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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
Design of a low pass FIR filter to remove the white noise that has corrupted the message received_1
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 (ni )
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 (n1)+...+h (N )x (nN )
N order of the filter
For a finite duration, the impulse response is given as,
To obtain the ideal low pass filter,
csin1( ) sinc2
c
c
cj n c
d
nh n Ae d A A nn






csin1( ) sinc2
c
c
cj n c
d
nh n Ae d A A nn







Design of a low pass FIR filter to remove the white noise that has corrupted the message received_2
For windowing,
hw (n)=hd (n )w (n)
¿1
2 π H d (ω)W (ω)
The impulse response of the FIR filter, following the Hamming window, is, therefore, given as,
h [n]=sin (ωc (nL ))
π (nL)w [n ]
Part 2
Evaluate the transfer function using DFT. Magnitude of the transfer functions.
H d (ω )=DTFT {hd (n )}=n=
+
hd (n )ejωn
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 {H d (ω )}
¿1
2 π ωc
+ωc
A ejωn
¿A(sin (ωc n )
πn )
¿A(ωc
π )sinc (ωc
π n)
Part iv
Applying the filter in the time domain to obtain the filtered signal y(n)
Design of a low pass FIR filter to remove the white noise that has corrupted the message received_3

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