Calculate the gain and phase response of an FIR digital filter

Calculate the gain and phase response of an FIR digital filter as in below Figure with A₀ = 1, A₁ = 2, A₂ = 3, A₃ = -4, A₄ = 5.

Another way of calculating the frequency response of H(e j ?) is to use a mathematical computer language called "MATLAB". Simply log into MATLAB and type:

A = [1 2 3 -4 5];

freqz( A );

This produces graphs of the gain and phase responses corresponding to H(e^j?) with a frequency scale normalised to half the sampling frequency; i.e. the scale is labelled 0 to 1 instead of 0 to π. In the next topic we will see how to calculate the coefficients (A₀, A₁, A₂, etc.) of an FIR filter to achieve a particular type of gain and phase response.

To calculate the gain and phase responses for the digital IIR filter as shown in above Figure would be difficult (though not impossible) by the method used above because the impulse response has an infinite number of non-zero terms.