Search results
Results from the WOW.Com Content Network
Plot of normalized function (i.e. ()) with its spectral frequency components.. The unitary Fourier transforms of the rectangular function are [2] = = (), using ordinary frequency f, where is the normalized form [10] of the sinc function and = (/) / = (/), using angular frequency , where is the unnormalized form of the sinc function.
Examples of pulse shapes: (a) rectangular pulse, (b) cosine squared (raised cosine) pulse, (c) Dirac pulse, (d) sinc pulse, (e) Gaussian pulse. A pulse in signal processing is a rapid, transient change in the amplitude of a signal from a baseline value to a higher or lower value, followed by a rapid return to the baseline value. [1]
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 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 ...
The square wave is a special case of a pulse wave which allows arbitrary durations at minimum and maximum amplitudes. The ratio of the high period to the total period of a pulse wave is called the duty cycle. A true square wave has a 50% duty cycle (equal high and low periods).
An example of PWM [clarification needed] in an idealized inductor driven by a voltage source modulated as a series of pulses, resulting in a sine-like current in the inductor. The rectangular voltage pulses nonetheless result in a more and more smooth current waveform, as the switching frequency increases. The current waveform is the integral ...
The pulse being of finite length, the amplitude is a rectangle function. If the transmitted signal has a duration T {\displaystyle T} , begins at t = 0 {\displaystyle t=0} and linearly sweeps the frequency band Δ f {\displaystyle \Delta f} centered on carrier f 0 {\displaystyle f_{0}} , it can be written:
The rectangular function is Lebesgue integrable. The sinc function, which is the Fourier transform of the rectangular function, is bounded and continuous, but not Lebesgue integrable. The Fourier transform may be defined in some cases for non-integrable functions, but the Fourier transforms of integrable functions have several strong properties.
The result so obtained is the convolution of a rectangular pulse with step size W with the impulses located at the sampling instants with weights equal to the sample values. [ 12 ] : 12 In consequence, the spectrum of interest will have superimposed upon it the frequency response of the sample and hold, [ 13 ] : 135 [ 14 ] : 36 and the spectrum ...