A very simple question which can't really figure out:
I have a simple discrete time rectangular integrator with Z transform H(z) = 1/(1-Z^(-1))
Plotting the frequency response with Matlab using freqz shows what it looks like a kind of low pass filter response.
However, when finding the freq response by sending an delta pulse through the integrator via filter Matlab function, and performing the FFT on its output, I just get a pulse (with amplitude equal to number of FFT points) followed of zeroes.
I guess this kind of makes sense mathematically, as the output of the integrator is a step function, which, after FFT, is the addition of as many samples of the step output as the FFT length.
Why does the freqz method does not match the impulse response + FFT approach?
Am I wrong in trying to look at an integrator as a digital filter?
Thanks a mill
PD: I forgot to mention that this is the closest to this question I could find on the site... However it is a leaky integrator not a rectangular (i.e. feedback multiplier is 1) integrator