15.02.2019 Audio Effects Processing Vesa Välimäki, Fabián Esqueda & Benoit Alary ELEC-E5620 Audio Signal Processing DEMO: Pink Noise Generators Eero Lehtimäki & Uljas Pulkkis 2 1 Course Schedule in 2019 (Periods III, IV) 0. General issues (Vesa & Benoit) 11.1.2019 1. History and future of audio DSP (Vesa) 18.1.2019 2. Digital filters in audio (Vesa) 25.1.2019 3. Audio filter design (Vesa) 1.2.2019 4. Analysis of audio signals (Vesa) 8.2.2019 5. Audio effects processing (Vesa) 15.2.2019 * No lecture (Evaluation week for Period III) 22.2.2019 6. Synthesis of audio signals (Fabian) 1.3.2019 7. Reverberation and 3-D sound (Benoit) 8.3.2019 8. Physics-based sound synthesis (Vesa) 15.3.2019 9. Sampling rate conversion (Vesa) 22.3.2019 10. Audio coding (Vesa) 29.3.2019 Välimäki, Parker, Esqueda & Alary 15.2.2019 3 Outline • Echo / Delay • Flanging and Phasing • Chorus • Pitch shifting / Time stretching • Dynamic processing (compression & expansion) • Other effects Demo • Beat-Aligning Looper • Pink Noise Generators Välimäki, Parker, Esqueda & Alary 15.2.2019 4 2 What is an audio effect? . Any kind of audio signal processing applied to a captured or synthesized sound for creative purposes . Possible purposes: . Impression of space (echo, reverb) . Increasing perceived size of a sound (chorus) . Introducing movement into a static sound (flanging, phasing) . Altering timbre (distortion) . Altering dynamics (compression, limiting) 5 Echo/Delay . One of the simplest and earliest audio effects . Initially they were made using tape loops . Digital version very simple . Delay line with feedback . Filtering or distortion can be added to the feedback loop . Extra taps can be added for more complex pattern . Real-time implementation using “circular buffer”.* Sound example taken from: http://en.wikipedia.org/wiki/Delay_%28audio_effect%29 *Good reference: The Audio Programming Book by R. Boulanger & V. Lazzarini Välimäki, Parker, Esqueda & Alary 15.2.2019 6 3 Bucket-Brigade Devices (BBDs) • Tape machines are expensive! • BBDs are discrete-time analog delay lines • Invented by F. Sangster and K. Teer at the Phillips Research Labs in 1968. • Input signal is sampled in time and passed through a series of capacitors and switches. • Charge in each capacitor is passed to subsequent stage at a rate determined by clock. http://www.electrosmash.com/mn3007-bucket-brigade-devices Välimäki, Parker, Esqueda & Alary 15.2.2019 7 BBDs (cont’d) • CLK 1 and 2 in anti-phase configuration. • BBD flangers typically have a single 1024-stage unit. • Number of stages fixed. Delay length determined by clock’s rate. Välimäki, Parker, Esqueda & Alary 15.2.2019 8 4 BBDs (cont’d) • Although analog, BBD delay samples input signal and we must adhere to Sampling Theorem • Appropriate anti-aliasing and anti-imaging filters required at input and output, respectively. • Signal-to-noise ratio (SNR) is typically poor. • To ameliorate this, BBD is preceded by compressor and succeeded by expander (compander). • Very smart but not so intuitive design! BBD Flanger http://ant-s4.unibw-hamburg.de/dafx/paper-archive/2005/P_155.pdf Välimäki, Parker, Esqueda & Alary 15.2.2019 9 Flanging . Invented by Les Paul (1915-2009) in 1945, but the name came from John Lennon in 1966 (http://en.wikipedia.org/wiki/Flanging) . Original analog method for flanging . Copy the same sound on two open-reel tapes . Play the 2 tapes on 2 synchronized tape machines . Touch the flange of one tape reel to slow it down . Get a nice “wooshing” phase-cancellation effect Välimäki, Parker, Esqueda & Alary 15.2.2019 10 5 Flanging: Analog-Era Realization http://www.audiotechnology.com/tape-flanging-in-the-new-world/ Välimäki, Parker, Esqueda & Alary 15.2.2019 11 Flanging Sounds Familiar . Many everyday cases . C. Huygens (1693): the sound of a fountain has a pitch when it reflects from a staircase . Moving and hissing sound source (or listener moving) . Jet airplane flying over a city . Direct sound and its echo . Time-varying delay Välimäki, Parker, Esqueda & Alary 15.2.2019 12 6 Digital Flanger – Naive Version . A copy of the signal is fed through a variable digital delay line and added to the original . Produces a time-varying comb filter . Magnitude response contains many uniformly spaced, moving notches Välimäki, Parker, Esqueda & Alary 15.2.2019 13 Digital Flanger – Naive Version with LFO . Delay-line length is modulated with a Low Frequency Oscillator (LFO) . Slow modulation frequency, approx. 