Analysis of Multistage Sampling Rate Conversion for Potential Optimal Factorization

Digital multistage sampling rate conversion has many engineering applications in fields of signal and image processing, which is to adapt the sampling rates to the flows of diverse audio and video signals. The FIR (Finite Impulse Response) polyphase sampling rate converter is one of typical schemes that are suitable for interpolation or decimation by an integer factor. It also guarantees the stability performance with the stable gain margin and phase margin. The big challenge occurs upon implementation when a very high order filter is needed with large values of L (positive integer factor of interpolator) and/or M (positive integer factor of decimator). Narrowband linear phase filter specifications are hard to achieve, however. It leads to extra storage space, additional computation expense and detrimental finite word length effects. The multistage sampling rate converter has been introduced to factorize the L and M ratio into a product of ratios of integers or prime numbers. The optimal number of stages and optimal converting factors are both critical terms to minimize the computation time and storage requirements. Filter structure analysis is conducted in this study to search for the potential factors that could have a remarkable impact to optimize the sampling rate conversion. KeywordsPolyphase FIR Filter, Interpolation, Decimation, Sampling Rate Conversion, Multistage, Multirate, Optimization