Digital Signal Processing Reference
In-Depth Information
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Input Frequency to Sampler
Figure 3.8:
Folding diagram for 100 Hz sample rate with sinusoidal inputs to the sampler of 8, 108,
208, 308 408, and 508 Hz, showing net output frequency of 8 Hz. for all input frequencies.
to the midpoint in time, and then the apparent frequency smoothly decreases to the starting frequency.
Listening to the chirp frequency go up and then suddenly reverse should fix in your mind what happens
in aliasing.
Running the experiment one more time, let's use 6000 Hz as the upper chirp frequency, with the
same sampling frequency of 3000 Hz. The result is shown in plot (e), with the spectrogram in plot (f ).
3.5
NORMALIZED FREQUENCY
Consider a 16-Hz cosine wave sampled at 32 Hz for one second, with proper anti-aliasing. The resulting
sequence would look like Fig. 3.10, plot (a). On the other hand, a 32-Hz cosine sampled at 64 Hz results
in the same apparent signal, an alternation between +1 and -1, as shown in Fig. 3.10, plot (b).
If the sample rate had been (for example) 2048 Hz, the Nyquist limit would have been 1024 Hz,
and a 1024 Hz cosine in the original analog signal would show up as an alternation with a two-sample
period. If instead, the cosine's frequency had been one-half the Nyquist limit (in this case 512 Hz), there
would have been four samples per cycle, and so on.