0.1 Hz – 10 Hz Pink noise Pink noise E-Guitar E-Guitar Drums Drums E-gtr examples by Timo Hiekkanen and Tuukka Lyly, TKK, 2007 Välimäki, Parker, Esqueda & Alary 15.2.2019 14 7 Digital Flanger – Thru Zero . Problem with naive implementation . Dry and delayed signal never coincide exactly . Solution: Add a static delay l to the ‘undelayed’ path, which is about half of the max value of m Välimäki, Parker, Esqueda & Alary 15.2.2019 15 Interpolated Variable Delay Line . In flanging, the delay-line length must vary smoothly to avoid discontinuities and clicks . Otherwise “zipper noise” is produced . A fractional delay is needed . Usually an FIR interpolation filter x(n) z-1 z-1 z-1 h(0) h(1) h(2) ... h(N) y(n) Välimäki, Parker, Esqueda & Alary 15.2.2019 16 8 Delay Line with Linear Interpolation • For digital audio effects, linear interpolation may be sufficiently good – The two-tap FIR is a mild lowpass filter, which varies with d x(n) z M z 1 1 d d y(n) xˆ(n M d ) Välimäki, Parker, Esqueda & Alary 15.2.2019 17 Flanging – The Movie Flanging - No Interpolation Flanging - Linear Interpolation (notches move in steps) (smooth sliding with filtering) Välimäki, Parker, Esqueda & Alary 15.2.2019 18 9 Phasing . Allpass-filtered signal is added to the original signal . Originally an analog electronic version of flanging (“a poor man’s flanger”) . Usually a series of allpass filters . Each allpass filter is of low order, e.g., first or second order . Phase shift of each allpass is modulated with LFO Välimäki, Parker, Esqueda & Alary 15.2.2019 19 Phasing - Notches . Notches are generated at frequencies where the phase response of filter chain is multiple of –π (or –180˚) . For example, four 2nd-order allpass filters in cascade → 4 notches . Change of coefficients moves the notches Phase response of the allpass chain Magnitude response of the overall system Frequency Frequency Välimäki, Parker, Esqueda & Alary 15.2.2019 20 10 The Allpass Filter RevisitedFilters • The z-domain transfer function of a digital allpass filter is given by • Parameter a1 determines break frequency. • The phase response of a single allpass and several cascaded units is then: One allpass filter Several allpass filters Välimäki, Parker, Esqueda & Alary 15.2.2019 21 Phaser with 10 Allpass Filters • Topology similar to that of MXR Phase 100 Pedal (5 notches, i.e. 10 filters). • DC Blocker at the input. • Naive approach; parameter a1 fully modulated. Not so useful! a1 = 0.1 a1 = 0.9 10 10 5 5 0 0 -5 -5 -10 -10 -15 -15 -20 Magnitude (dB) Magnitude -20 Magnitude (dB) Magnitude -25 -25 -30 -30 -35 -35 -40 100 1k 10k 20k -40 Frequency (Hz) 100 1k 10k 20k Frequency (Hz) Välimäki, Parker, Esqueda & Alary 15.2.2019 22 11 Phaser Measurements • Time-varying behavior of pedal can be measured using an allpass chirp train • Modulation patterns and notch locations can be extracted from measurements • Case Study: Fame Sweet Tone Phaser (MXR 100 clone) R. Kiiski, F. Esqueda and V. Välimäki, “Time-variant gray-box modeling of a phaser pedal”, DAFx-16. Välimäki, Parker, Esqueda & Alary 15.2.2019 23 Gray-Box Phaser Model • Same topology as previous example. • Measurement-based, modulation of a1 restricted to frequencies of interest. • Measurement also exhibited LFO waveform. a1 = –0.8 a1 = –0.4 10 10 5 5 0 0 -5 -5 -10 -10 -15 -15 -20 Magnitude (dB) -20 Magnitude (dB) Magnitude -25 -25 -30 -30 -35 -35 Original -40 100 1k 10k 20k -40 Frequency (Hz) 100 1k 10k 20k Frequency (Hz) Sound examples by Ricardo Falcón and Aleksi Myöhänen, ASP 2017 Välimäki, Parker, Esqueda & Alary 15.2.2019 24 12 Gray-Box Phaser Model R. Kiiski, F. Esqueda and V. Välimäki, “Time-variant gray-box modeling of a phaser pedal”, DAFx-16. Välimäki, Parker, Esqueda & Alary 15.2.2019 25 Flanging vs. Phasing . Flanging . Phasing . Variable time-delay . Variable phase shift . Short delay (< 10ms) . Very short delay . Hundreds of notches . Few notches (1-10) . Notches harmonically related . Notches not harmonic . Number of notches is time- . Notches can be individually varying modulated . Number of notches is fixed Välimäki, Parker, Esqueda & Alary 15.2.2019 26 13 Flanging or Phasing? Flanger Phaser Phaser Flanger Phaser Flanger Välimäki, Parker, Esqueda & Alary 15.2.2019 27 DEMO: Beat-Aligning Looper Jon & Petteri 28 14 Chorus . The goal: make one source sound like many sources . Useful for vocals and electrical instrument sounds . Very similar structure to flanger and echo effects Välimäki, Parker, Esqueda & Alary 15.2.2019 29 Famous Chorus Examples Chorus Unit: Boss Chorus CE-2 Chorus Unit: EHX Small Clone Välimäki, Parker, Esqueda & Alary 15.2.2019 30 15 Chorus Implementations (1) . One choice: multiple feedforward paths with modulated delay-lines (Orfanidis, 1996) . Modulation waveforms may be sinewaves or lowpass-filtered noise (“random walk” signal) Välimäki, Parker, Esqueda & Alary 15.2.2019 31 Chorus Implementations (2) . “Industry standard” (Dattorro, 1997) Välimäki, Parker, Esqueda & Alary 15.2.2019 32 16 Chorus Implementations (3) . The “industry standard” structure is cheap to implement . Use one for each stereo channel, or more . Generalized allpass-comb filter . Becomes an allpass filter, when delays and coefficients are equal . Negative feedback is used for flattening the spectrum (“white chorus”) .