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A sine wave, sinusoidal wave, or sinusoid (symbol: ∿) is a periodic wave whose waveform (shape) is the trigonometric sine function. In mechanics , as a linear motion over time, this is simple harmonic motion ; as rotation , it corresponds to uniform circular motion .
The phase of a simple harmonic oscillation or sinusoidal signal is the value of in the following functions: = (+) = (+) = (+) where , , and are constant parameters called the amplitude, frequency, and phase of the sinusoid.
The harmonic distribution of a sine wave carrier modulated by such a sinusoidal signal can be represented with Bessel functions; this provides the basis for a mathematical understanding of frequency modulation in the frequency domain.
A modulated wave resulting from adding two sine waves of identical amplitude and nearly identical wavelength and frequency. A common situation resulting in an envelope function in both space x and time t is the superposition of two waves of almost the same wavelength and frequency: [2]
The sinc function for a non-Cartesian lattice (e.g., hexagonal lattice) is a function whose Fourier transform is the indicator function of the Brillouin zone of that lattice. For example, the sinc function for the hexagonal lattice is a function whose Fourier transform is the indicator function of the unit hexagon in the frequency space. For a ...
The corresponding time-domain function for a sinusoidal exponential chirp is the sine of the phase in radians: = [+ ( ())] As was the case for the Linear Chirp, the instantaneous frequency of the Exponential Chirp consists of the fundamental frequency f ( t ) = f 0 k t T {\displaystyle f(t)=f_{0}k^{\frac {t}{T}}} accompanied by ...
The motion is sinusoidal in time and demonstrates a single resonant frequency. ... equation above produces a solution that is a sinusoidal function: () ...
This sinusoidal model can be fit using nonlinear least squares; to obtain a good fit, routines may require good starting values for the unknown parameters. Fitting a model with a single sinusoid is a special case of spectral density estimation and least-squares spectral analysis .