EFFICIENT, ADAPTIVE PRECISION FIXED POINT DIGITAL FILTER

Publication Summary

The use of infinite impulse response (IIR) fil- ters is prevalent in audio applications. IIR filters gen- erally offer reduced filter order for an equivalent fil- ter transfer function as compared to finite impulse response filters (FIR). One of the drawbacks of efft- cient, high order IIR fixed point filter implementa- tions is their tendency to be subject to zero input limit cycles. That is, even when the input to the filter is zero the output can still (potentially) be non- zero. This zero input limit cycling is due to the quan- tization of the output of and subsequent feedback states to the fixed point precision of the processor, In audio applications these limit cycles can, under certain circumstances, be audible to the listener.

Country	United States
Language	English (United States)
Related Person(s)	(AUTHOR)  Michael W. Loos
Copyright	Motorola Inc. July 1995

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MOTVROLA Technical Developments

EFFICIENT, ADAPTIVE PRECISION FIXED POINT DIGITAL FILTER

by Michael W. Loos

INTRODUCTION

  The use of infinite impulse response (IIR) fil- ters is prevalent in audio applications. IIR filters gen- erally offer reduced filter order for an equivalent fil- ter transfer function as compared to finite impulse response filters (FIR). One of the drawbacks of efft- cient, high order IIR fixed point filter implementa- tions is their tendency to be subject to zero input limit cycles. That is, even when the input to the filter is zero the output can still (potentially) be non- zero. This zero input limit cycling is due to the quan- tization of the output of and subsequent feedback states to the fixed point precision of the processor, In audio applications these limit cycles can, under certain circumstances, be audible to the listener.

  The following is a discussion of an approach which preserves the high efficiency of a direct form IIR filter implementation while eliminating observ- able zero input limit cycles on the output. The approach discussed is based upon using knowledge about the energy of the input signal to adapt the filter structure of the filter. The approach is discussed in terms of interpolation ofthe output a code excited linear predictive (CELP) type speech decoder although it generalizes to many applications.

DESCRIPTION

   A general CELP coder operates by encoding and decoding blocks of digital speech samples of size 5 to 10 msec. At a typical sampling rate of8 kHz, this corresponds to blocks of 160 to 320 samples. If the digital to analog converter operates at a higher sam- pling rate the CELP coder output undergoes inter- polation to this higher sampling rate. Block IIR filtering of a zero stuffed version of the CELP out- put is performed as a part of this sample rate con- version. Since the output of the speech coder is a block of samples which becomes available (as input) to the interpolation filter at essentially the same moment, we can make use of our knowledge about

the entire block to modify the filter implementation.

  The general form of an IIR digital filter of order N, when implemented as a linear difference equa- tion is:

y(n) = (l/a,) [b,+(n) + b,x(n-1) + + b,x(n-N) - a,y(n-1) - a,y(n-2) - -aNy(n-N)]

  To demonstrate the technique a second order (biquad) filter will be examined. The general differ- ence equation for this second order filter is:

y(n) = (l/a,,) [box(n) + b,x(n-1) + b,x(n-2) -

a,y(n-1) - a,y(n-2)1

  The zero input limit cycles arise as a result of the quantization of the output, y(n), to the (single) precision of the processor prior to calculation of the next output sample, y(n+l). For non-low energy inputs, the input itself serves to prevent the filter from exhibiting (non-overtlow) limit cycles. For zero input, however, limit cycles may arise. The approach used to eliminate these zero input limit cycles is to adapt the filter structure to one ofthe following form:

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