Design of FIR using Frequency Sampling Method

The frequency sampling method allows us to design recursive and nonrecursive FIR filters for both standard frequency selective and filters with arbitrary frequency response. The frequency response of LPF and HPF are plotted using frequency sampling method. Ripples in the stopband are obtained by decreasing amplitude. The phase plot is linear and similar for both LPF and HPF if order of the two filters is same. Since phase is linear, output is not distorted.

In this the desired frequency response Hd(w) is sampled at w=(2*pi*k)/N and the frequency samples thus obtained are taken as DFT coefficients. FIR filter with impulse response is then calculated by IDFT.

Thus, for the same values of attenuation in stop band and pass band, pass band and stop band frequencies and sampling frequencies we observe that the order of the FIR filter is much higher compared to that of the IIR filter.