Digital Signal Processing Reference
In-Depth Information
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Figure 3.24:
Original Analog Signal (Dashed); Ideal (i.e., Quantized to Infinite Precision) Samples
(Circles); Quantized Samples at DAC output (Solid).
other sampled at 22.05 kHz. To do this, one of the sequences must have its sample rate converted to
match that of the other prior to addition.
In this section we look at two important processes, interpolation and decimation by whole number
ratios, and the combination of the two techniques, which allows change of sample rate by a whole number
ratio, such as 4:3, for example. We include a basic discussion of interpolation using the
sinc
function, and
compare it to linear interpolation.
3.16.1 INTERPOLATION
From time to time, it is necessary to either increase the sampling rate of a given sequence, or decrease the
frequencies contained in the sequence by a common factor. Let's consider a concrete example.
Supposing one second's worth of samples were taken at a sampling rate of 65,536 Hz of a signal
composed of three sine waves having respective frequencies of 3000 Hz, 4000 Hz, and 5000 Hz (any
other collection or mixture of frequencies would have been possible provided, of course, that the highest
frequency was less than half of 65,536).
