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Pulse Wave
A pulse wave or pulse train or rectangular wave is a non-sinusoidal waveform that is the periodic version of the rectangular function. It is held high a percent each cycle ( period) called the duty cycle and for the remainder of each cycle is low. A duty cycle of 50% produces a square wave, a specific case of a rectangular wave. The average level of a rectangular wave is also given by the duty cycle. A pulse wave is used as a basis for other waveforms that modulate an aspect of the pulse wave. In pulse-width modulation (PWM) information is encoded by varying the duty cycle of a pulse wave. Pulse-amplitude modulation (PAM) encodes information by varying the amplitude. Frequency-domain representation The Fourier series expansion for a rectangular pulse wave with period T, amplitude A and pulse length \tau is x(t) = A \frac + \frac \sum_^ \left(\frac \sin\left(\pi n\frac\right) \cos\left(2\pi nft\right)\right) where f = \frac. Equivalently, if duty cycle d = \frac is used, and ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Waveform
In electronics, acoustics, and related fields, the waveform of a signal is the shape of its Graph of a function, graph as a function of time, independent of its time and Magnitude (mathematics), magnitude Scale (ratio), scales and of any displacement in time.David Crecraft, David Gorham, ''Electronics'', 2nd ed., , CRC Press, 2002, p. 62 ''Periodic waveforms'' repeat regularly at a constant wave period, period. The term can also be used for non-periodic or aperiodic signals, like chirps and pulse (signal processing), pulses. In electronics, the term is usually applied to time-varying voltages, electric current, currents, or electromagnetic fields. In acoustics, it is usually applied to steady periodic sounds — variations of air pressure, pressure in air or other media. In these cases, the waveform is an attribute that is independent of the frequency, amplitude, or phase shift of the signal. The waveform of an electrical signal can be visualized with an oscilloscope or an ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Fourier Series
A Fourier series () is an Series expansion, expansion of a periodic function into a sum of trigonometric functions. The Fourier series is an example of a trigonometric series. By expressing a function as a sum of sines and cosines, many problems involving the function become easier to analyze because trigonometric functions are well understood. For example, Fourier series were first used by Joseph Fourier to find solutions to the heat equation. This application is possible because the derivatives of trigonometric functions fall into simple patterns. Fourier series cannot be used to approximate arbitrary functions, because most functions have infinitely many terms in their Fourier series, and the series do not always Convergent series, converge. Well-behaved functions, for example Smoothness, smooth functions, have Fourier series that converge to the original function. The coefficients of the Fourier series are determined by integrals of the function multiplied by trigonometric func ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Pulse Shaping
In electronics and telecommunications, pulse shaping is the process of changing a transmitted pulses' waveform to optimize the signal for its intended purpose or the communication channel. This is often done by limiting the bandwidth of the transmission and filtering the pulses to control intersymbol interference. Pulse shaping is particularly important in RF communication for fitting the signal within a certain frequency band and is typically applied after line coding and modulation. Need for pulse shaping Transmitting a signal at high modulation rate through a band-limited channel can create intersymbol interference. The reason for this is Fourier correspondences (see Fourier transform). A bandlimited signal corresponds to an infinite time signal, that causes neighboring pulses to overlap. As the modulation rate increases, the signal's bandwidth increases. When the spectrum of the signal is uniformly rectangular, a sinc shape results in the time domain. This happens if the b ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Gibbs Phenomenon
In mathematics, the Gibbs phenomenon is the oscillatory behavior of the Fourier series of a piecewise continuously differentiable periodic function around a jump discontinuity. The Nth partial Fourier series of the function (formed by summing the N lowest constituent sinusoids of the Fourier series of the function) produces large peaks around the jump which overshoot and undershoot the function values. As more sinusoids are used, this approximation error approaches a limit of about 9% of the jump, though the infinite Fourier series sum does eventually converge almost everywhere. The Gibbs phenomenon was observed by experimental physicists and was believed to be due to imperfections in the measuring apparatus, but it is in fact a mathematical result. It is one cause of ringing artifacts in signal processing. It is named after Josiah Willard Gibbs. Description The Gibbs phenomenon is a behavior of the Fourier series of a function with a jump discontinuity and is ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
While You See A Chance
"While You See a Chance" is a song performed by Steve Winwood in 1980, written by Winwood and Will Jennings. It was released on his album '' Arc of a Diver'' and peaked at number 7 on the ''Billboard'' Hot 100 in April 1981 and number 68 on the ''Billboard'' Top 100 for 1981. The song was a bigger hit in Canada, where it peaked at number 3. It also reached number 45 in the UK. Background Winwood co-wrote "While You See a Chance" with Will Jennings, who came up with the song's lyrics. Jennings did not discuss the song's lyrical subject matter with Winwood, who nonetheless decided that the song was suitable to record. He said that he "learned about discipline from Will. He just came up with the lyrics and it was right for me, right for him, and right for the song." While the song was being mixed, Nobby Clark, who served as an engineer for the recording sessions, accidentally deleted the drum tracks by hitting the "record" feature on the mixing console. Attempts to fully restore t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Steve Winwood
