The DFT: An Owners' Manual for the Discrete Fourier TransformJust as a prism separates white light into its component bands of colored light, so the discrete Fourier transform (DFT) is used to separate a signal into its constituent frequencies. Just as a pair of sunglasses reduces the glare of white light, permitting only the softer green light to pass, so the DFT may be used to modify a signal to achieve a desired effect. In fact, by analyzing the component frequencies of a signal or any system, the DFT can be used in an astonishing variety of problems. Among the applications of the DFT are digital signal processing, oil and gas exploration, medical imaging, aircraft and spacecraft guidance, and the solution of differential equations of physics and engineering. The DFT: An Owner's Manual for the Discrete Fourier Transform explores both the practical and theoretical aspects of the DFT, one of the most widely used tools in science and engineering. |
Contents
OT45_ch1 | 1 |
OT45_ch2 | 15 |
OT45_ch3 | 65 |
OT45_ch4 | 117 |
OT45_ch5 | 143 |
OT45_ch6 | 179 |
OT45_ch7 | 235 |
OT45_ch8 | 309 |
OT45_ch9 | 357 |
OT45_ch10 | 379 |
OT45_appendixa | 401 |
OT45_backmatter | 409 |
Other editions - View all
The DFT: An Owners' Manual for the Discrete Fourier Transform William L. Briggs,Van Emden Henson No preview available - 1995 |
Common terms and phrases
algorithm aliasing approximate the Fourier array assume band-limited boundary conditions Chapter Chebyshev polynomials coefficients ck complex DFT conjugate convolution cosine decrease defined denote derivatives DFT coefficients DFTs of length difference equation discrete Fourier transform endpoints error example factor Figure filter Fourier coefficients Fourier series frequency domain frequency grid frequency modes function ƒ given grid points grid spacing Hartley transform IDFT input sequence integral interpolation interval A/2 inverse DFT inverse transform Laplace transform linear matrix method multiplications N-point DFT one-dimensional orthogonal polynomials output periodic Poisson Summation Formula postprocessing Radon transform RDFT real DFT real sequence reciprocity relations replication representation result sampled sequence fn sequence of length Show shown sine solution spatial domain symmetric DFTs symmetry theorem trapezoid rule two-dimensional DFT Un+1 vector w₁ wave wavelength z-transform zero