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Then the function f(t) = −ωt + θ has slope −ω, which is called a negative frequency. But when the function is used as the argument of a cosine operator, the result is indistinguishable from cos(ωt − θ). Similarly, sin(−ωt + θ) is indistinguishable from sin(ωt − θ + π). Thus any sinusoid can be represented in terms of a ...
In signal processing, the power spectrum () of a continuous time signal describes the distribution of power into frequency components composing that signal. [1] According to Fourier analysis, any physical signal can be decomposed into a number of discrete frequencies, or a spectrum of frequencies over a continuous range.
The component frequencies, extended for the whole frequency spectrum, are shown as peaks in the domain of the frequency. Functions that are localized in the time domain have Fourier transforms that are spread out across the frequency domain and vice versa, a phenomenon known as the uncertainty principle.
In the physical sciences, the wavenumber (or wave number), also known as repetency, [1] is the spatial frequency of a wave. Ordinary wavenumber is defined as the number of wave cycles divided by length; it is a physical quantity with dimension of reciprocal length, expressed in SI units of cycles per metre or reciprocal metre (m −1).
The Q factor is a parameter that describes the resonance behavior of an underdamped harmonic oscillator (resonator). Sinusoidally driven resonators having higher Q factors resonate with greater amplitudes (at the resonant frequency) but have a smaller range of frequencies around that frequency for which they resonate; the range of frequencies for which the oscillator resonates is called the ...
Therefore, H(u)(t) has the effect of shifting the phase of the negative frequency components of u(t) by +90° (π ⁄ 2 radians) and the phase of the positive frequency components by −90°, and i·H(u)(t) has the effect of restoring the positive frequency components while shifting the negative frequency ones an additional +90°, resulting in ...
The group delay and phase delay properties of a linear time-invariant (LTI) system are functions of frequency, giving the time from when a frequency component of a time varying physical quantity—for example a voltage signal—appears at the LTI system input, to the time when a copy of that same frequency component—perhaps of a different physical phenomenon—appears at the LTI system output.
The characteristic impedance () of an infinite transmission line at a given angular frequency is the ratio of the voltage and current of a pure sinusoidal wave of the same frequency travelling along the line. This relation is also the case for finite transmission lines until the wave reaches the end of the line.