Design of a low pass FIR filter to remove the white noise that has corrupted the message received
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Added on 2021-11-19
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MR=load('MessageReceived.mat'); testData=MR.UNKNOWNSIGNAL(); Msig=abs(testData); t=1:length(Msig); figure(1) plot(Msig) grid on title('Corrupted Received Message y(n)') %Designing the Low Pass filter for FIR Mb=fir1(42,fc,chebwin(43,30) figure(2) freqz(Mb,1,Mb;length(
Design of a low pass FIR filter to remove the white noise that has corrupted the message received
Added on 2021-11-19
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DIGITAL SIGNAL PROCESSING NEE3208 SIGNAL PROCESSING ASSIGNMENT 3 STUDENT NAME STUDENT ID NUMBER INSTRUCTOR (PROFESSOR/TUTOR) DATE OF SUBMISSION
TASK Design of a low pass FIR filter to remove the white noise that has corrupted the message received. The FIR filter is of the form, y(n)=∑i=0 M−1 h(i)x(n−i) Part 1 Designing the kernel filter h(n) by defining its impulse response. The non-recursive finite impulse response is given as, y(n)=h(0)x(n)+h(1)x(n−1)+...+h(N)x(n−N) N−orderofthefilter For a finite duration, the impulse response is given as, To obtain the ideal low pass filter, csin1()sinc2 c c cjnc d nhnAedAAnn csin1()sinc2 c c cjnc d nhnAedAAnn
For windowing, hw(n)=hd(n)w(n) ¿1 2πHd(ω)∗W(ω) The impulse response of the FIR filter, following the Hamming window, is, therefore, given as, h[n]=sin(ωc(n−L)) π(n−L)w[n] Part 2 Evaluate the transfer function using DFT. Magnitude of the transfer functions. Hd(ω)=DTFT{hd(n)}=∑n=−∞ +∞ hd(n)e−jωn Part iii Apply the filter in the frequency domain to X(k). Obtaining the inverse DFT to get filtered signal and determining the cut-off frequency hd(n)=IDTFT{Hd(ω)} ¿1 2π−ωc +ωc Ae−jωndω ¿A(sin(ωcn) πn) ¿A(ωc π)sinc(ωc πn) Part iv Applying the filter in the time domain to obtain the filtered signal y(n)
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