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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 .
Tracing the y component of a circle while going around the circle results in a sine wave (red). Tracing the x component results in a cosine wave (blue). Both waves are sinusoids of the same frequency but different phases. A sine wave, sinusoidal wave, or sinusoid (symbol: ∿) is a periodic wave whose waveform (shape) is the trigonometric sine ...
The zeta distribution has uses in applied statistics and statistical mechanics, and perhaps may be of interest to number theorists. It is the Zipf distribution for an infinite number of elements. The Hardy distribution , which describes the probabilities of the hole scores for a given golf player.
In this simple sinusoidal example, the constant θ is also commonly referred to as phase or phase offset. φ(t) is a function of time; θ is not. In the next example, we also see that the phase offset of a real-valued sinusoid is ambiguous unless a reference (sin or cos) is specified. φ(t) is unambiguously defined.
Left: the real part of a plane wave moving from top to bottom. Right: the same wave after a central section underwent a phase shift, for example, by passing through a glass of different thickness than the other parts. Out of phase AE. A real-world example of a sonic phase difference occurs in the warble of a Native American flute.
Graphs of roses are composed of petals.A petal is the shape formed by the graph of a half-cycle of the sinusoid that specifies the rose. (A cycle is a portion of a sinusoid that is one period T = 2π / k long and consists of a positive half-cycle, the continuous set of points where r ≥ 0 and is T / 2 = π / k long, and a negative half-cycle is the other half where r ...
In the branch of mathematics known as topology, the topologist's sine curve or Warsaw sine curve is a topological space with several interesting properties that make it an important textbook example. It can be defined as the graph of the function sin(1/ x ) on the half-open interval (0, 1], together with the origin, under the topology induced ...
The magnitude axis is in [Decibel] (dB). The phase axis is in either degrees or radians. The frequency axes are in a [logarithmic scale]. These are useful because for sinusoidal inputs, the output is the input multiplied by the value of the magnitude plot at the frequency and shifted by the value of the phase plot at the frequency.