Question

Algorithm

1. Enter the pass band ripple (rp) and stop band ripple (rs).
2. Enter the pass band frequency (wp) and stop band frequency (ws).
3. Get the sampling frequency (fs).
4. Calculate normalized pass band frequency, and normalized stop band frequency w1 and w2 respectively.           

w1 = 2 * wp /fs            

w2 = 2 * ws /fs

5. Make use of the following function to calculate order of filter

Butterworth filter order                       

[n,wn]=buttord(w1,w2,rp,rs)

6. Design an n^th order digital lowpass Butterworth filter using the following statements. Butterworth filter [b, a]=butter (n, wn)

OR

Design an n^th order digital high pass Butterworth filter using the following statement. Butterworth filter [b,a]=butter (n, wn,’high’)

7. Find the digital frequency response of the filter by using ‘freqz( )’ function

[H,w]=freqz(b,a,512,fs)

8. Calculate the magnitude of the frequency response in decibels (dB)

mag=20*log10 (abs (H))

9. Plot the magnitude response [magnitude in dBversus normalized frequency (Hz)]
10. Calculate the phase response using an = angle (H)
11. Plot the phase response [phase in radians Vs normalized frequency (Hz)]

Program

Output

Answer 1