Using the smallest possible number of z-plane poles and zeros, design a digital filter with the following parameters: (i) Complete frequency rejection at Q2 = 0 radians, (ii) Complete frequency rejection at = /4 radians, (iii) A narrow frequency passband at 2 = 2/3 radians with poles at r = 0.9, (iv) No delay in the output y[n]. Find the Z-Transform of the filter H(z) and also the difference equation describing this filter, y[n] = f(x[n]).
Using the smallest possible number of z-plane poles and zeros, design a digital filter with the following parameters: (i) Complete frequency rejection at Q2 = 0 radians, (ii) Complete frequency rejection at = /4 radians, (iii) A narrow frequency passband at 2 = 2/3 radians with poles at r = 0.9, (iv) No delay in the output y[n]. Find the Z-Transform of the filter H(z) and also the difference equation describing this filter, y[n] = f(x[n]).
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Please answer all parts of this digital signal processing question accurately and in great detail.
![Using the smallest possible number of z-plane poles and zeros, design a
digital filter with the following parameters:
Complete frequency rejection at 2 = 0 radians,
Complete frequency rejection at Q2 = π/4 radians,
A narrow frequency passband at 2 = 2/3 radians with poles at r =
0.9,
(iv) No delay in the output y[n].
(i)
(ii)
(iii)
Find the Z-Transform of the filter H(z) and also the difference equation
describing this filter, y[n] = f(x[n]).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F59091a48-954d-47f5-a3a3-685495100fb0%2F2b8c0a6a-c60d-481c-af7b-50fbc85fa23f%2F0arqfol_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Using the smallest possible number of z-plane poles and zeros, design a
digital filter with the following parameters:
Complete frequency rejection at 2 = 0 radians,
Complete frequency rejection at Q2 = π/4 radians,
A narrow frequency passband at 2 = 2/3 radians with poles at r =
0.9,
(iv) No delay in the output y[n].
(i)
(ii)
(iii)
Find the Z-Transform of the filter H(z) and also the difference equation
describing this filter, y[n] = f(x[n]).
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