We Eliminated EQ Frequency Cramping Without Oversampling — Here's How (DAFx26 Paper)

#audio #dsp #cpp #opensource

We Eliminated EQ Frequency Cramping Without Oversampling

If you've ever pushed a parametric EQ boost to 16 kHz and wondered why the curve looks wrong — you've hit frequency cramping. Traditional biquad filters using the bilinear transform exhibit 199% Q distortion at 16 kHz (44.1 kHz sample rate). The filter becomes almost 3× narrower than intended.

The industry solutions? Brute-force 4× oversampling (adds latency, burns CPU) or proprietary analog-matching curves (FabFilter's approach, closed-source).

We took a third path: the Simper State Variable Filter (SVF).

The Results

Topology	Magnitude at 16 kHz	Error
RBJ @ 44.1 kHz	+0.73 dB	−5.27 dB (cramped)
SVF @ 44.1 kHz	+6.00 dB	0.00 dB (exact)
RBJ @ 4× Oversampling	+4.82 dB	−1.18 dB

The SVF achieves exact gain at the center frequency — no oversampling, no proprietary tricks.

How It Works

The SVF pre-warps the cutoff frequency:

g = tan(π · fc / fs)

This single line eliminates the bilinear transform's frequency warping. All 8 filter types (Bell, Shelf, LP, HP, BP, Notch, AllPass) emerge from one two-integrator core.

Performance

We're not trading accuracy for CPU. Running 8-band stereo EQ at 44.1 kHz:

SVF path: 72.7 ns/sample → 0.62% CPU → 161× headroom
RBJ path: 41.0 ns/sample → 0.36% CPU → 277× headroom

The overhead is 1.73× — worth it for de-cramped high frequencies.

Lock-Free Real-Time Architecture

The plugin uses a SPSC triple-buffer for spectrum data:

Audio thread writes, atomically swaps with memory_order_release
UI thread reads, swaps with memory_order_acquire
Zero mutex, zero blocking, zero tears

Stress tested on 2012 Ivy Bridge hardware: 0 data tears across 239M samples.

Variable-Cadence Dynamic EQ

Dynamic EQ normally recomputes coefficients every sample. We observed that during sustained notes, changes < 0.1 dB are inaudible within a 4-sample batch (0.09 ms).

Result: 80% reduction in coefficient updates with no audible difference. Transients immediately restore per-sample accuracy.