Lecture 4: Analog Synthesizers
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1 ELEN E4896 MUSIC SIGNAL PROCESSING Lecture 4: Analog Synthesizers 1. The Problem Of Electronic Synthesis 2. Oscillators 3. Envelopes 4. Filters Dan Ellis Dept. Electrical Engineering, Columbia University E4896 Music Signal Processing (Dan Ellis) /17
2 1. The Problem of Electronic Synthesis How can we synthesize notes and music... and have it sound as good as real instruments? Real instrument tones are complex Piano Trumpet Plucked Violin Bowed Violin E4896 Music Signal Processing (Dan Ellis) /17
3 The Analog Synthesizer Minimum useful configuration Pitch + harmonics Amplitude variation (dynamics) Spectral variation (197s technology) Trigger Pitch + Oscillator Vibrato t + Filter Cutoff freq f Envelope t Sound + Gain Minimoog, 1972 E4896 Music Signal Processing (Dan Ellis) /17
4 Digital Simulation of Analog E.g. Loomer Aspect E4896 Music Signal Processing (Dan Ellis) /17
5 PureData (Pd) Visual metaphor based on analog synths wires connect modules Tutorial: E4896 Music Signal Processing (Dan Ellis) /17
6 2. Oscillators Pitch = sinusoid? only a single color Real instruments have more harmonics static spectrum determines instrument sound? Additive: Combine individual harmonics calculating sinusoids in real time is expensive... Subtractive: Shape harmonics with filters start with a spectrally rich signal shape harmonics efficiently with LTI filters E4896 Music Signal Processing (Dan Ellis) /17
7 Sinusoid Basic waveforms Square wave Pulse waveform Sawtooth Triangle E4896 Music Signal Processing (Dan Ellis) /17
8 Aside: Bandlimiting It s easy to sample ideal simple waveforms but the ideal ones are not bandlimited lots of aliased energy Solution: Bandlimited waveforms e.g. fill a table with precalculated sum of sinusoids up to a fixed frequency Variable waveforms can be derived PWM by integrating bandlimited impulses E4896 Music Signal Processing (Dan Ellis) /17
9 Modulation Stationary spectra sound unnatural real sources have random jitter Variations in pitch Low Frequency Oscillator frequency modulation random noise Variations in timbre can be imposed by filters... Pulse-width modulation E4896 Music Signal Processing (Dan Ellis) /17
10 Aside: PWM Spectrum What are harmonics of Pulse-Width Modulated (PWM) waveforms? consider as impulses convolved with a pulse W Fourier transforms multiply = time frequency or integral of sum of two opposite impulse trains with relative delay W (good for bandlimiting) p w (t) = p(t) p(t W )dt E4896 Music Signal Processing (Dan Ellis) /17
11 3. Envelopes Notes need to be limited in time simple gating not enough amplitude envelope Different (real) instruments have clear variations in envelope struck/plucked vs. bowed/blown E4896 Music Signal Processing (Dan Ellis) /17
12 ADSR 4-parameter classic envelope model Attack - initial rise time Decay - fall time immediately following initial attack Sustain - amplitude of asymptote of decay while key is held down Key depressed Release - decay from sustain to zero after key released Tobias R. - Metoc E4896 Music Signal Processing (Dan Ellis) /17
13 Pd ADSR Abstraction Any patch can become a unit E4896 Music Signal Processing (Dan Ellis) /17
14 4. Filtering Amplitude modulation alone is not enough real instruments have time-varying spectra e.g. plucked string Generally just LPF (+ resonance) high frequencies die away after initial transient resonance can give some BPF effect E4896 Music Signal Processing (Dan Ellis) /17
15 The Biquad filter Flexible circuit design to achieve variable cutoff frequency but just single pole-pair LPF (or repeats) constant Q (bandwidth/center freq) resonance Imag Imag s plane -1 1 Real z plane -1 1 Real gain / db gain / db freq / rad/s norm freq / π Analog synths provided db/oct rolloff E4896 Music Signal Processing (Dan Ellis) /17
16 5. Examples Juno-16 preset patches from Brass Trumpet Piano Strings E4896 Music Signal Processing (Dan Ellis) /17
17 Summary Analog synthesizers provided musical flexibility with simple units 2 years of evolution Need instrument-like dynamics to make an interesting sound but only up to a point... Analog synths provide intuitive controls each knob has a distinct effect E4896 Music Signal Processing (Dan Ellis) /17
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