Solution 1 a) As per the theory the filtering will be ok here as we can easily remove overlapping noise through filter processing. In case if we apply filtering then two popular filtering method of adaptive nature, namely noise cancellation in adaptivemanner and signal enhancement in adaptive manner, are perfect techniques for processing this. b)Now we can have Design: Transfer function of filter is: H(z)=Y(z) X(z)= ∑ k=0 M bkz−k 1+∑ k=0 N akz−k So here M is the fir filter length. Order of filter is given by N=M-1. Response of filter is y(n)=∑ k=0 M−1 bkx(n−k) y(n)=∑ k=0 M−1 h(k)x(n−k) Coefficients: Without Window b =0.01690.25280.56670.25280.0169
Rectangular Window b =0.01690.25280.56670.25280.0169 At 95% unity**, the poles are: p1,2=.95[.5878±j.8090 p1,2=.5584±j.7686 H(z)=(z−.5878+j.8090)(z−.5878−j.8090) (z−.5584+j.7686)(z−.5584−j.7686) With the reduced canonical form: H(z)=1−1.175z−1+z−2 1−1.117z−1+.903z−2 The recursive algorithm becomes: yn=xn−1.175xn−1+xn−2+1.117yn−1−.903yn−2 Output: Without Window
Rectangular Window
c) Zeroes of the functions are: z1,2=cos(54°)±jsin(54°) z1,2=.5878±j.8090
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