TABLE OF CONTENTS The sampling rate conversion techniques that we have discussed thus far assume that the ratio of input to output sampling rates is an integer or a ratio of integers. However, in certain cases where the ratio is an irrational number or a ratio of integers requiring high upsampling and downsampling rates, it becomes more practical to implement the rate change operation with the help of a fractional delay filter. One such example is to change the sampling rate, say by the ratio of 64/65 = 0.984. Obviously, polyphase filter structure would be impractical. In this section, we will discuss techniques that may be used to perform such sampling-rate conversion with the aid of fractional delay filters.
An ideal fractional delay filter is a filter through which the signal is simply delayed by an arbitrary amount
where x( n) and y( n) are the input and output signals respectively. In the frequency domain, this simply implies that H ideal (z) = z ?D. In the frequency domain, the filter response is given as
The group delay can be derived from the phase as
Note that the implication of (10.115) in the z- domain is that
This in essence implies that D must be an integer. In reality z ?D cannot be simply realized for non-integer values of D. Therefore, an approximation of this all pass function is then in order.
