Digital Signal Processing Reference
In-Depth Information
CHAPTER
3
Sampling and Binary
Representation
3.1
OVERVIEW
Having equipped ourselves with the knowledge of a number of common signal types and the basic concepts
of LTI systems in the previous chapter, we continue our study of DSP with the conversion of an analog
signal from the continuous domain to the discrete or sampled domain, and back again. Real-world analog
signals (such as audio and video signals) first enter the digital realm via the process of sampling. We begin
our discussion with two very important requirements of sampling, namely, the minimum acceptable or
Nyquist
sample rate and the need for bandlimiting a signal prior to sampling. With these all-important
principles established, we discuss normalized frequency, which is the basis for evaluating and describing
frequency content and response in the digital domain. Nyquist rate and normalized frequency are among
the most fundamental of concepts associated with digital signal processing, and little further discussion
of the topic can be meaningfully had until the reader understands them well.
In this chapter, in addition to the Nyquist rate and normalized frequency, we also discuss the
basics of binary counting and formats and analog-to-digital and digital-to-analog conversion. These are
important topics since they refer to implementation, which is always with limited precision representation
of numbers. The theory of digital signal processing, such as digital filtering, the DFT, etc., is usually
taught as though all numbers are of perfect accuracy or infinite precision. When digital signal processing
algorithms are implemented on a computer, for example, all numbers are stored and all computations are
made with only finite precision, which can adversely affect results. Much of the DSP literature concerns
these issues, and thus familiarity with the principles and nomenclature of conversion and quantization is
essential.
3.2
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.
