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Digital Filters Design for Signal and Image Processing by Mohamed Najim

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7.4. Realizing finite precision filters

7.4.1. Introduction

In Chapters 5 and 6, we discussed FIR and IIR filter synthesis. The methods presented there allow us to obtain the transfer function of the filter, generally in the direct canonic form. However, in practice, and more especially when a filter is implanted in a processor dedicated to digital signal processing (DSP), the coefficients and values of the samples are coded on a finite number of bits. Quantifying these values requires several constraints that must be taken into account.

With IIR filters, we will show the influence quantification errors can have on a filter coefficient of the frequency response of a filter, in the case of a direct canonic, then cascade structure. This observation allows us to deduce the most adaptive choice for implementing digital filters. Then, we will look at other problems related to implementing filters, such as saturation.

We should remember that this section does not look at parallel structures; however, a similar study can be made to compare the influence of coefficient quantification on the frequency response of a filter.

7.4.2. Examples of FIR filters

Let the following formula be the transfer function of an FIR filter:

images

During implantation, the coefficients of the impulse response h(n) will never have exact theoretical value as predicted; they will be rounded off to the value [h(n)]r, the ...

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