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Suppose we want to use a 16-point DFT to approximate the CFT of f(t) in Figure 3-20(a). The 16 discrete samples of f(t), spanning the three periods of f(t)’s sinusoid, are those shown on the left side of Figure 3-21(a). Applying those time samples to a 16-point DFT results in discrete frequency-domain samples, the positive frequencies of which are represented by the dots on the right side of Figure 3-21(a). We can see that the DFT output comprises samples of Figure 3-20(b)’s CFT. If we append (or zero-pad) 16 zeros to the input sequence and take a 32-point DFT, we get the output shown on the right side of Figure 3-21(b), where we’ve increased our DFT frequency sampling by a factor of two. Our DFT is sampling the input function’s CFT more often now. Adding 32 more zeros and taking a 64-point DFT, we get the output shown on the right side of Figure 3-21(c). The 64-point DFT output now begins to show the true shape of the CFT. Adding 64 more zeros and taking a 128-point DFT, we get the output shown on the right side of Figure 3-21(d). The DFT frequency-domain sampling characteristic is obvious now, but notice that the bin index for the center of the main lobe is different for each of the DFT outputs in Figure 3-21.
Figure 3-21 DFT frequency-domain sampling: (a) 16 input data samples and N = 16; (b) 16 input data samples, 16 padded zeros, and N = 32; (c) 16 input data samples, 48 padded zeros, and N = 64; (d) 16 input data samples, 112 padded zeros, and N = 128.
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发表于 2016-5-27 18:14
显身卡
发表于 2016-5-28 16:32
