Abstract: In this paper, we define the Windowed Octonion Quadratic Phase Fourier Transform (WOQPFT) and derive its inversion formula, including its essential properties, such as linearity, ...

When you listen to digital music, the harmonies and chords that you hear have probably been reconstructed from a file that stored them as components of different frequencies, broken down by a process ...

Two hundred years ago, Joseph Fourier introduced a major concept in mathematics, the so-called Fourier transform (FT). It was not until 1965, when Cooley and Tukey developed the ‘fast Fourier ...

Fourier series is an expansion of a periodic function in terms of an infinite sum of sines and cosines. Fourier series make use of the orthogonality relationships of the sine and cosine functions.

What is a Fourier Transform? In mathematics, the transformation technique is used for mapping a function into a different function space from its original function space, and when we talk about the ...

As you know, the Fourier transform operates by convolving a signal with a series of sinusoidal signals of different frequencies. In fact, through this method, we can determine which frequencies exist ...

Many authors have studied the rate of average decay of the Fourier transform of measures because of its relationship with the Falconer’s conjecture. Although examples have been given showing that the ...