MATHEMATICS OF THE
DISCRETE FOURIER TRANSFORM (DFT)
WITH AUDIO APPLICATIONS
SECOND EDITION

JULIUS O. SMITH III

2007

Known errata and Clarifications for Future Editions:

• Page 50: Replace the first sentence of the last paragraph with the following (clarified) sentence:
  • It is well known that sinusoidal frequency-modulation of a sinusoid creates sinusoidal components that are uniformly spaced in frequency by multiples of the modulation frequency, with amplitudes given by the Bessel functions of the first kind [12].
• Page 255: The summation in Equation (G.1) should extend to N-1, not N-2.
• Page 261: Change "Companding" to "Coding" in the title of Section G.2.3, and replace the first paragraph with the following:
  • Digital telephone CODECs have historically used (for land-line switching networks) a simple 8-bit format called mu-law that compresses large amplitudes in a manner loosely corresponding to human loudness perception.
  The purpose of this change is to avoid confusion between dynamic-range compression/expansion based on signal level (which is still called companding), and compression/expansion based on instantaneous signal amplitude, such as mu-law coding. Such coding is in fact called companding by some, but future editions of this book will call "instantaneous companding" of this nature a form of waveform coding. Thus, "companding" will be said to refer to compression or expansion of the signal level, as opposed to instantaneous amplitude, where the signal level at any given time is computed using a group of samples near that time (more than one sample).

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