Page 224 - Electrical Engineering Dictionary

For images that exhibit high pixel to pixel discrete multipath the result of multi-
correlation, the DCT is indistinguishable path propagation observed as clearly separa-
from the Karhunen–Loeve transform (KLT). ble, discrete signal components, seen in the
There is a family of DCTs, of which the delay power spectrum as a set of discrete
DCT-II described above is the one commonly peaks at various delays. See also multipath
used. These other types of DCT, specifically propagation, delay power spectrum, specular
the DCT-IV, are sometimes used in calculat- reflection.
ing fast transforms. The N = 8 element
DCT is particularly important for image data discrete network an electronic network
compression and is central to the JPEG and composed of separate, i.e., individual, com-
MPEG standards. As a matrix, the 8-element ponents.
DCT is as in the figure for DCT .
discrete sine transform (DST) a unitary
discrete data channel the concatenation transform mapping N samples g(n) to N co-
of all communication system elements be- efficients G(k) according to:
tween and including the modulator and de- r N−1
2 X nkπ
modulator. G(k) = g(n) sin
N + 1 N + 1
n=0
discrete Fourier transform (DFT) the
with inverse
sum of complex exponentials representing
r N−1
a sampled sequence. This transform is ob- 2 X nkπ
g(n) = G(k) sin
tained to represent a reasonable approxima- N + 1 N + 1
tion of a signal for which only a finite sample k=0
exists. Defined as As with the discrete cosine transform there
is a family of DSTs, the other members of
N−1
X −j(2π/N)nk which are rarely used. While the DST is
X(x) = x(n)e closely related to the DCT, the latter is the
n=0 form which has attained supremacy for im-
age data compression.
where x(n) represents a sequence of finite
samples of a signal; N is the number of sam-
discrete spectrum the eigenvalues of a
ples in the sequence.
differential equation with real coefficients
and finite boundary conditions form a dis-
discrete fuzzy set a fuzzy set that includes
crete spectrum. By extension, also the modes
onlythosesamplepointsofacontinuousvari-
of closed waveguides originate a discrete
able.
spectrum.
discrete Hadamard transform See
discrete time Fourier series representa-
Hada-
tion of a periodic sequence x n with period N
mard transform.
by the sum of a series of harmonically related
complex exponential sequences:
discrete Hopfield network a single layer,
fully connected network that stores (usually 1 N−1 j2πkn
X
bipolar) patterns by setting its weight values x n = X k e N .
N
w ij equal to the (i, j) entry in the sum of the k=0
outer products of the patterns. The network The X k are the Fourier series coefficients, ob-
can be used as an associative memory so long tained by
as the number of stored patterns is less than N−1
about 14% of the number of neural elements. X − j2πkn
X k = x n e N .
ComparewithcontinuousHopfieldnetwork.
n=0

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2000 by CRC Press LLC