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== Week7 Quiz Pool == | == Week7 Quiz Pool == | ||
| − | Q1: | + | Q1: As part of the first stage in a radix 2 FFT, a sequence x[n] of length N = 8 is decomposed |
| + | into two sequences of length 4 as | ||
| + | |||
| + | <math>f_0[n] = x[2n]\text{ , n = 0, 1, 2, 3}</math> | ||
| + | |||
| + | <math>f_1[n] = x[2n + 1]\text{ , n = 0, 1, 2, 3}</math> | ||
| + | |||
| + | The 4-pt. DFT of each of these two sequences is <math>F_0[k]\text{ and }F_1[k]</math> respectively. | ||
| + | |||
| + | The specific values of <math>F_0[k]\text{ and }F_1[k]</math>, k = 0, 1, 2, 3, obtained from the length N = 8 sequence | ||
| + | in question are listed in the Table below. | ||
| + | |||
| + | |||
| + | |||
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| + | From the values of <math>F_0[k] \text{ and }F_1[k]</math>, k = 0, 1, 2, 3, and the values of | ||
| + | |||
| + | <math>W_8^k = e^{\frac{-j2\pi k}{8}}, k = 0, 1, 2, 3</math> | ||
| + | |||
| + | provided in the Table, determine the numerical values of the actual N = 8-pt. DFT of x[n] denoted <math>X_8[k]</math> for k = 0, 1, 2, 3, 4, 5, 6, 7. | ||
| + | |||
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Revision as of 14:45, 3 October 2010
Week7 Quiz Pool
Q1: As part of the first stage in a radix 2 FFT, a sequence x[n] of length N = 8 is decomposed into two sequences of length 4 as
$ f_0[n] = x[2n]\text{ , n = 0, 1, 2, 3} $
$ f_1[n] = x[2n + 1]\text{ , n = 0, 1, 2, 3} $
The 4-pt. DFT of each of these two sequences is $ F_0[k]\text{ and }F_1[k] $ respectively.
The specific values of $ F_0[k]\text{ and }F_1[k] $, k = 0, 1, 2, 3, obtained from the length N = 8 sequence in question are listed in the Table below.
From the values of $ F_0[k] \text{ and }F_1[k] $, k = 0, 1, 2, 3, and the values of
$ W_8^k = e^{\frac{-j2\pi k}{8}}, k = 0, 1, 2, 3 $
provided in the Table, determine the numerical values of the actual N = 8-pt. DFT of x[n] denoted $ X_8[k] $ for k = 0, 1, 2, 3, 4, 5, 6, 7.
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