Digital Signal Processing Reference
In-Depth Information
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(a) Time, sec; SR = 240 Hz
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(b) Time, sec; SR = 24 Hz
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(c) Time, sec; SR = 17.5 Hz
Figure 3.3:
(a) Eight cycles of a sine wave taken over a 1 second period, with a stem plot of 240 samples
thereof superimposed; (b) The same eight-cycle sine, sampled at a rate of 24 Hz; (c) Sampled at 17.5 Hz.
3.4
FOLDING DIAGRAM
• For any given sampling rate, a
Folding Diagram
that shows the periodic nature of the sampling
function can be constructed. Such a diagram allows easy determination of the apparent output
frequency of the sampler for a given input frequency. The sampling function, as illustrated by a
folding diagram, “folds” input frequencies around odd multiplies of half the sampling rate.
Example 3.2.
Construct a Folding Diagram fora9Hzsampling rate and determine the output fre-
quency and phase if an 8 Hz signal is input to the sampler.
Figure 3.5, plot (a), shows a standard Folding Diagram using a sampling rate of 9 Hz. Use is
self-explanatory, except for the phase of the output signal compared to the input signal. When the slope
of the folding diagram is positive, the output frequency is in-phase with the input, and when the slope
of the folding diagram is negative, the output frequency's phase is inverted when compared to the input
signal's phase.
