42 pages matching negative frequencies in this book
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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 create defined delay line derivative discrete displacement dissipation encoding energy example force Fourier transform frequency domain frequency response fundamental analysis 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 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