CPU-free hardware synthesis and spatialization with linear feedback shift registers.
A hardware pseudorandom-sequence system for multichannel sound. A linear feedback shift register (LFSR), built from ordinary logic chips, generates pseudorandom bit streams whose clock rate and feedback taps determine both the sound and its spatial distribution across a loudspeaker constellation. Synthesis and spatialization are coupled in the hardware itself, with no CPU in the signal path.
This repository is a concept overview of the approach: what it is, how it works, and short demonstrations of it running. The hardware itself is under active development. The early discrete-logic prototype is being reworked, and current research and testing center on an FPGA implementation, alongside a custom-silicon version built via Tiny Tapeout. Detailed designs, verified results, and fuller documentation will follow as the work matures.
Status: ongoing research project. Presented at AudioMostly 2022 (St. Pölten).
System architecture: an n-stage shift register with XNOR feedback, two n-channel multiplexers for dynamic tap and output selection, and parallel register outputs feeding a multichannel loudspeaker system.
Logic chips are a familiar material in electronic music, where they have long been used to build oscillators, sequencers and noise sources. This project uses one such circuit, the linear feedback shift register, as the basis for both sound synthesis and spatial composition at once.
Working in hardware rather than software is a deliberate choice. There is no buffering latency, so the system reacts immediately to events; modulation can run well into the MHz range, far above any audio sample rate; and, most important here, a large number of register outputs (more than 32) are directly accessible in parallel for multichannel use. Because each output is a phase-shifted copy of the same sequence, changing the sound necessarily changes how it is distributed in space. Sound and space are two readings of the same circuit.
The sonic range is wide: from individual clicks at slow clock rates, through grainy textures and stuttering tonal loops, to pink and white noise at high rates.
An LFSR is a chain of D flip-flops clocked in step. Feedback is formed by taking two or more bits from within the chain, adding them modulo 2 (an XOR, or an XNOR for the inverted sequence), and feeding the result back to the first stage. Because the number of states is finite, the output is deterministic and repeats after a fixed period.
A Galois configuration places the feedback between stages; a Fibonacci configuration (used by the discrete prototype) does the addition externally. Both reach the same sequence lengths.
Feedback taps that follow a primitive polynomial produce a maximum length sequence (MLS) of length 2ⁿ − 1, the longest possible before repeating. MLS have near-perfectly balanced ones and zeros and are maximally uncorrelated with shifted copies of themselves (Golomb), which is what makes them read as noise and decorrelate cleanly across channels. A 32-stage two-tap LFSR has 496 possible tap pairs, only a few of which produce a maximum-length sequence.
Each stage must start from a non-trivial seed. With XOR feedback the all-zero state is forbidden (it locks the output at zero); with XNOR it is the all-ones state. A small detector circuit spots the forbidden state and forces an escape, which extends the usable sequence to a full 2ⁿ.
Clock rate and sequence length are the two primary controls. Below roughly 10 Hz a long sequence produces random clicks; above about 50 Hz it becomes grainy; above 10 kHz it turns into noise. Short sequences at audio rates give tonal and rhythmic loops. Two different sequences over two speakers interlock into cross-rhythms that sound markedly less random than either alone.
The register length itself can be changed live with a multiplexer, whose binary select input can be driven by control logic, by pushbuttons, or by a second LFSR for pseudorandom tap selection.
Each successive register holds the previous register's state, so every output carries the same sequence delayed by one clock step. Mapping registers to loudspeakers turns these phase offsets into spatial motion: short delays give reverberant, phase-shifting effects; longer delays give rhythmic patterns at slow rates and whirring sound clouds at high rates. Used as a demultiplexer, one register's output can instead be scanned around the ring one speaker at a time.
Beyond clock rate and sequence length, a few further controls shape the result:
- Clock modulation. The clock can be modulated with pulse-width modulation (PWM), or the trigger pulses of an analog sequencer, so the texture shifts continuously instead of sitting at a fixed rate.
- Coupled LFSRs. Feeding the pseudorandom bit stream of a second LFSR into the clock input of the first couples the two registers; two LFSRs at different clock rates build markedly more complex, less predictable rhythms. This is the same coupling later built into the custom chip.
