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A METHOD OF SAMPLE RATE CONVERSION FOR DIGITALLY SAMPLED DATA

IP.com Disclosure Number: IPCOM000007452D
Original Publication Date: 1995-Jul-01
Included in the Prior Art Database: 2002-Mar-27
Document File: 4 page(s) / 231K

Publishing Venue

Motorola

Related People

J. E. Lane: AUTHOR

Abstract

A method of sample rate conversion is presented which has two primary beneJts over previous methods. Thefirst advantage is the minimization of on-line data storage needed by the often large coefficient matrix required by the interpolation filter By evaluating a trun- cated Taylor series expansion of the matrix elements, each filter coefficient is calculated in real-time, as it is needed, eliminating the need to store the coefficient matrix in memory. The second benefit of this method is that the matrix elements can be reevaluated in real- time based on new short term values of sample rate frequency in order to re-align the input and output data streams due to asynchronous sample clocks. The primary drawback of this method is the increase in instruction cycles (MIPS) required to perform the coef- ficient calculations. This method is well suited to the implementation of a single DSP chip solution without the need of external memory.

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MOTVROLA Technical Developments

8

A METHOD OF SAMPLE RATE CONVERSION FOR DIGITALLY SAMPLED DATA

by J. E. Lane

  A method of sample rate conversion is presented which has two primary beneJts over previous methods. Thefirst advantage is the minimization of on-line data storage needed by the often large coefficient matrix required by the interpolation filter By evaluating a trun- cated Taylor series expansion of the matrix elements, each filter coefficient is calculated in real-time, as it is needed, eliminating the need to store the coefficient matrix in memory. The second benefit of this method is that the matrix elements can be reevaluated in real- time based on new short term values of sample rate frequency in order to re-align the input and output data streams due to asynchronous sample clocks. The primary drawback of this method is the increase in instruction cycles (MIPS) required to perform the coef- ficient calculations. This method is well suited to the implementation of a single DSP chip solution without the need of external memory.

INTRODUCTION

   A common technique of sample rate conversion can be viewed as converting an input block of M data points to an output block of N data points such that only the first point in each block are aligned. All other points in the output block are interpolated values of the M input data points. The input sample rate fx and output sample rate f, are related by M/fx = Nlfy.which is the amount of ttme required to read M mput samples or write N output samples. If N > M, the spectrum (discrete or fast Fourier trans- form) of the output block should, in the ideal case, differ from the spectrum of the input block only by the addition ofa relatively flat region extending from the Nyquist of the input sample frequency fx/2 to the Nyquist of the output sample frequency jj,/2. On the other hand, if N < M, the output spectrum will differ from the input spectrum only by the sup- pression of frequencies between fxl2 and fy/2 since the final Nyquist (folding frequency) is at a new lower value.

Since the input and output sample rates are not

always synchronized, M and N may not always be precisely the same value over a period oftime much longer than M/fx, which is especially true when fx and fy are derived horn separate clocks. In this case, it would be useful to periodically modify the inter- polation method based on new values ofMand N in order to maintain time alignment between the input and output data streams.

BACKGROUND

  It has been shown [l] that for a block of sam- pled input data, x(/c) of length M, a block of output data, y(n) of length N, can be generated by the fol- lowing interpolation process (convolution sum of L coefficients):

L-l

Yn = c 4s" Q-" (la)

IF0

(lb)

where k = 10.. .M-I) and n = 10.. .N-Il. The input sample index k, is a function of the output sample index n withy = N/M and can easily be evaluated using the INT hmction '(same as FORTRAN IN7: for example). The normalized interpolation...