Musimathics: The Mathematical Foundations of Music, Volume 2'Mathematics can be as effortless as humming a tune, if you know the tune, ' writes Gareth Loy. In Musimathics, Loy teaches us the tune, providing a friendly and spirited tour of the mathematics of music - a commonsense, self-contained introduction for the nonspecialist reader. Volume 2 of Musimathics continues the story of music engineering begun in volume 1, focusing on the digital and computational domain. Loy goes deeper into the mathematics of music and sound, beginning with digital audio, sampling, and binary numbers, as well as complex numbers and how they simplify representation of musical signals. Chapters cover the Fourier transform, convolution, filtering, resonance, the wave equation, acoustical systems, sound synthesis, the short-time Fourier transform, and the wavelet transform. These subjects provide the theoretical underpinnings of today's music technology. The material in volume 1 is all preparatory to the subjects presented in this volume, although either volume can be read independently. Cross-references to volume 1 are provided for concepts introduced in the earlier volume, and additional mathematical orientation is offered where necessary. The topics are all subjects that contemporary composers, musicians, and music engineers have found to be important. The examples given are all practical problems in music and audio. The level of scholarship and the pedagogical approach also make Musimathics ideal for classroom use. Additional material can be found at a companion web site. |
From inside the book
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Page 36
... Output Function 0 8 Input Function c ) Clipping System Function Output Function 2π A max OL Figure 1.28 Input Function Linear and nonlinear system functions . b ) Nonlinear System System Function 2π Output Function کر Input Function d ...
... Output Function 0 8 Input Function c ) Clipping System Function Output Function 2π A max OL Figure 1.28 Input Function Linear and nonlinear system functions . b ) Nonlinear System System Function 2π Output Function کر Input Function d ...
Page 219
... output ( but not current or future output ) . The FIR filter section accesses only current and past input because it can only retrieve input in the range x ( n − 0 ) tox ( n - M ) . The IIR filter section accesses only past output ...
... output ( but not current or future output ) . The FIR filter section accesses only current and past input because it can only retrieve input in the range x ( n − 0 ) tox ( n - M ) . The IIR filter section accesses only past output ...
Page 262
... output to produce the output signal . The impulse response of such filters is therefore infinite . The canonical filter is the combination of an FIR filter and an IIR filter . We can break down a filter's impulse response into a linear ...
... output to produce the output signal . The impulse response of such filters is therefore infinite . The canonical filter is the combination of an FIR filter and an IIR filter . We can break down a filter's impulse response into a linear ...
Common terms and phrases
acoustical aliasing allpass filter amplitude analyzed angle audio band coefficients complex number complex plane components constant convolution convolved corresponding cosine wave counterclockwise defined delay line derivative discrete displacement energy example force frequency domain frequency f frequency response fundamental analysis fundamental analysis frequency harmonic Hilbert transform IDFT impedance impulse response impulse train infinite input signal integer length linear lowpass filter magnitude spectrum modulation multiply musical negative frequencies noise nonlinear Nyquist frequency oscillator output periodic phase response playback heads positive frequencies probe phasor quantization quency radians range ratio reactance real number rectangular function resonant result rotation sampling rate scaled sequence shown in figure shows signal x(n sinc function sine wave sinusoid sound spectral STFT string synthesis test signal transfer function tube unit circle vector velocity vibration volume wave equation waveform window function Z transform zero