A Simple Approach to Digital Signal Processing

5

Transforming Signals into the Frequency Domain

In previous chapters we have used the description of a signal in both the time domain and the frequency domain interchangeably. For example, in Chapter 4 we used the time domain to demonstrate how a DSP program would be written to implement the filter algorithm, but we always used the frequency domain description to describe the type of filter to be used, e.g., low-pass, band-pass, etc.

We do this generally without thinking. Our intelligent minds have no difficulty thinking in these two directions simultaneously. Unfortunately, the humble DSP is not quite so smart. In order to compute the output of a system for a given input signal, we must provide it with a logical, step-by-step method of computing the result. We are then faced with a dilemma: If the input signal is a sequential series of digital pulses, i.e., a time domain signal, and the system is described by its frequency response, how do we program the DSP?

The answer is quite simple. We either transform the input signal into the frequency domain, or the system response into the time domain. Whichever we choose we shall easily be able to compute our algorithm. Both types of transformations are used in digital signal processing. For example, we often transform the frequency response into the time domain to allow us to build digital filters, as we saw in Chapter 4.

With FIR or IIR filters we produce a time domain representation of the filter response, which we convolve with the ...