Non-Integer-Rate Conversion
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Table of Contents
3.2.4 Non-Integer-Rate Conversion
In Sections 3.2.1 and 3.2.2, integer downsampling by a factor of D and upsampling by a
factor of I were discussed. In both cases, only integer-rate conversions were discussed.
However, integer-rate conversions3 are not always the desired operation. Non-integer-rate
conversions are achievable through the use of cascaded interpolations/decimations such
that a total rate change of I/D is achieved.
Figure 3.22 shows a block diagram of the implementation of a non-integer-rate conversion.
Since the input vector x(n) is interpolated by a factor of I, then
Since the filter H(z) acts both as a decimation and an interpolation filter, then its frequency
response should be
where the gain of I is used to compensate for the upsampling process to achieve the same
output power.
Figure 3.22: Non-Integer-Rate Conversion Block Diagram.
Equation 3.36 clearly shows that the sampling rate has been changed by a factor of 
Although this method allows non-integer-rate conversions, it is limited to changing rates
by rational numbers.
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