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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.
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 standard Lomb–Scargle periodogram is only valid for a model with a zero mean. Commonly, this is approximated — by subtracting the mean of the data before calculating the periodogram. However, this is an inaccurate assumption when the mean of the model (the fitted sinusoids) is non-zero.
Sinusoidal model; Sinkov statistic; Size (statistics) Skellam distribution; Skew normal distribution; Skewness; Skorokhod's representation theorem; Slash distribution; Slice sampling; Sliced inverse regression; Slutsky's theorem; Small area estimation; Smearing retransformation; Smoothing; Smoothing spline; Smoothness (probability theory ...
Simple harmonic motion can serve as a mathematical model for a variety of motions, but is typified by the oscillation of a mass on a spring when it is subject to the linear elastic restoring force given by Hooke's law. The motion is sinusoidal in time and demonstrates a single resonant frequency.
Airy wave theory is a linear theory for the propagation of waves on the surface of a potential flow and above a horizontal bottom. The free surface elevation η(x,t) of one wave component is sinusoidal, as a function of horizontal position x and time t: (,) = where
LO is the local oscillator - the carrier sine wave being modulated I(t) and Q(t) are the time-series data for the in-phase and quadrature components. S is the signal . IQ data has extensive use in many signal processing contexts, including for radio modulation, software-defined radio, audio signal processing and electrical engineering.
A sinusoidal plane wave could be a suitable model for a sound wave within a volume of air that is small compared to the distance of the source (provided that there are no echos from nearly objects). In that case, F ( x → , t ) {\displaystyle F({\vec {x}},t)\,} would be a scalar field, the deviation of air pressure at point x → ...