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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 two amplitude-modulated components are known as the in-phase component (I, thin blue, decreasing) and the quadrature component (Q, thin red, increasing). A sinusoid with modulation can be decomposed into, or synthesized from, two amplitude-modulated sinusoids that are in quadrature phase , i.e., with a phase offset of one-quarter cycle (90 ...
It is related to a more general concept called analytic representation, [3] which decomposes a sinusoid into the product of a complex constant and a factor depending on time and frequency. The complex constant, which depends on amplitude and phase, is known as a phasor, or complex amplitude, [4] [5] and (in older texts) sinor [6] or even ...
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.
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 root mean square of the detrended data can be scaled by the square root of two to obtain an estimate of the sinusoid amplitude. A complex demodulation amplitude plot can be used to find a good starting value for the amplitude.
A pure tone's pressure waveform versus time looks like this; its frequency determines the x axis scale; its amplitude determines the y axis scale; and its phase determines the x origin. In psychoacoustics, a pure tone is a sound with a sinusoidal waveform; that is, a sine wave of constant frequency, phase-shift, and amplitude. [1]