Integral Transforms - Fourier Analysis, Fourier Transform, List of Fourier-Related Transforms, Laplace Transform, Hilbert Transform (Paperback)

Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. Pages: 58. Chapters: Fourier analysis, Fourier transform, List of Fourier-related transforms, Laplace transform, Hilbert transform, Weierstrass transform, Hankel transform, Radon transform, Fractional Fourier transform, Integral transform, Linear canonical transformation, Mellin transform, Abel transform, Riemann-Liouville integral, Continuous wavelet transform, Sumudu transform, Motions in the time-frequency distribution, Laplace-Stieltjes transform, Hartley transform, Riesz transform, Nachbin's theorem, Projection-slice theorem, Two-sided Laplace transform, Funk transform, Gabor transform, Constant Q transform, Triple correlation, N rlund-Rice integral, Sine and cosine transforms, Mellin inversion theorem, Bicoherence, Inverse Laplace transform, X-ray transform, Stieltjes transformation, Bispectrum, Oscillatory integral operator, Gabor-Wigner transform, Perron's formula, Laplace transform applied to differential equations, Fourier operator, Post's inversion formula, Kontorovich-Lebedev transform. Excerpt: The Fourier transform is a mathematical operation that decomposes a signal into its constituent frequencies. Thus the Fourier transform of a musical chord is a mathematical representation of the amplitudes of the individual notes that make it up. The original signal depends on time, and therefore is called the time domain representation of the signal, whereas the Fourier transform depends on frequency and is called the frequency domain representation of the signal. The term Fourier transform refers both to the frequency domain representation of the signal and the process that transforms the signal to its frequency domain representation. In mathematical terms, the Fourier transform 'transforms' one complex-valued function of a real variable into another. In effect, the Fourier transform decomposes a function into oscillatory functions...