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In this section, we provide precise mathematical definitions for the d@0: transforms that FFTW computes. These transform definitions are fairly d@0: standard, but some authors follow slightly different conventions for the d@0: normalization of the transform (the constant factor in front) and the d@0: sign of the complex exponent. We begin by presenting the d@0: one-dimensional (1d) transform definitions, and then give the d@0: straightforward extension to multi-dimensional transforms. d@0: d@0:
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