Page 335 - Electrical Engineering Dictionary

The scaling factor allows the same matrix to These are known as the Sylvester matrices.
be used for the inverse transform. The 4 × 4 Because of their properties, Hadamard matri-
Haar transform can be interpreted as follows: ces find application in the theory of error con-
first apply the 2 × 2 transform to two in- trol codes, and code division multiple access.
dependent pairs of samples; then apply the Named after Jacques Salomon Hadamard
2×2transformtothetwoaveragecoefficients (1865–1963). See also orthogonal, Walsh
just computed. Larger Haar transforms are cover.
constructed by continuing this process recur-
sively. Hadamard transform a unitary trans-
The Haar transform yields coefficients form mapping N samples g(n) to N coeffi-
equal to the subband values generated by cientsG(k)accordingtothetransformmatrix
dyadic decomposition with the Haar wavelet. H N , where
This transform has achieved rather less use 1 1 1
than the other transforms in this family, H 2 = √ 1 −1
2
such as the Discrete Cosine, Fourier and
Hadamard transforms. and larger arrays are formed by the recursive
definition
!
Haar wavelet the orthonormal wavelet 1 H N H N
1 1 1 −1 2 2
pair ( √ , √ ), ( √ , √ ). Analysis and syn- H N = √ .
2 2 2 2 2 H N −H N
thesis pairs are identical. This is the most 2 2
compact wavelet pair. Dyadic subband de- The inverse transform is identical. The
composition with the Haar wavelets yields Hadamard transform was formerly used for
coefficients equal to those from the Haar data compression because its entries are all
transform. 1or −1, allowing computation without mul-
tiplications. In this context it is now super-
Haas effect states that the first sound seded by the discrete cosine transform. See
heard will mask subsequent short delay ar- also Walsh–Hadamard transform.
riving sounds, the combination appearing as
a louder source. Also called law of the first half adder a logic circuit thatproduces the
wavefront. sum and carry outputs for two input signals.
A half adder has no carry input.
hacker a person who explores computer
half bridge amplifier a class-D amplifier
and communication systems, usually for in-
based on a half-bridge inverter configuration.
tellectual challenge, commonly applied to
Not suitable for amplification of DC to low-
those who try to circumvent security barri-
frequency signals because the capacitor leg
ers (crackers).
cannot provide unidirectional current.
Hadamardmatrix ann×nmatrixH with
half subtracter a logic circuit that pro-
elements ±1 is a Hadamard matrix of order n vides the difference and borrow outputs for
if HH T = nI, i.e., the rows are all mutually
two input signals. A half subtracter has no
orthogonal, as are the columns. Hadamard
borrow input.
matrices can only exist for n = 1, 2or n an
integer multiple of 4. Hadamard matrices of half-band filter a filter whose even-
i
order 2 can be constructed by the recursion
indexed coefficients are all zeros except the
one in the filter center.
H 1 = (1)

H n H n half-height point a point at which the
H 2n =
H n −H n membership grade is equal to 0.5.
c
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