A Quadrature Signals Tutorial: Complex, But Not Complicated

Understanding the 'Phasing Method' of Single Sideband Demodulation

Complex Digital Signal Processing in Telecommunications

Introduction to Sound Processing

Introduction of C Programming for DSP Applications

Fourier Transforms for Continuous/Discrete Time/Frequency

Fourier Transform (FT) and Inverse

Existence of the Fourier Transform

**Search Spectral Audio Signal Processing**

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Conditions for the *existence* of the Fourier transform are
complicated to state in general [35], but it is *sufficient*
for to be *absolutely integrable*, *i.e.*,

There is never a question of existence, of course, for Fourier
transforms of real-world signals encountered in practice. However,
*idealized* signals, such as sinusoids that go on forever in
time, do pose normalization difficulties. In practical engineering
analysis, these difficulties are resolved using Dirac's ``generalized
functions'' such as the *impulse* (also called the
*delta function*), discussed in §B.1.10.

Julius Smith's background is in electrical engineering (BS Rice 1975, PhD Stanford 1983). He is presently Professor of Music and Associate Professor (by courtesy) of Electrical Engineering at Stanford's Center for Computer Research in Music and Acoustics (CCRMA), teaching courses and pursuing research related to signal processing applied to music and audio systems. See http://ccrma.stanford.edu/~jos/ for details.

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