## Musimathics: The Mathematical Foundations of Music, Volume 2 |

### From inside the book

Results 1-3 of 48

Page 210

The function H(eiwT) given in equation (5.20) is called the

filter because it shows how much of x is transferred to y depending on frequency.

Note that the function does not depend upon the passage of time; the ...

The function H(eiwT) given in equation (5.20) is called the

**transfer function**of thefilter because it shows how much of x is transferred to y depending on frequency.

Note that the function does not depend upon the passage of time; the ...

Page 211

a) b) z = 2 + 3 1 • z = 2 + 3/ Re{z}=2 Im{z}=3 Figure 5.12 Real function of a

complex variable. In general, functions can be said to ... It would be nice to

reduce the complexity of the

a way to ...

a) b) z = 2 + 3 1 • z = 2 + 3/ Re{z}=2 Im{z}=3 Figure 5.12 Real function of a

complex variable. In general, functions can be said to ... It would be nice to

reduce the complexity of the

**transfer function**to facilitate understanding. Is therea way to ...

Page 212

Remembering that the magnitude of a complex number is the real-valued length

of a vector drawn to it from the origin of the complex plane, we define the

frequency response for frequency ft) as the magnitude of the

))s ...

Remembering that the magnitude of a complex number is the real-valued length

of a vector drawn to it from the origin of the complex plane, we define the

frequency response for frequency ft) as the magnitude of the

**transfer function**: G(ft))s ...

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### Contents

Digital Signals and Sampling | 1 |

Musical Signals | 49 |

Spectral Analysis and Synthesis | 103 |

Copyright | |

10 other sections not shown

### Common terms and phrases

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 response fundamental analysis harmonic Hilbert transform imaginary number impedance impulse response impulse train increases infinite input signal integer inverse length linear lowpass filter magnitude modulation motion multiply negative frequencies noise nonlinear Nyquist frequency oscillator output period phasor positive frequencies pressure probe phasor quantization quency radians range ratio reactance real number rectangular function reflected resonant result rotation sampling rate scaled sequence shown in figure shows sidebands sine wave sinusoid sound spectral spectrum STFT string synthesis theorem timbre transfer function tube unit circle vector velocity vibration volume wave equation waveform waveguide Xk(n Z transform zero