?
I am considering a filter  with an  impulse response of the kind:

h(t)=exp(-(alfa/2)*t^2)

or in discrete form

h(n)=exp(-(alfa/2)*(n/Fs)^2)

where Fs is the sampling frequency

Low pass Gaussian shape filters are very common in image processing. Usually
the smoothing factor is controlled by the variance parameter (where the
variance controls, as usual, the bell amplitude).
Actually I wanted to use a Gaussian filter for 1-D signal processing. In
this case, it would be much more comfortable to control the filter
characteristic by its -3dB cut-off as it is usually done for many other
filters.
There is also a Matlab implementation of Gaussian filters (FIRGAUSS) but
also there, the cut-off is controlled by the variance.

Any help will be appreciated.

Best regards
Massimiliano Tonelli