Computer Sound Synthesis 2

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Presentation transcript:

Computer Sound Synthesis 2 MUS_TECH 335 Selected Topics Computer Sound Synthesis 2

Filter: a frequency-dependant attenuator It enhances some frequencies and diminishes others.

Amplitude Response a no filtering f low high a filtering f low high

Basic Types of Amplitude Response low-pass high-pass f f band-pass band-reject

a 1.0 3 dB .7071 stop-band pass-band f fc cutoff frequency (half power point or -3 dB point) a 1.0 .7071 bandwidth f fc center frequency

Source/Filter Interaction transfer function Filter f Result f

How are they perceived? resonance anti-resonance Induced pitch

Special Signals time frequency sine t f dc t f Nyquist t f impulse t f 1/2 SR impulse t f

Impulse Response input output filter time t t frequency f f 1., 0., 0., 0., .1, .6, .7, .4, -.3, -.1, time t t frequency f f

Graphic Symbols signal flow multiply a + add z-1 unit delay x(nT) input y(nT) output z-m delay of m samples

Digital Filters Two Types non-recursive feed forward “notches” FIR in k a out z-1 out recursive feed back “peaks” IIR in k z-1 a first-order filters

spectral features recursive (poles) non-recursive (zeros) filter type acoustic analog stored energy resonance cancelled energy anti-resonance

non-recursive x(nT) k a y(nT) z-1 a = 1 a = -1 n 1 2 3 4 x(nT) 1 y(nT) 1 2 3 4 x(nT) 1 y(nT) 1 2 x(nT) 1 -1 y(nT) 1 n 1 2 3 4 x(nT) 1 y(nT) 1 x(nT) 1 -1 y(nT) 1 -2 2

recursive y(nT) x(nT) k z-1 b b = .9 n 1 2 3 4 5 x(nT) 1 y(nT) 1.0 1.9 1 2 3 4 5 x(nT) 1 y(nT) 1.0 1.9 2.7 3.4 4.1 4.7 x(nT) 1 -1 y(nT) 1.0 -.10 .91 -.18 .84 -.25