(1) Using FFT method to design a 21 tap (coefficient) high-pass FIR filter with a cut-off frequency at 125 Hz. Explain y

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(1) Using FFT method to design a 21 tap (coefficient) high-passFIR filter with a cut-off frequency at 125 Hz. Explain your designprocedure. Show by giving the frequency response that your filteris working as designed or close to it.
(2) Design an IIR filter with 4 poles and 4 zeros. Use the samedesign specification as that of Question 2(1). Outline the designprocedure. Produce MATLAB code to give results which prove thatyour filter is working as designed or close to it. Draw the z-planeplot for your filter and discuss how it relates to the frequencyresponse.
(3) Write a short essay up to 500 words to further extend themethod you used in Question 2 (1) to the design of FIR filter withan arbitrarily defined magnitude-frequency response compare.