Design an FIR filter to eliminate a high range of frequencie

Design an FIR filter to eliminate a high range of frequencies: Sampling rate = 25000 Hz Range of frequencies to be passed = 0 - 3500 Hz Stop band = 4500 - 20000 Hz Hamming window design Verify the frequency response using MATLAB. Paste a copy of your code and snapshot of your plot to support your calculations.

Solution

M=63; Wp=0.5*pi;%the number of samples and the passband cutoff frequency

m=0:(M+1)/2; Wm=2*pi*m./(M+1);%the sampling points and the stopband cutoff frequency

mtr=floor(Wp*(M+1)/(2*pi))+2;%round to negative part,i.e.floor(3.5)=3;floor(-3.2)=-4

Ad=[Wm<=Wp];Ad(mtr)=0.38;

Hd=Ad.*exp(-j*0.5*M*Wm);%define frequency-domain sampling vector H(k)

Hd=[Hd conj(fliplr(Hd(2:(M+1)/2)))];

%fliplr is to realize the fliplr of matrix and conj

h=real(ifft(Hd));% h(n)=IDFT[H(k)

w=linspace(0,pi,1000);%get 1000 row vectors between 0 and pi

H=freqz(h,[1],w);%the amplitude -frequency characteristic diagram of the filter

figure(1)

plot(w/pi,20*log10(abs(H)));%parameters are respectively the normalized frequency and amplitude

xlabel(\'the normailzed frequency\');ylabel(\'gian/dB\');title(\'The gain response of lowpass filter\');

axis([0 1 -50 0.5]);

f1=100;f2=300;f3=700;fs=2000;%the frequencies of sines signal that needs filtered and the sample frequency

figure(2) 38

subplot(211)

t=0:1/fs:0.25;%define the time domain and steplength

s=sin(2*pi*f1*t)+sin(2*pi*f2*t)+sin(2*pi*f3*t);%signal before filtering

plot(t,s);%plot the diagram before filtering

xlabel(\'time/s\');ylabel(\'amplitude\');title(\'Time-domain diagram before filtering\');

subplot(212)

Fs=fft(s,512); AFs=abs(Fs);%transform to the frequency domain

f=(0:255)*fs/512;%frequency sampling

plot(f,AFs(1:256));%plot the frequency domain diagram before filtering

xlabel(\'frequency/Hz\');ylabel(\'amplitude\');title(\'Frequency-domain diagram before filtering\');

figure(3)

sf=filter(h,1,s);%use function filter

subplot(211)

plot(t,sf)%plot the diagram after filtering

xlabel(\'time/s\');ylabel(\'amplitude\');title(\'Time-domain diagram after filtering\')

axis([0.2 0.25 -2 2]);%set the range of image coordinates

subplot(212)

Fsf=fft(sf,512); AFsf=abs(Fsf);%frequency-domain and the amplitude diagram

f=(0:255)*fs/512;%frequency sampling

plot(f,AFsf(1:256))%plot the frequency domain diagram before filtering

xlabel(\'frequency/Hz\');ylabel(\'amplitude\');title(\'Frequency-domain diagram after filtering\');

(2) Design a highpass filter using frequency sampling method

M=32;%the number of samples

Wp=0.6*pi;%passband cutoff frequency

m=0:M/2;%the sampling points

Wm=2*pi*m./(M+1);%stopband cutoff frequency

mtr=ceil(Wp*(M+1)/(2*pi));%round to positive part,i.e.ceil(3.5)=4;ceil(-3.2)=-3;

Ad=[Wm>=Wp];

Ad(mtr)=0.28;

Hd=Ad.*exp(-j*0.5*M*Wm);%define frequency-domain sampling vector H(k))

Hd=[Hd conj(fliplr(Hd(2:M/2+1)))];

%fliplr is to realize the fliplr of matrix and conj is the conjugate

h=real(ifft(Hd));%h(n)=IDFT[H(k)]

w=linspace(0,pi,1000);%get 1000 row vectors between 0 and pi 39

H=freqz(h,[1],w);%the amplitude -frequency characteristic diagram of the filter

figure(1)

plot(w/pi,20*log10(abs(H)));%parameters are respectively the noemalized frequency and amplitude

xlabel(\'the normailzed frequency\');ylabel(\'gian/dB\');title(\'The gain response of highpass filter\');

axis([0 1 -50 0]);

f1=200;f2=700;f3=800;%the frequencies of sines signal that needs filtered

fs=2000;%the sample frequency

figure(2)

subplot(211)

t=0:1/fs:0.25;%define the time domain and steplength

s=sin(2*pi*f1*t)+sin(2*pi*f2*t)+sin(2*pi*f3*t);%signal before filtering

plot(t,s);%plot the diagram before filtering

xlabel(\'time/s\');ylabel(\'amplitude\');title(\'Time-domain diagram before filtering\');

subplot(212)

Fs=fft(s,512);%transform to the frequency domain

AFs=abs(Fs);%the amplitude

f=(0:255)*fs/512;%frequency sampling

plot(f,AFs(1:256));%plot the frequency domain diagram before filtering

xlabel(\'frequency/Hz\');ylabel(\'amplitude\');title(\'Frequency-domain diagram before filtering\');

figure(3)

sf=filter(h,1,s);%use function filter

subplot(211)

plot(t,sf)%plot the diagram after filtering

xlabel(\'time/s\');ylabel(\'amplitude\');title(\'Time-domain diagram after filtering\')

axis([0.2 0.25 -2 2]);%set the range of image coordinates

subplot(212)

Fsf=fft(sf,512);AFsf=abs(Fsf);

f=(0:255)*fs/512;%frequency sampling

plot(f,AFsf(1:256))%plot the frequency domain diagram before filtering

xlabel(\'frequency/Hz\');ylabel(\'amplitude\');title(\'Frequency-domain diagram after filtering\');