Digital Signal Processing Reference
In-Depth Information
// End of the DSP algorithm
lcnew
¼
y[0]; /* Send to DAC */
rcnew
¼
y[0];
AIC23_data.channel[LEFT]
¼
(short) lcnew;
AIC23_data.channel[RIGHT]
¼
(short) rcnew;
output_sample(AIC23_data.combo);
}
12.7
SUMMARY
1.
Downsampling (decimation) by an integer factor of
M
means taking one sample from the data
sequence
xðnÞ
for every
M
samples and discarding the last
M
1 samples.
2.
Upsampling (interpolation) by an integer factor of
L
means inserting
L
1 zeros for every sample
in the data sequence
xðnÞ
.
3.
Downsampling requires a decimation (anti-aliasing) filter to avoid frequency aliasing before
downsampling.
4.
Upsampling requires an interpolation (anti-image) filter to remove the images after interpolation.
5.
Changing the sampling rate by a noninteger factor of
L=M
requires two stages: an interpolation
stage and a downsampling stage.
6.
Two-stage decimation can dramatically reduce the anti-aliasing filter length.
7.
Polyphase implementations of the decimation filter and interpolation filter can reduce the
complexity of the filter operations, that is, fewer multiplications and additions.
8.
Using oversampling can improve the regular ADC resolution. Sigma-delta modulation ADC can
achieve even higher ADC resolution, using the noise shaping effect for further reduction of
quantization noise.
9.
The audio CD player uses multirate signal processing and oversampling.
10.
Undersampling can be used to sample the bandpass signal,
leading to applications in
communications.
12.8
PROBLEMS
12.1. Consider a single-stage decimator with the following specifications:
Original sampling rate
¼
1 kHz
Decimation factor
M ¼
2
Frequency of interest
¼
0
e
100 Hz
Passband ripple
¼
0.015 dB
Stopband attenuation
¼
40 dB
a. Draw the block diagram for the decimator.
b. Determine the window type, filter length, and cutoff frequency if the window method is
used for the anti-aliasing FIR filter design.
12.2. Consider a single-stage interpolator with the following specifications:
Original sampling rate
¼
1 kHz
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