Digital Signal Processing Reference
In-Depth Information
of samples of the signal using a discrete time processing system, which typically consists of registers
or memory elements, delay elements, multipliers, and adders. Each of the preceding elements may be
implemented as distinct pieces of hardware in an efficient arrangement designed to function for a particular
purpose (often referred to as a
Pipeline Processor
), or, the equivalent functions of all elements may be
implemented on a general purpose computer by specifically designed software.
1.3.2 FREQUENCY TRANSFORMS
A time-to-frequency transform operates on a block of time domain samples and evaluates the frequency
content thereof. A set of frequency coefficients is derived which can be used to quantify the amplitudes
(and usually phases) of frequency components of the original signal, or the coefficients can be used to
reconstruct the original time domain samples using an inverse transform (a frequency-to-time transform).
The most well-known and widely-used of these transforms is the
Discrete Fourier Transform (DF T)
,
usually implemented by the
FF T
(for
Fast Fourier Transform)
, the name of a class of algorithms that
allow efficient computation of the DFT.
1.3.3 FREQUENCY DOMAIN PROCESSING
Most signal processing that can be done in the time domain can be also equivalently done in the frequency
domain. Each domain has certain advantages for a given type of problem.
Time domain filtering, for example, can be performed using frequency transforms such as the
DFT, and in certain cases efficiency can be greatly improved using this technique.
A second use is in digital filter design, in which the desired filter frequency response is specified
in the frequency domain, i.e., as a set of DFT coefficients, for example.
Yet a third and very prevalent use is
Transform Coding
, in which signals are coded using a frequency
transform (usually eliminating as much redundant information as possible) and then reconstructed from
the transform coefficients. Transform Coding is a powerful tool for compression algorithms, such as those
employed with MP3 (MPEG II, Level 3) for audio signals, JPEG, a common image compression format,
etc. The use of such compression algorithms has revolutionized the audio and video fields, making storage
of audio and video data very economical and deliverable via Internet.
1.4 ORGANIZATION OF THIS VOLUME OF THE SERIES
The present volume provides basic information on digital signal processing and has four chapters as
follows:
• Chapter 1 (the present chapter) gives a brief overview of DSP. It defines sampling, contrasts the
areas of continuous and discrete signal processing, as well as time domain and frequency domain
processing, and introduces very basic signal processing nomenclature.
• Chapter 2 introduces many useful signals and sequences, followed by a basic introduction to Linear,
Time Invariant (LTI) systems, including convolution, stability and causality, basic FIR and IIR
filters, and difference equations.
• Chapter 3 discusses the fundamental concepts of sampling, analog-to-digital conversion, and
digital-to-analog conversion. The topics of aliasing, normalized frequency, binary formats, zero-
order hold conversion, interpolation, decimation, frequency generation, and Mu-law compression
are also covered.
