Digital Signal Processing Reference
In-Depth Information
1.5
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Sample
Figure 3.33:
Continuous-domain signal (solid), simulated with 1000 samples; 10 samples of the (sim-
ulated) continuous-domain signal (stem plot); a reconstruction (dashed line) of the continuous-domain
signal from the 10 samples. Note that the reconstruction is only a good approximation from about samples
400-700 of the original (simulated) continuous-domain signal.
Reference [4] discusses ideal sinc interpolation in Section 4.2, and covers sampling rate conversion
in Chapter 10.
Example 3.29.
Devise a simple (not necessarily efficient) method to convert a sequence sampled at
44,100 Hz to an equivalent one sampled at 48,000 Hz.
The sample rate ratio can be approximated as 160:147. Assuming that a sequence
Sig
sampled at
44.1 kHz has indices 1,2,3, ..., the indices of samples, had the sample rate been 48 kHz instead of 44.1
kHz, would be
1:147/160:length(Sig) = 1, 1.9188, 2.8375, 3.7562...
This generates a total number of new samples of 160/147*length(Sig), which, when read out at
the new sample rate of 48 kHz, will produce the same apparent frequencies as the original sequence read
out at 44.1 kHz. To obtain the sample values, sinc interpolation as discussed above can be used. The more
densely sampled the sinc function, and the larger the number of original sequence samples included in
the approximation, the more accurate will be the interpolated values.
The script (see exercises below)
