Page 202 - DSP Integrated Circuits

FINITE WORD LENGTH

EFFECTS

5.1 INTRODUCTION

In order to implement a recursive algorithm, all sequence values and coefficients
must be represented with a finite word length. The effect of finite word length
depends on the filter structure, pole-zero configuration, representation of negative
numbers, rounding or truncation of products, overflow characteristics, and the
input signal. Finite word length gives rise to a large number of phenomena caused
by different types of nonlinearities.

• Overflow of the number range: Large errors in the output signal occur
when the available number range is exceeded—overflow. Overflow
nonlinearities can be the cause of so-called parasitic oscillations.
• Round-off errors: Rounding or truncation of products must be done in
recursive loops so that the word length does not increase for each
iteration. The errors that occur under normal operating conditions can be
modeled as white noise, but both rounding and truncation are nonlinear
operations that may cause parasitic oscillations. Floating-point addition
also causes errors because of the denormalization and normalization of
the numbers involved.
• Aliasing errors: Aliasing and imaging errors occur in A/D and D/A
converters and when the sample rate is changed in multirate systems.
These nonlinearities may cause nonharmonic distortion.
• Coefficient errors: Coefficients can only be represented with finite
precision. This results in a static deviation from the ideal frequency
response for a digital filter.
The effect on the filtering due to these errors is difficult to predict, except in
special cases, and the acceptable distortion depends on the application. It is there-
fore important to determine experimentally the performance of the filter through
extensive simulation. Parasitic oscillations cause various forms of nonideal filter
behavior—for example, large amplitude oscillations that are independent of the

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