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For a given signal, the power spectrum gives a plot of the portion of a signal's power (energy per unit time) falling within given frequency bins. The most common way of ...

A transform which localizes a function both in space and scaling and has some desirable properties compared to the Fourier transform. The transform is based on a wavelet ...

In music, if a note has frequency f, integer multiples of that frequency, 2f,3f,4f and so on, are known as harmonics. As a result, the mathematical study of overlapping waves ...

Writing a Fourier series as f(theta)=1/2a_0+sum_(n=1)^(m-1)sinc((npi)/(2m))[a_ncos(ntheta)+b_nsin(ntheta)], where m is the last term, reduces the Gibbs phenomenon. The ...

A fast Fourier transform-like algorithm which produces a hologram of an image.

The important property of Fourier transforms that F_x[cos(2pik_0x)f(x)](k) can be expressed in terms of F[f(x)]=F(k) as follows, ...

A discrete fast Fourier transform algorithm which can be implemented for N=2, 3, 4, 5, 7, 8, 11, 13, and 16 points.

The Cesàro means of a function f are the arithmetic means sigma_n=1/n(s_0+...+s_(n-1)), (1) n=1, 2, ..., where the addend s_k is the kth partial sum ...

Leakage, more explicitly called spectral leakage, is a smearing of power across a frequency spectrum that occurs when the signal being measured is not periodic in the sample ...

Let a piecewise smooth function f with only finitely many discontinuities (which are all jumps) be defined on [-pi,pi] with Fourier series a_k = 1/piint_(-pi)^pif(t)cos(kt)dt ...