I need to decimate a signal by a factor of q.
More specifically my signal is a 3D "image": $\ I(x_i,y_j,z_k)$, which I need to downsample by a factor of two in the z direction.
I want to do lowpass filtering before decimation by convolving with a Gaussian kernel of size n.
I create my Gaussian kernels 2 standard deviations below and above 0 since this accounts for 95 % of the distribution.
I am looking for a rule of thumb that tells me how large n should be.
Am I right in thinking that the Gaussian should filter out all frequencies above fN/q, where fN: Nyquist frequency of original signal?
I know that the Fourier of a Gaussian with standard deviation $\ \sigma $ is another Gaussian with standard deviation $\ \sigma^* =1/\sigma $. I am not sure how strict my lowpass filter should be. Should the cut frequency, fc, be at 2 or 3 standard deviations?
What is then the equation for the cut frequency, fc, of a Gaussian kernel with size n: fc(n)=?
Below is the frequency response of some Gaussian kernels calculated in Matlab:
My actual problem involves q = 2, and from this figure I see that n=5 should work nicely. It would have been good to have a rule of thumb do, so I did not have to do this for each q I encounter.