For the following: f1=1.7e3; fs=38e3; 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=720; 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 on plot(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 off X=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 on plot(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 off What band of frequencies will this filter keep? Minimum frequency = Answer field 1 kHz. Maximum frequency = Answer field 2 kHz.
Question
For the following:
f1=1.7e3; fs=38e3; 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=720; 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 on plot(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 off X=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 on plot(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 off
What band of frequencies will this filter keep?
Minimum frequency = Answer field 1 kHz.
Maximum frequency = Answer field 2 kHz.
Solution
The filter will keep a band of frequencies from 720 kHz to 1700 kHz.
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