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# Harmonic definitions

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```hard magnetic material a ferromagnetic
material that retains its magnetization when
the magnetizing field is removed; a magnetic
material with significant coercivity.
hard real-time
See hard real-time system.
hard real-time system a real-time system
in which missing even one deadline results in
system failure. Compare with soft real-time,
firm real-time.
hard X-ray
having sufficient photon energy to penetrate “hard” material; usually
hard-decision decoding
decoding of encoded information given symbol decisions
of the individually coded message symbols.
Compare with soft-decision decoding.
hardware
computer constructs that have
a physical manifestation.
hardware accelerator
a piece of hardware dedicated to performing a particular function (such as image convolution or
matrix-vector products) which would otherwise be performed in software. Although
much less flexible, dedicated hardware implementations can give significant speed improvements over software, and are especially
useful for real-time applications.
hardware interrupt
an interrupt generated by a hardware device, for example, keyboard, the DMA, PIC, the serial adapter, the
printer adapter, etc. Other hardware interrupts can be generated by the control unit or
by the ALU, for example, for the presence of
a division per zero, for attempting to execute
an unknown instruction. This last class of
hardware interrupts is called internal exception.
hardware noise
radio frequency emissions due to arcing of utility lines at defective
connectors.
harmonic (1) the name associated with a
number used to denote the frequency components that exist in a certain fourier series
representation for a certain function of time
f (t). The Fourier series representation is
given
f (t) =
∞
Fn ∗[cos (nωo t) + j sin (nωo t)]
n=−∞
where
n = 0, 1, 2, 3, . . ., ωo = 2π/T , j =
√
−1, T is the period of the function f (t),
Fn is the coefficient of the Fourier series for
a certain value of n:
1st harmonic has Fn = F1 and
[cos (1ω0 t) + j sin (1ω0 t)]
2nd harmonic has Fn = F2 and
[cos (2ω0 t) + j sin (2ω0 t)]
3rd harmonic has Fn = F3 and
[cos (3ω0 t) + j sin (3ω0 t)]
etc.
(2) sinusoidal component of a periodic
waveform that has a frequency equal to an
integer multiple of the basic frequency (or
fundamental frequency). Thus the third harmonic of a power system voltage in the U.S.
has a frequency of 3&times;60, or 180 Hz. For electric systems powered by sinusoidal sources,
harmonics are introduced by nonlinear devices such as saturated iron cores and power
electronic devices.
harmonic amplifier
a type of amplifier
that utilizes various forms of harmonic and
mixing actions. These amplifiers may pump
up the fundamental by increasing the switching efficiency of the active device. Others
may actually be used as frequency multipliers
or frequency converters (mixers). All class
F, G, and H amplifiers fit into this general
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group. Parameters such as device characteristics, quiescent bias point, RF load line, significant harmonic and/or mixing frequencies,
and amplitude and waveform of the applied
signal(s) should be included with the class
definition, thus defining the major contributors to the physical actions taking place in
one of these amplifiers.
harmonic analysis
the branch of mathematics dealing with the decomposition of
signal functions as a linear combination of
basis functions which represent “waves” of
various frequencies. When the basis functions are sines and cosines each with a frequency that is an integer multiple of the
signal’s frequency, we have trigonometric
harmonic analysis, in other words classical
Fourier analysis, which provides the amplitudes and phases of the constituent sinusoids.
( See Fourier transform. ) With other basis
functions, for example wavelets, we have
non-trigonometric harmonic analysis ( See
wavelet, wavelet transform). Abstract harmonic analysis studies the generalization of
Fourier analysis to abstract spaces.
harmonic balance technique one of several techniques for analyzing nonlinear circuits. The nonlinear circuit is divided into
two portions of linear and nonlinear elements, and a portion of linear elements is calculated in a frequency domain and a portion
of nonlinear elements is calculated in a time
domain, respectively. The calculated voltages or currents at connecting nodes of these
portions are balanced by using Fourier transforming or inverse Fourier transforming.
harmonic component
a Fourier component of order greater than one of a periodic
waveform.
harmonic content
the internally generated, harmonically related spectral output
from a device or circuit. Harmonic energy
is that energy that is at exact multiples of
the fundamental frequency, generated by the
nonlinearities within the device or circuit acting on the fundamental frequency.
