Digital Signal Processing Reference
In-Depth Information
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Figure 3.30:
(a) Signal containing a five-cycle cosine; (b) DFT of signal in (a); (c) Signal containing a
5.3 cycle cosine; (d) DFT of signal in (c).
3.17.2 AVOIDING DF T LEAKAGE-WINDOWING
When the DFT of a sequence is taken, off-bin frequencies leak to some extent into all bins. The result
can be, in the general case, a greatly diminished ability to distinguish discrete frequencies from each other
when they are close. Leakage can, however, be reduced by multiplying the signal sequence by a smoothing
function called a
Window
prior to taking the DFT.
Example 3.33.
Demonstrate windowing on two 64-sample sequences, one of which contains a five-cycle
cosine and the other of which contains a 5.3 cycle cosine.
Figure 3.31 shows what happens when a smoothing function, in this case a Hamming window
(discussed in more detail below), is used to smooth each sequence. Note that the on-bin signal is somewhat
degraded, but the off-bin signal is considerably improved. In most cases, when the frequency content of
a signal is unknown or random, use of a window similar to that shown in Fig. 3.31 is advantageous. This
is explored in detail immediately below.