- Freezing the feedback. Stopping the feedback and letting the stored bits rotate shortens the active sequence and breaks smaller loops out of a longer one.
In one two-channel demonstration, a 31-stage and a 29-stage maximum-length sequence (lengths 2,147,483,647 and 536,870,911) clocked at 5 Hz interlock into cross-rhythms that read as far less random than either sequence alone.
Short clips of the running system, with sound. (The second clip keeps its unusually wide, oscilloscope-style format.)
Aperiodic sequence (taps 30 and 27, varying clock rate, 8 speakers, one LFSR):
aperiodic_msl_30-27_10hz_8sp_1lfsr.mp4
Periodic sequences (taps 12-8 and 9-7, 10 Hz and 60 Hz, 16 speakers, two LFSRs):
periodic_msl_12-8_9-7_10hz_60hz_16sp_2lfsr.mp4
The compressed source files are in assets/video/.
Discrete logic boards. A stack of SMD shields with stacking headers: a shift register with XNOR feedback, two 32-channel analog multiplexers (ADG732), and a lock-up-protection board. Register outputs are broken out on 8-channel Sub-D 25 connectors for patching to the loudspeaker system. Key ICs are the CD4094B shift register, CD4077B XNOR, ADG732 multiplexer, CD4068B AND/NAND, and a 555-type timer for the clock.
Board layout from the discrete-logic prototype.
FPGA. An iCE40 FPGA (the same device family Tiny Tapeout uses for its FPGA work) provides a reconfigurable, scalable route. The logic-gate structure can be multiplied and elaborated in place: many parallel LFSRs, longer registers, and richer coupled feedback, all without re-spinning physical hardware, which suits larger and more complex multichannel setups.
Custom silicon. The LFSR core re-implemented as a real chip in Verilog and laid out by the open-source flow (LibreLane) on the SKY130 process via Tiny Tapeout. The first build passed all Tiny Tapeout prechecks, with an added de Bruijn feedback modification (full 2ⁿ sequences) and a coupled modulator LFSR for pseudorandom output-tap hopping. This layout is a work in progress, not the final version. Chip repository: SCLW/tt-lfsr32.
GDS layout render of the 32-stage LFSR core on Tiny Tapeout (SKY130). Work in progress, not the final layout.
This remains a work in progress, and several directions stay open: a systematic study of the variation and modulation techniques above; an interface design with inlets, switches, and control elements for live performance; and a strategy for integrating the synthesis-and-spatialization approach into a modular system. The longer-term aim is to use it compositionally in electronic music.
The assembled stack: shift register, multiplexers, and lock-up protection. © Lorenz Schwarz.
Testing the system on the bench. © Holger Förterer.
Testing the boards. © Holger Förterer.
Schwarz, Lorenz. "Musical Application of Linear Feedback Shift Registers for Multichannel Loudspeaker Systems." Presented at AudioMostly 2022, St. Pölten University of Applied Sciences (abstract).
Pieces built on counting, logic, and combinatorial or pseudorandom process, included as background and inspiration:
- Tom Johnson, various works grounded in logic and number.
- Masahiro Miwa, Four-Bit Counter.
- Clarence Barlow, 2 aus 13 / Chronometrie.
- Robin Minard and Norbert Schnell, Soundbits.
A selection of the literature behind the project:
- Alfke, Peter. Efficient Shift Registers, LFSR Counters, and Long Pseudo-Random Sequence Generators. Application Note XAPP052, Xilinx, 1996.
- Golomb, Solomon W. Shift Register Sequences. Aegean Park Press, 1982.
- Lidl, Rudolf, and Harald Niederreiter. Introduction to Finite Fields and Their Applications. Revised ed., Cambridge University Press, 1994.
- Weste, Neil H. E., and David Money Harris. CMOS VLSI Design: A Circuits and Systems Perspective. 4th ed., Pearson, 2010.
The content of this documentation is licensed under the Creative Commons Attribution 4.0 International license. Copyright remains with the author.