Digital Signal Processing Reference
In-Depth Information
FIGURE 6.9.
Decomposition of two four-point DFTs into four two-point DFTs using DIT.
FIGURE 6.10.
Eight-point FFT flow graph using DIT.
sequence
x
(
n
) scrambled, the resulting output sequence
X
(
k
) becomes properly
ordered. Identical results are obtained with an FFT using either the DIF or the DIT
process. An alternative DIT flow graph to the one shown in Figure 6.10, with ordered
input and scrambled output, can also be obtained.
The following exercise shows that the same results are obtained for an eight-
point FFT with the DIT process as in Exercise 6.1 with the DIF process.
Exercise 6.3: Eight-Point FFT Using DIT
Given the input sequence
x
(
n
) representing a rectangular waveform as in Exercise
6.1, the output sequence
X
(
k
), using the DIT flow graph in Figure 6.10, is the same
as in Exercise 6.1. The twiddle constants are the same as in Exercise 6.1. Note that
the twiddle constant
W
is multiplied with the second term only (not with the first).
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