FIR FILTER DESIGN

Assignment 05

(Part A) Design with frequency sampling

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There two methods for FIR Design

• (A) Design with frequency sampling

• (B) Design with window functions

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FIR filter design

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Types of Linear phase filters

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The main lobe as narrow as possible.

The problem is not the height of the side lobes. The matter is

how you accumulate the area as you integrate through it.

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Design FIR (Type I)

wo=0.3*pi; % Passband edge

len=23; % Length of filter

pass_len=fix(wo*len/(2*pi))+1; % Passband

length

Ad=[ones(1,pass_len),zeros(1,len-

2*pass_len+1),ones(1,pass_len-1)];

stem((1:len)/len,Ad);

xlabel('normalized frequency');

ylabel('Amplitude');

title('ideal filter')

M=(len-1)/2; % Type 1

k=0:(len-1);

pd=exp(2*pi*j*(-M)*k/len);

Hd=Ad.*pd;

h=real(ifft(Hd));

h2=imag(ifft(Hd));

figure; stem(h);hold on;

stem(h2, 'r');

legend('real','imaginary'); xlabel(‘n');

Illustration of (a) &(b)

n Shifted by M

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cont

[resp,omeg]=freqz(h);

figure;

subplot(211);plot(omeg,abs(resp));grid;

title('Magnitude Response');

subplot(212); plot(omeg,angle(resp), 'r.-');

hold on;

plot(omeg,unwrap(angle(resp))); title('Phase

Response');

hold

off;legend('wraped','unwraped','location','be

st')

figure;

plot(omeg,abs(resp)); title('Magnitude

Response');

hold on; plot(omeg,unwrap(angle(resp))/10,

'k'); title('Phase Response');

M=11

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F) Now design an even length filter of length 22, using the same approach as in a). Find the resulting impulse response h[n], and the magnitude

and phase frequency response of this filter h[n]. Note that an symmetric even-length linear-phase FIR filter always have a zero at (type 2 or 4)

Type IV

Ad=[ones(1,pass_len),zeros(1,len-2*pass_len+1),-1*ones(1,pass_len-1)]; % Must use negative type4!!!

The ideal Filter:

h=real(ifft(Hd))+1i.*imag(ifft(Hd));

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Now Follow these steps to complete all the assignment

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FIR FILTER DESIGN

Assignment 05

(Part B) Design with window functions

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h) Design a length-23 linear-phase FIR low-pass filter with a passband edge of .

radians/sample using a window approach. Do not use a frequency sampling technique as in

a). Use the windowing approach with the following windows: rectangular, Hanning,

Hamming and Kaiser with Find the frequency response of the resulting filters,

and compare with the filter found in a).

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6

b1=fir1(len,wn,rectwin(N+1)); b2=fir1(len,wn,hann(N+1));

b3=fir1(len,wn,hamming(N+1)); b4=fir1(len,wn,kaiser(N+1,beta));

The cut-off frequency “wn” must be

normalized between 0 < Wn < 1.0,

0 5 10 15 20 25-0.1

-0.05

0

0.05

0.1

0.15

0.2

0.25

0.3

Am

plit

ude

n samples

Windowed Coeffecients

rectangular

Hanning

Hamming

Kaiser

0 0.5 1 1.5 2 2.5 3 3.5-140

-120

-100

-80

-60

-40

-20

0

20

dB

rad/sec

Magnitude response

rectangular

Hanning

Hamming

Kaiser

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remez has been changed with firpm

(i) Design a length-23 linear-phase FIR low-pass filter with a passband edge of

radians/sample and a stopband edge of radians/sample, using the

remez Matlab function (you can also use the remezord function). What is the

particular characteristic of the magnitude of the filter frequency response ? How

does the frequency response compare with the responses from b) and h) ?

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Hint: see this example.https://www.mathworks.com/help/signal/ug/fir-filter-design.html

>>b = firpm(N,f,a)f: is a vector of pairs of normalized frequency points, specified in the range between 0 and 1

a: is a vector containing the desired amplitudes at the points specified in f

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j) Transform one of the low-pass filters that you have designed in this assignment

to a band-pass filter. Hint : use the frequency shifting property or the modulation

property of the Fourier transform.

[ ] [ ]. jn

BPb n b n e use: = /2

Modulation of filters

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[ ];p sdev

[n,fo,ao,w] = firpmord(f, a, dev, fs);

f = [fp fc];a = [1 0];

Compute FIR Order

b = firpm(n,fo,ao,w);

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Finish the lab and submit your report

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