A band pass FIR filter is required to pass frequencies from 5KHz to 8KHz, using a sample rate of 40K

i) Explain how this would map to normalization sampling frequencies in radians per sample, Include a diagram shown the passband, stop band and other areas of interest

ii) Derive a mathematical expression for the filter coefficients

iii) Write a MATLAB script to calculate the frequency response of the filter and briefly explain how it works.