Multistage conversion The composite anti-imaging and anti-aliasing LP filter band width is π/L or π/M whichever is shorter. That is, the filter band width is calculated by the larger number of L and M. However, if either L or M is a very large number the filter bandwidth is very short.
Narrowband FIR (linear phase) filters may require a very large number of coefficients . This can pose problems in
1. Increased storage space for coefficients,
2. Long computation time, and
3. Detrimental finite word length effects
The latter drawback is minimized by using a multistage sampling rate converter where the conversion ratio L/M is factored into the product of several ratios each of which has its own smaller L and M values. If, for instance, the ratio L/M is split into the product of two ratios
where the L's and M's on the right hand side are smaller, we may implement the rate conversion in two stages as shown below
Example Rational sampling rate converter: Digital audio tape (DAT) used in sound recording studios has a sampling rate of 48 kHz, while a compact disc (CD) is recorded at a sampling rate of 44.1 kHz. Design a sampling rate converter that will convert the DAT signal x(n) to a signal y(n) for CD recording.
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