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Spectral Analysis and Synthesis
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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 magnitude 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 spectrum STFT string synthesis theorem timbre transfer function tube unit circle vector velocity vibration volume wave equation waveform waveguide Z transform zero