For the following:f1=2.05e3;fs=62e3;Ts=1/fs;tlen=.4;t=0:Ts:tlen-Ts;N=length(t);x=sin(2*pi*f1*t);standev=1;noise=randn(1,N)*standev;xn=x+noise;fcf=858;Omegacf=2*pi*fcf/fs;fo=f1;Omegao=2*pi*fo/fs;M=1001;n=(0:M-1)-floor(M/2);h=Omegacf/pi*sinc(n*Omegacf/pi);w=hamming(M)';A=1;B=h.*w.*cos(n*Omegao);y=filter(B,A,xn);subplot(2,1,1)plot(t,x,'LineWidth',3);hold onplot(t,xn,'LineWidth',1);plot(t,y,'g','LineWidth',2);axis([1/f1*100 1/f1*110 -4 4]);xlabel('time,s');ylabel('amplitude, arbitrary units');legend('original signal','with noise','filtered');hold offX=fft(x);Xn=fft(xn);Y=fft(y);subplot(2,1,2)fbin=fs/N;f=0:fbin:fs-fbin;plot(f,20*log10(abs(X)),'LineWidth',3);hold onplot(f,20*log10(abs(Xn)),'LineWidth',1);plot(f,20*log10(abs(Y)),'g','LineWidth',2);xlabel('frequency, Hz');ylabel('magnitude response, dB');legend('noisy signal spectrum','filtered spectrum')axis([1e2 fs/2 -40 100])hold offWhat band of frequencies will this filter keep?
Question
For the following:f1=2.05e3;fs=62e3;Ts=1/fs;tlen=.4;t=0:Ts:tlen-Ts;N=length(t);x=sin(2pif1t);standev=1;noise=randn(1,N)standev;xn=x+noise;fcf=858;Omegacf=2pifcf/fs;fo=f1;Omegao=2pifo/fs;M=1001;n=(0:M-1)-floor(M/2);h=Omegacf/pisinc(nOmegacf/pi);w=hamming(M)';A=1;B=h.w.cos(nOmegao);y=filter(B,A,xn);subplot(2,1,1)plot(t,x,'LineWidth',3);hold onplot(t,xn,'LineWidth',1);plot(t,y,'g','LineWidth',2);axis([1/f1100 1/f1110 -4 4]);xlabel('time,s');ylabel('amplitude, arbitrary units');legend('original signal','with noise','filtered');hold offX=fft(x);Xn=fft(xn);Y=fft(y);subplot(2,1,2)fbin=fs/N;f=0:fbin:fs-fbin;plot(f,20log10(abs(X)),'LineWidth',3);hold onplot(f,20log10(abs(Xn)),'LineWidth',1);plot(f,20log10(abs(Y)),'g','LineWidth',2);xlabel('frequency, Hz');ylabel('magnitude response, dB');legend('noisy signal spectrum','filtered spectrum')axis([1e2 fs/2 -40 100])hold offWhat band of frequencies will this filter keep?
Solution
The band of frequencies that this filter will keep is centered around the cutoff frequency 'fcf' which is 858 Hz. The filter is a bandpass filter designed to allow frequencies in the vicinity of 'fcf' to pass through while attenuating frequencies that are significantly higher or lower. The exact range of frequencies that will be kept depends on the specific design of the filter, including the shape and width of the passband and stopband. However, the code does not provide enough information to determine the exact range of frequencies.
Similar Questions
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Hint: Create your own frequency table and use the formula from the reference sheet!
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