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

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

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

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

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

6. Source/Filter Interaction
transfer function
Filter f
Result f

7. How are they perceived?
resonance
anti-resonance
Induced pitch

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

9. 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

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

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

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

13. 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

14. recursive y(nT) x(nT) k z-1 b b = .9 n 1 2 3 4 5 x(nT) 1 y(nT) 1.0 1.91 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