Stephen Lawrence Winwood (born 12 May 1948) is an English musician and songwriter whose genres include blue-eyed soul, rhythm and blues, blues rock, and pop rock. Though primarily a guitarist, keyboard player, and vocalist prominent for his distinctive Soul music, soulful high tenor voice, Winwood plays other instruments proficiently, including drums, mandolin, bass, and saxophone. Winwood achieved fame during the 1960s and 1970s as an integral member of three successful bands: the Spencer Davis Group (1964–1967), Traffic (band), Traffic (1967–1969 and 1970–1974), and Blind Faith (1969). During the 1980s, his solo career flourished and he had a number of hit singles, including "While You See a Chance" (1980) from the album ''Arc of a Diver'' and "Valerie (Steve Winwood song), Valerie" (1982) from ''Talking Back to the Night'' ("Valerie" became a hit when it was re-released with a remix from Winwood's 1987 compilation album ''Chronicles (Steve Winwood album), Chronicles''). ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Sound
In physics, sound is a vibration that propagates as an acoustic wave through a transmission medium such as a gas, liquid or solid. In human physiology and psychology, sound is the ''reception'' of such waves and their ''perception'' by the brain. Only acoustic waves that have frequency, frequencies lying between about 20 Hz and 20 kHz, the audio frequency range, elicit an auditory percept in humans. In air at atmospheric pressure, these represent sound waves with wavelengths of to . Sound waves above 20 kHz are known as ultrasound and are not audible to humans. Sound waves below 20 Hz are known as infrasound. Different animal species have varying hearing ranges, allowing some to even hear ultrasounds. Definition Sound is defined as "(a) Oscillation in pressure, stress, particle displacement, particle velocity, etc., propagated in a medium with internal forces (e.g., elastic or viscous), or the superposition of such propagated oscillation. (b) Auditory sen ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Harmonic Spectrum
A harmonic spectrum is a spectrum containing only frequency components whose frequencies are whole number multiples of the fundamental frequency; such frequencies are known as harmonics. "The individual partials are not heard separately but are blended together by the ear into a single tone." In other words, if \omega is the fundamental frequency, then a harmonic spectrum has the form :\. A standard result of Fourier analysis is that a function has a harmonic spectrum if and only if it is periodic. See also * Fourier series * Harmonic series (music) * Periodic function * Scale of harmonics * Undertone series In music, the undertone series or subharmonic series is a sequence of notes that results from inverting the intervals of the overtone series. While overtones naturally occur with the physical production of music on instruments, undertones mus ... References {{Signal-processing-stub Functional analysis Acoustics Sound ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Bandlimited
Bandlimiting is the process of reducing a signal’s energy outside a specific frequency range, keeping only the desired part of the signal’s spectrum. This technique is crucial in signal processing and communications to ensure signals stay clear and effective. For example, it helps prevent interference between radio frequency signals, like those used in radio or TV broadcasts, and reduces aliasing distortion (a type of error) when converting signals to digital form for digital signal processing. Bandlimited signals A bandlimited signal is a signal that, in strict terms, has no energy outside a specific frequency range. In practical use, a signal is called bandlimited if the energy beyond this range is so small that it can be ignored for a particular purpose, like audio recording or radio transmission. These signals can be either random (unpredictable, also called stochastic) or non-random (predictable, known as deterministic). In mathematical terms, a bandlimited signal rel ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Sawtooth Wave
The sawtooth wave (or saw wave) is a kind of non-sinusoidal waveform. It is so named based on its resemblance to the teeth of a plain-toothed saw with a zero rake angle. A single sawtooth, or an intermittently triggered sawtooth, is called a ramp waveform. The convention is that a sawtooth wave ramps upward and then sharply drops. In a reverse (or inverse) sawtooth wave, the wave ramps downward and then sharply rises. It can also be considered the extreme case of an asymmetric triangle wave. The equivalent piecewise linear functions x(t) = t - \lfloor t \rfloor x(t) = t \bmod 1 based on the floor function of time ''t'' is an example of a sawtooth wave with period 1. A more general form, in the range −1 to 1, and with period ''p'', is 2\left( - \left\lfloor + \right\rfloor\right) This sawtooth function has the same phase as the sine function. While a square wave is constructed from only odd harmonics, a sawtooth wave's sound is harsh and clear and its spectrum cont ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Sinc Function
In mathematics, physics and engineering, the sinc function ( ), denoted by , has two forms, normalized and unnormalized.. In mathematics, the historical unnormalized sinc function is defined for by \operatorname(x) = \frac. Alternatively, the unnormalized sinc function is often called the sampling function, indicated as Sa(''x''). In digital signal processing and information theory, the normalized sinc function is commonly defined for by \operatorname(x) = \frac. In either case, the value at is defined to be the limiting value \operatorname(0) := \lim_\frac = 1 for all real (the limit can be proven using the squeeze theorem). The normalization causes the definite integral of the function over the real numbers to equal 1 (whereas the same integral of the unnormalized sinc function has a value of ). As a further useful property, the zeros of the normalized sinc function are the nonzero integer values of . The normalized sinc function is the Fourier transform of the r ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Pulse Wave 33
In medicine, the pulse refers to the rhythmic pulsations (expansion and contraction) of an artery in response to the cardiac cycle (heartbeat). The pulse may be felt (palpated) in any place that allows an artery to be compressed near the surface of the body close to the skin, such as at the neck (carotid artery), wrist (radial artery or ulnar artery), at the groin (femoral artery), behind the knee (popliteal artery), near the ankle joint (posterior tibial artery), and on foot (dorsalis pedis artery). The pulse is most commonly measured at the wrist or neck for adults and at the brachial artery (inner upper arm between the shoulder and elbow) for infants and very young children. A sphygmograph is an instrument for measuring the pulse. Physiology Claudius Galen was perhaps the first physiologist to describe the pulse. The pulse is an expedient tactile method of determination of systolic blood pressure to a trained observer. Diastolic blood pressure is non-palpable and unobser ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
