E4896 Music Signal Processing (Dan Ellis) 2013-02-11 - /17 Lecture 4: Analog Synthesizers Dan Ellis Dept. Electrical Engineering, Columbia University [email protected]http://www.ee.columbia.edu/~dpwe/e4896/ 1 1. The Problem Of Electronic Synthesis 2. Oscillators 3. Envelopes 4. Filters ELEN E4896 MUSIC SIGNAL PROCESSING
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E4896 Music Signal Processing (Dan Ellis) 2013-02-11 - /17
Lecture 4:Analog Synthesizers
Dan EllisDept. Electrical Engineering, Columbia University
E4896 Music Signal Processing (Dan Ellis) 2013-02-11 - /17
Modulation• Stationary spectra sound unnatural
real sources have random “jitter”
• Variations in pitch“Low Frequency Oscillator” frequency modulation
random noise
• Variations in timbrecan be imposed by filters...Pulse-width modulation
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E4896 Music Signal Processing (Dan Ellis) 2013-02-11 - /17
Aside: PWM Spectrum• What are harmonics of Pulse-Width Modulated
(PWM) waveforms?consider as impulses convolved with a pulse W➝ Fourier transforms multiply
or integral of sum of two opposite impulse trains with relative delay W(good for bandlimiting)
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0 500 1000-0.50
0.51
1.5
0 500 1000-0.50
0.51
1.5
0 500 1000-0.50
0.51
1.5
0 200 400-40
-20
0
20
40
0 200 400-40
-20
0
20
40
0 200 400-40
-20
0
20
40
time
frequency
=
pw(t) =�
p(t)� p(t�W )dt
E4896 Music Signal Processing (Dan Ellis) 2013-02-11 - /17
3. Envelopes• Notes need to be limited in time
simple gating not enoughamplitude envelope
• Different (real) instruments have clear variations in envelopestruck/plucked vs. bowed/blown
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E4896 Music Signal Processing (Dan Ellis) 2013-02-11 - /17
ADSR• 4-parameter classic envelope model
Attack - initial rise timeDecay - fall time immediately following initial attackSustain - amplitude of asymptote of decaywhile key is held downRelease - decay from sustain to zero after key released
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Tobi
as R
. - M
etoc
Key depressed
E4896 Music Signal Processing (Dan Ellis) 2013-02-11 - /17
Pd ADSR Abstraction• Any patch can become a “unit”
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E4896 Music Signal Processing (Dan Ellis) 2013-02-11 - /17
4. Filtering• Amplitude modulation alone is not enough
real instruments have time-varying spectrae.g. plucked string
• Generally just LPF (+ resonance)high frequencies die away after initial transientresonance can give some BPF effect
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E4896 Music Signal Processing (Dan Ellis) 2013-02-11 - /17
The Biquad filter• Flexible circuit design to achieve
variable cutoff frequencybut just single pole-pair LPF (or repeats)constant Q (bandwidth/center freq) resonance
• Analog synths provided 12-24 dB/oct rolloff15
-1 0 1-1
-0.50
0.51
s plane
10-1 100 101-50
0
50
gain
/ dB
freq / rad/s
-1 0 1-1
-0.50
0.51
Real
Imag
Real
Imag
z plane
0 0.2 0.4 0.6 0.8 1-50
0
50
norm freq / π
gain
/ dB
E4896 Music Signal Processing (Dan Ellis) 2013-02-11 - /17