The basic butterfly in the radix 2 decimation in time FFT algorithm is X n 1 (k) X n ( k ) W m N X n ( l ) X n 1 ( l ) X n ( k ) W m N X n ( l ) (a) If we require that X n (k) and X n ( l ) , show that Re X n 1 (k) 1, Re X n 1 ( l ) 1 lm X n 1 (k) 1 lm X n 1 ( l ) 1 Thus overflow does not occur (b)...

a The other inequalities are verified similarly b By similarly means using it can be sh ...

The basic butterfly in the radix-2 decimation-in-time FFT algorithm is X n+1 (k) = X n (

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The basic butterfly in the radix-2 decimation-in-time FFT algorithm is

X_n+1(k) = X_n(k) + W^m_NX_n(l)

X_n+1(l) = X_n(k) + W^m_NX_n(l)

(a) If we require that | X_n(k)| < ½ and | X_n(l)| < ½, show that

| Re[X_n+1(k)]| < 1, | Re[X_n+1(l)]| < 1

| lm[X_n+1(k)]| < 1 | lm[X_n+1(l)]| < 1

Thus overflow does not occur.

(b) Prove that

max[| X_n+1(k)|, | X_n+1(l)|] ≥ max[| X_n(k)|, |X_n(l)|]

max[| X_n+1(k)|, | X_n+1(l)|] ≤ 2 max[| X_n(k)|, |X_n(l)|]

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Digital Signal Processing

ISBN: ?978-0133737622

3rd Edition

Authors: Jonh G. Proakis, Dimitris G.Manolakis

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Question Posted: May 26, 2011 02:59 AM

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The basic butterfly in the radix-2 decimation-in-time FFT algorithm is X n+1 (k) = X n (

Question:

(6.4.2) 12 12

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a The other inequalities are verified similarly b By similarly means using it can be sh...View the full answer

Digital Signal Processing

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