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Books > Science & Mathematics > Mathematics > Calculus & mathematical analysis > Functional analysis
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The Regularized Fast Hartley Transform - Optimal Formulation of Real-Data Fast Fourier Transform for Silicon-Based Implementation in Resource-Constrained Environments (Paperback, 2010 ed.)
Loot Price: R4,969
Discovery Miles 49 690
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The Regularized Fast Hartley Transform - Optimal Formulation of Real-Data Fast Fourier Transform for Silicon-Based Implementation in Resource-Constrained Environments (Paperback, 2010 ed.)
Series: Signals and Communication Technology
Expected to ship within 10 - 15 working days
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Most real-world spectrum analysis problems involve the computation
of the real-data discrete Fourier transform (DFT), a unitary
transform that maps elements N of the linear space of real-valued
N-tuples, R , to elements of its complex-valued N counterpart, C ,
and when carried out in hardware it is conventionally achieved via
a real-from-complex strategy using a complex-data version of the
fast Fourier transform (FFT), the generic name given to the class
of fast algorithms used for the ef?cient computation of the DFT.
Such algorithms are typically derived by explo- ing the property of
symmetry, whether it exists just in the transform kernel or, in
certain circumstances, in the input data and/or output data as
well. In order to make effective use of a complex-data FFT,
however, via the chosen real-from-complex N strategy, the input
data to the DFT must ?rst be converted from elements of R to N
elements of C . The reason for choosing the computational domain of
real-data problems such N N as this to be C , rather than R , is
due in part to the fact that computing equ- ment manufacturers have
invested so heavily in producing digital signal processing (DSP)
devices built around the design of the complex-data fast multiplier
and accumulator (MAC), an arithmetic unit ideally suited to the
implementation of the complex-data radix-2 butter?y, the
computational unit used by the familiar class of recursive radix-2
FFT algorithms.
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