The moving average filter is a crude, but common, technique for smoothing a noisy data sequence. For an input signal vector, x[n], it operates by averaging the sequence over N+1 samples such that the output, y[n], is computed as the average of x[n] and the N preceding samples x[n – 1], x[n – 2], ..., x[n – N], which may be described as: N 1 y[n] = E«[n – k] N +1 k=0 (a) Determine the corresponding impulse response, h[n], of this system (b) Determine the system function, H(z), for this system (c) Determine the zero and/or pole locations for H(z)

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The moving average filter is a crude, but common, technique for smoothing a noisy data
sequence. For an input signal vector, x[n], it operates by averaging the sequence over N+1
samples such that the output, y[n], is computed as the average of x[n] and the N preceding
samples x[n – 1], x[n – 2], ..., x[n – N], which may be described as:
N
1
y/n] :
E r[n – k]
N +1
k=0
(a) Determine the corresponding impulse response, h[n], of this system
(b) Determine the system function, H(2), for this system
(c) Determine the zero and/or pole locations for H(z)
Transcribed Image Text:The moving average filter is a crude, but common, technique for smoothing a noisy data sequence. For an input signal vector, x[n], it operates by averaging the sequence over N+1 samples such that the output, y[n], is computed as the average of x[n] and the N preceding samples x[n – 1], x[n – 2], ..., x[n – N], which may be described as: N 1 y/n] : E r[n – k] N +1 k=0 (a) Determine the corresponding impulse response, h[n], of this system (b) Determine the system function, H(2), for this system (c) Determine the zero and/or pole locations for H(z)
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