Digital Signal Processing Reference
In-Depth Information
such as x(t), or it may be discrete as x[n].
X means either the z-transform or Fourier transform of x.
y is used throughout to mean a signal, usually an output.
It may be continu-
ous, such as y(t), or it may be discrete as y[n].
z usually stands for a complex variable, such as in the z-transform. It is also used
as the name for a signal, if x and y are already used.
Anytime there is a lowercase letter, the same letter in uppercase means the upper
limit, or the frequency-domain information, depending on whether the lowercase
letter is an index or a signal. For example, Y [m] would be considered the Fourier
transform (or z-transform) of signal y[n], where m and n are integer indices, likely
ranging from 0 to N1.
A.3
Symbols Common in DSP Literature
2is used to indicate \element of." For example, \b2f0; 1g" means that b's value
must be in the set, that b is either 0 or 1.
N is the set of all natural numbers, starting with 1. That is,f1, 2, 3, ...g.
Z
Z is like
dening \unsigned int i;" in a C/C++ program (except that some integers are
too big for the range dened by the programming language).
is the set of all natural numbers, with 0 also included.
Saying i2
R is the set of all real numbers. For example, a2
R means that a is a real number.
This is like saying float a; in C/C++, except that oats have some limitations
that abstract mathematical variables do not, such as limits on precision.
R
n
is the set of all vectors of real numbers of length n.
This is similar to all
R
n
" is to think of c as if it
were dened as a real array, e.g., float c[n];. (Note the limits mentioned above.)
possible arrays of real values. A way to think about \c2
