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208 CHAPTER EIGHT
DSP Filter Design
DSP filters are engines that do just exactly that: They process digital signals. DSP filters
process digital data in an organized way. DSP can be accomplished in hardware Field-
Programmable Gate Array (FPGAs) or the processing can be done in software. Even a
general-purpose computer can perform DSP calculations. DSP filters are a mathemati-
cal construct that can be realized in various physical ways. We will discuss the mathe-
matical structure first and the physical implementation much later in a separate section.
Until we get to that section, none of the following discussion refers to specific physical
implementations. This is a discussion in mathematical terms.
DSP filters process a digital stream that represents a signal. The stream of data will
be recomputed in a coordinated way to form the output stream of the filter. It is the
nature of the computation that gives the DSP filter the desired frequency transfer func-
tion. DSP filters can be constructed in many ways, but a few standard ways exist for
building such a filter. A standard DSP filter is defined by its structure: a generic
sequence of arithmetic operations executed on the input data stream. To make a custom
filter, designers take a standard DSP filter and modify it. Tools and formulae convert
the custom filter transfer function to a set of alterations of the standard DSP filter. The
alterations, when made, turn the standard DSP filter into the custom filter. To actually
construct the custom filter, the designers map both the standard DSP filter and the cus-
tom alterations to a physical implementation.
One of the simpler standard structures for a DSP filter is the Finite Impulse Response
(FIR) filter shown in Figure 8-11. The data sequences through a linear series of regis-
ters called taps. At each sampling clock, the data moves to the next tap. After the last
tap, the data is discarded. The output of the FIR filter at each clock is generally a sin-
gle data element formed by combining all the data in all the taps. The data in each tap
is multiplied by that tap’s coefficient and the results are summed to make the output
data. It is the vector of coefficients that turns the standard DSP FIR structure into the
custom FIR filter. Once the designers decide that a custom FIR filter can be built with
the standard FIR structure (a process to be discussed later), few design tasks remain
other than the generation of the coefficients.
The coefficients for a FIR filter can be designed in many ways. We would need
another whole book to describe all the methods. Instead, we’re going to describe per-
haps the simplest, most general way to design a FIR filter. The technique uses Fourier
transforms and a technique called windowing. We won’t go fully into exactly why this
technique works, but rather how it works.
The technique is general because it enables the construction of a filter with an arbi-
trary frequency transfer function. The designer can describe a custom-shaped frequency