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EXP9

The document describes designing a Butterworth filter to meet specifications of 1 dB ripple in the pass band from 0 to pi radians and at least 40 dB attenuation in the stop band from 0.8pi to pi radians. It provides the theory of Butterworth filters, which have a maximally flat pass band and roll off at 20 dB per decade in the stop band. Code is then provided to design a digital Butterworth filter to meet the given specifications.

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Anisha Agarwal
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29 views2 pages

EXP9

The document describes designing a Butterworth filter to meet specifications of 1 dB ripple in the pass band from 0 to pi radians and at least 40 dB attenuation in the stop band from 0.8pi to pi radians. It provides the theory of Butterworth filters, which have a maximally flat pass band and roll off at 20 dB per decade in the stop band. Code is then provided to design a digital Butterworth filter to meet the given specifications.

Uploaded by

Anisha Agarwal
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
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Download as DOCX, PDF, TXT or read online on Scribd
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EXP9: Design a butterworth filter that meets the following specifications:

a) 1 dB ripple in pass band 0<=w<=pi


b) Atleast 40 dB attenuation in stop band08.pi<=w<=pi

THEORY:
The frequency response of the Butterworth Filter approximation function is
also often referred to as “maximally flat” (no ripples) response because the
pass band is designed to have a frequency response which is as flat as
mathematically possible from 0Hz (DC) until the cut-off frequency at -3dB with
no ripples. Higher frequencies beyond the cut-off point rolls-off down to zero
in the stop band at 20dB/decade or 6dB/octave. This is because it has a
“quality factor”, “Q” of just 0.707.
However, one main disadvantage of the Butterworth filter is that it achieves
this pass band flatness at the expense of a wide transition band as the filter
changes from the pass band to the stop band. It also has poor phase
characteristics as well.

CODE:
clc; clear all;
T=1; wp=0.3*pi; ws=0.8*pi;
Ap=1; As=40;
Wp=(2/T)*tan(wp/2); %analog pass band edge freq
Ws=(2/T)*tan(ws/2); %analog stop band edge freq
R=(10^(0.1*Ap)-10)/(10^(0.1*As)-1);
N=ceil((1/2)*(log10(R)/log10(Wp/Ws)));
Wc=Wp/((10^(0.1*Ap)-1)^(1/(2*N)));
[b,a]=butter(N,Wc,'low','s');
Hs=tf(b,a);
[numd,dend]=bilinear(b,a,1/T);
Hz=tf(numd,dend,T);
w=0:0.01:pi;
Hw=freqz(numd,dend,w);
subplot(121);
plot(w,abs(Hw));
xlabel('frequency');
ylabel('magnitude');
subplot(122);
plot(w,20*log10(abs(Hw)));
xlabel('frequency');
ylabel('Magnitude(db)');
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