Fast algorithms for signal processing
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Fast Algorithms for Signal Processing and Error Control
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Attend an Event Conferences Meet colleagues and advance your career Distinguished Lectures Learn from experts in signal processing. Seasonal Schools For graduate students and early stage researchers. Chapter Locator Find your local chapter and connect with fellow industry professionals, academics and students. This is the motivation for the evolution of the fast algorithms in the digital signal processing Field.
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Consequently, many of the real-world applications make use of these efficient Algorithms for fast computations. This is mathematically represented as follows:. Of course this is dependent on the Region of Support of the input as well as the impulse response.
The key point here to be noted is that we need to perform so many complex multiplications and additions to obtain 1 output value. The output can be computed efficiently if one can exploit some characteristics of the system.
We encounter a similar scenario when we have to compute the discrete Fourier Transforms of a signal of interest. As described in the next section we can develop Fast Fourier transforms for calculating 2-D or higher dimensional DFTs as well .
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Now let's talk about the computational savings we get using this approach. The 1-D DFT of a signal whose length is a power of 2, can be expressed in terms of two half-length DFTs, each of these can again be expressed as a combination of quarter length DFTs and so on. Each butterfly requires three complex multiplications and eight complex additions for the calculation of outputs from the inputs. From Wikipedia, the free encyclopedia.
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Dudgeon, Russell M. Categories : Multidimensional signal processing Digital signal processing.
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