In section 8 2, we stated the property that if x 1 n x n m , then X 1 k W km N X k Where X k and X 1 k are the DFS coefficients of x n and x 1 n , respectively In this problem, we consider the proof of that property (a) Using Eq (8 11) together with an appropriate substitution of variables, show th...

a b c We know from Eq 811 th ...

In section 8.2, we stated the property that if? x 1 [n] = x[n ? m], ?then?

Question:

In section 8.2, we stated the property that if?

x₁[n] = x[n ? m],

?then?

X₁[k] = W^km_N X[k].

Where X[k] and X₁[k] are the DFS coefficients of x[n] and x₁[n], respectively. In this problem, we consider the proof of that property. ??

(a) Using Eq (8.11) together with an appropriate substitution of variables, show that X₁[k] can be expressed as?

(b) The summation in Eq. (p8.52-1) can be rewritten as, using the fact that x[r] and W^kr_N are both periodic, show that

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Discrete Time Signal Processing

ISBN: 978-0137549207

2nd Edition

Authors: Alan V. Oppenheim, Rolan W. Schafer

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Question Posted: May 26, 2011 02:57 AM

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In section 8.2, we stated the property that if? x 1 [n] = x[n ? m], ?then?

Question:

N-1 χμ-Σn] W". (8.11) n=0 Part a N-1-m Χ( (]- W" Σj W. (P8.52-1) Τ-η Part b N-I-m N-1-m Σ wy +Σ jw. (P8.52-2) rel) N-1 Σw. Σ Σw r]W. (P8.52-3) r=N-m [ΞΠ! Part c Χ. (k-wΣ]WW = WW'X1k %3D τ-0

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a b c We know from Eq 811 th...View the full answer

Discrete Time Signal Processing

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