harmonic converter
found in a microwave receiver, this component uses the
technique of harmonic mixing to convert the
RF signal to a lower IF frequency for further processing. Harmonic converters can be
used as part of a vector network analyzer.
harmonic distortion
caused by the nonlinear transfer characteristics of a device or
circuit. When a sinusoidal signal of a single
frequency (the fundamental frequency) is applied at the input of a nonlinear circuit, the
output contains frequency components that
are integer multiples of the fundamental frequency (harmonics). The resulting distortion
is called harmonic distortion.
harmonic frequency
integral multiples
of fundamental frequency. For example, for
a 60-Hz supply, the harmonic frequencies are
120, 180, 240, 300, . . ..
harmonic generation
in nonlinear optics, the process in which a laser beam interacts with a material system to produce
new frequency components at integer multiples of the frequency of the incident beam.
Under carefully controlled circumstances,
the lower-order harmonics (e.g., second and
third) can be generated with high (&gt; 50%) efficiency. Under different circumstances, harmonics as high as the 30th can be generated.
a
measurement method where transfer characteristics of a device at the fundamental
frequency can be measured by electrically
changing the load impedance at harmonic
frequencies.
harmonic orthogonal set the set of functions ej ωt . It is called harmonic because
each basis function is a harmonic of a certain frequency and because the inner product
between any two functions is zero:
+∞ j ω t j ω t
1 e
2 dt = 0, ω = ω
1
2
−∞ e
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+∞
−∞
ej ωt1 ej ωt2 dω = 0, t1 = t2 .
harmonic tuning the process of tuning an
amplifier circuit to a frequency that is an integral multiple of the fundamental frequency
at which the circuit would normally operate.
harmonically pumped mixer
mixer
where the intermediate frequency (IF) signal is at a frequency which is the sum or
difference of the RF and an integer multiple (usually two) of the LO (local oscillator)
frequency.
Hartley oscillator a particular case of LCoscillators when X1 + X2 + 2Xm is realized
as a single tapped coil, and X3 is a capacitor.
Well suited for variable-frequency operation
by varying a single capacitor.
Hartley oscillators are usually not used at
VHFs of higher frequencies. Similarly, the
circuit is avoided at very low audio frequencies. It is important to distinguish the Hartley
oscillator from the Armstrong topology. In
the Armstrong oscillator, no ohmic connection exists between the two inductors. Instead, coupling is entirely magnetic.
Harvard architecture a computer design
feature where there are two separate memory units: one for instructions and the other
for data only. The name originates from an
early computer development project at Harvard University in the late 1940s. Compare
with Princeton architecture.
hash table a table storing a mapping function whose domain is sparsely used and that is
accessed by indices that are computed from
the search field (“key”) using a many–one
mapping (called a hash function). Hash tables are used for many memory and name
mapping functions, such as symbol tables in
assemblers and compilers.
hashed page table
a page table where
the translation of each virtual page number
is stored in a position determined by a hash
function applied to the virtual page number.
2000 by CRC Press LLC
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This technique is used to reduce the size of
page tables.
hashing the act of translating a search key
into a table index using a many–one mapping.
Hausdorff distance an important distance
measure, used in fractal geometry, among
other places. Given a distance function d
defined on a Euclidean space E, one derives
from it the Hausdorff distance Hd on the family of all compact (i.e., bounded and topologically closed) subsets of E; for any two
compact subsets K, L of E, Hd (K, L) is the
least r ≥ 0 such that each one of K, L is contained in the other’s dilation by a closed ball
Br (p) and L ⊆
Br (p),
K⊆
p∈L
p∈K
where
Br (p) = {q ∈ E | d(p, q) ≤ r}.
Hayes-compatible modem
refers to a
modem when it is capable of responding at
the commands of modems made by Hayes
Microcomputer Products. The Hayes set of
commands represents a sort of standard for
modems.
haystack response
bandpass frequency
response characterized by flat midband response with sloping sides.
hazard a momentary output error that occurs in a logic circuit because of input signal
propagation along different delay paths in the
circuit.
hazardous location
a classification system used to define locations that are susceptible to fire and explosion hazards associated
with normal electrical arcing. A class I hazardous location contains a flammable concentration of flammable vapors. A class II
hazardous location contains a combustible
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