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498 Chapter 9 SAMPLING RATE CONVERSION
1
Original Sequence x(n) Sample Rate I/D: I = 3, D = 2
1
Amplitude
0
Amplitude
0
−1
0 16 32
−1
0 16 32
Sample Rate I/D: I = 3, D = 4
Sample Rate I/D: I = 5, D = 8
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1
Amplitude
0
Amplitude
0
−1
−1
0 16 32
0 16 32
n
n
FIGURE 9.17 Original and resampled signals in Example 9.6
conversion by 3/2 isgreater than one, the overall effect is to interpolate x(n).
The resulting signal has 16 × 3/2 =24 samples in one period. The other two
sampling rate conversion factors are less than one; thus, overall effect is to
decimate x(n). The resulting signals have 16 × 3/4 =12and 16 × 5/8 =10
samples per period, respectively.
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9.5 FIR FILTER DESIGNS FOR SAMPLING RATE CONVERSION
In practical implementation of sampling rate converters we must replace
the ideal lowpass filters of equations (9.20), (9.30), and (9.36) by a practical
finite-order filter. The lowpass filter can be designed to have linear
phase, a specified passband ripple, and stopband attenuation. Any of the
standard, well-known FIR filter design techniques (e.g., window method,
frequency sampling method) can be used to carry out this design. We
consider linear-phase FIR filters for this purpose because of their ease
of design and because they fit very nicely into a decimator stage where
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