Sample Rate Conversion Principles
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3.2 Sample Rate Conversion Principles
The conversion of a data stream’s sample rate is an important part of digital signal processing.
A data stream can be downsampled to a lower sampling rate or upsampled to a
higher sampling rate. Figure 3.2 represents the process of sample rate conversion. A signal,
x(n), sampled at Fs,x is passed through a sampling rate converter. The output signal
is the waveform y(m) sampled at Fs,y. The sampling rate converter can be thought of as
the time-varying filter h(n,m). Note that n and m are indices for different time scales.
The sampling rate conversion factor is expressed as the ratio of two relatively prime
numbers, i.e., numbers whose greatest common divisor is one. Therefore, the filter h(n,m)
is a rate converter whose sampling ratio is determined by Equation 3.1.
Figure 3.2: Sampling Rate Converter.
The factors I and D in Equation 3.1 are the interpolation and decimation factors, respectively,
both of which are relatively prime. In the following decimation example and analysis,
I is assumed to be 1 [31, 32].
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