Musimathics: The Mathematical Foundations of Music, Volume 2MIT Press, 2007 - Composition (Music) |
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Page 89
... Multiplying Phasors In section 2.3.4 we observed that to multiply two complex numbers , we multiply their magnitudes and add their angles . Similarly , to multiply two phasors , we multiply their magnitudes and add their angles . For ...
... Multiplying Phasors In section 2.3.4 we observed that to multiply two complex numbers , we multiply their magnitudes and add their angles . Similarly , to multiply two phasors , we multiply their magnitudes and add their angles . For ...
Page 107
The Mathematical Foundations of Music D. Gareth Loy. Multiplying Signals There are four rules of multiplication : 1. + x + y is a one - quadrant multiply ( a positive number times a positive number is a positive number ) . 2. + x ± y and ...
The Mathematical Foundations of Music D. Gareth Loy. Multiplying Signals There are four rules of multiplication : 1. + x + y is a one - quadrant multiply ( a positive number times a positive number is a positive number ) . 2. + x ± y and ...
Page 172
... Multiply - > Convolve Multiply Convolve In this section we consider the opposite approach : Time domain : Frequency domain Convolve Convolve - > Multiply ← Multiply So now we want to prove that · • When spectra are multiplied , their ...
... Multiply - > Convolve Multiply Convolve In this section we consider the opposite approach : Time domain : Frequency domain Convolve Convolve - > Multiply ← Multiply So now we want to prove that · • When spectra are multiplied , their ...
Contents
Digital Signals and Sampling | 1 |
Musical Signals | 49 |
Spectral Analysis and Synthesis | 103 |
Copyright | |
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acceleration acoustical aliasing allpass filter amplitude angle audio band bandwidth binary coefficients complex number complex plane components constant convolution convolved corresponding cosine wave counterclockwise defined delay line derivative discrete displacement dissipation encoding energy example force Fourier transform frequency domain frequency f frequency response fundamental analysis harmonic Hilbert transform impedance impulse response impulse train infinite input signal integer inverse length linear lowpass filter modulation motion multiply negative frequencies noise nonlinear Nyquist frequency oscillator output period phasor positive frequencies pressure probe phasor quantization quency radians ratio reactance real number rectangular function reflected resonant result rotation sampling rate scaled sequence shown in figure shows sidebands sine wave sinusoid sound spectral STFT string synthesis theorem timbre transfer function tube unit circle vector velocity vibration volume wave equation waveform waveguide Z transform zero