Discrete Transforms
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Discrete Transforms: Discrete Cosine Transform, Discrete Fourier Transform, Fast Fourier Transform, Modified Discrete Cosine Transform

Discrete Transforms: Discrete Cosine Transform, Discrete Fourier Transform, Fast Fourier Transform, Modified Discrete Cosine Transform


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About the Book

Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. Pages: 26. Chapters: Discrete cosine transform, Discrete Fourier transform, Fast Fourier transform, Modified discrete cosine transform, Discrete wavelet transform, Discrete Hartley transform, Discrete sine transform, Number-theoretic transform, Fast wavelet transform, Discrete transform, Irrational base discrete weighted transform. Excerpt: In mathematics, the discrete Fourier transform (DFT) is a specific kind of discrete transform, used in Fourier analysis. It transforms one function into another, which is called the frequency domain representation, or simply the DFT, of the original function (which is often a function in the time domain). But the DFT requires an input function that is discrete and whose non-zero values have a limited (finite) duration. Such inputs are often created by sampling a continuous function, like a person's voice. Unlike the discrete-time Fourier transform (DTFT), it only evaluates enough frequency components to reconstruct the finite segment that was analyzed. Using the DFT implies that the finite segment that is analyzed is one period of an infinitely extended periodic signal; if this is not actually true, a window function has to be used to reduce the artifacts in the spectrum. For the same reason, the inverse DFT cannot reproduce the entire time domain, unless the input happens to be periodic (forever). Therefore it is often said that the DFT is a transform for Fourier analysis of finite-domain discrete-time functions. The sinusoidal basis functions of the decomposition have the same properties. The input to the DFT is a finite sequence of real or complex numbers (with more abstract generalizations discussed below), making the DFT ideal for processing information stored in computers. In particular, the DFT is widely employed in signal processing and related fields to analyze the frequencies contained in a...


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Product Details
  • ISBN-13: 9781233160020
  • Publisher: Books LLC, Wiki Series
  • Publisher Imprint: Books LLC, Wiki Series
  • Height: 246 mm
  • No of Pages: 28
  • Spine Width: 2 mm
  • Weight: 68 gr
  • ISBN-10: 1233160028
  • Publisher Date: 20 Aug 2011
  • Binding: Paperback
  • Language: English
  • Returnable: N
  • Sub Title: Discrete Cosine Transform, Discrete Fourier Transform, Fast Fourier Transform, Modified Discrete Cosine Transform
  • Width: 189 mm


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