Digital Signal Processing Reference
In-Depth Information
CHAPTER
2
Discrete Signals and Concepts
2.1 OVERVIEW
If the study of digital signal processing is likened to a story, this chapter can be viewed as an introduction
of the main characters in the story-they are the various types of signals (or their sampled versions, called
sequences) and fundamental processes that we will see time and time again. Acquiring a good working
knowledge of these is essential to understanding the rest of the story, just as is knowing the characters in
a novel.
In the first part of the chapter, we introduce discrete sequence notation and many standard test
signals including the unit impulse, the unit step, the exponential sequence (both real and complex), the
chirp, etc., and we learn to add and multiply sequences that are offset in time. Any serious study of digital
signal processing relies heavily on the representation of sinusoids by the complex exponential, and hence
this is covered in detail in the chapter. In the latter part of the chapter, we introduce the concepts of
linear, time-invariant (LTI) systems, convolution, stability and causality, the FIR, the IIR, and difference
equations.
By the end of this chapter, the reader will be prepared for the next chapter in the story of DSP,
namely, the process and requirements for obtaining sequences via sampling, formatting sample values in
binary notation, converting sequences back into continuous domain signals, and changing the sample
rate of a sequence.
2.2 SOF TWARE FOR USE WITH THIS TOPIC
The software files needed for use with this topic (consisting of m-code (.m) files, VI files (.vi), and related
support files) are available for download from the following website:
http://www.morganclaypool.com/page/isen
The entire software package should be stored in a single folder on the user's computer, and the full
file name of the folder must be placed on the MATLAB or LabVIEW search path in accordance with the
instructions provided by the respective software vendor (in case you have encountered this notice before,
which is repeated for convenience in each chapter of the topic, the software download only needs to be
done once, as files for the entire series of four volumes are all contained in the one downloadable folder).
See Appendix A for more information.
2.3 DISCRETE SEQUENCE NOTATION
Digital Signal Processing must necessarily begin with a signal, and most signals, such as sound, images,
etc., originate as continuous-valued (or analog) signals, and must be converted into a sequence of samples
to be processed using digital techniques.
Figure 2.1 depicts a continuous-domain sine wave, with eight samples marked, sequentially ob-
tained every 0.125 second. The signal values input to the ADC at sample times 0, 0.125, 0.25, 0.375, 0.5,
0.625, 0.75, etc., are 0, 0.707, 1, 0.707, 0, -0.707, -1, etc.
