Question

Design lowpass IIR filter with the following specifications: Filter order = 2, Butterworth type Cut-off frequency=800 Hz Sampling rate =8000 Hz Design using the bilinear z-transform design method

Print the lowpass IIR filter coefficients and plot the frequency responses using MATLAB. MATLAB>>freqz(bLP,aLP,512,8000); axis([0 4000 –40 1]);

Label and print your graph. What is the filter gain at the cut-off frequency 800 Hz? What are the filter gains for the stopband at 2000 Hz and the passband at 50 Hz based on the plot of the magnitude frequency response?

Answer 1

clc;clear all;
Fs = 8000;
atmax =3;
wp =800*2*pi;
Wp=2*atan(wp/2);
N=2;
Whp=Wp/((10^(.1*atmax)-1)^(1/(2*N)));
whp=2*atan(Whp/2);
wn=whp/pi;
[b,a]=butter(N,wn);
[H,w]=freqz(b,a,512);
fq=Fs*w/(2*pi);
mag=abs(H);
plot(fq,mag)
ylabel('Amplitude');
xlabel('Frequency [Hz]'); grid

filter coefficients:

a =

1.0000 0.5169 0.2192

>> b

b =

0.4340 0.8681 0.4340

File Edit View Insert Tools Debug Desktop Window Help 田卬日タD Figure 1 0.9 0.7 0.6 0.4 0.3 1.1 500 1000 1500 2000 Frequency [Hz] 2500 3000 3500 4000 Property Editor | 18:52 빚4 @..d 25-04.2019