Analog wavelets

Taking the 3-level LeGall 5/3 cascade from the Bloodhoney’s DSP and trying to sandwich it purely in the analog domain between your OPA2134 buffers is a fascinating thought experiment. However, the short answer is no—at least, not without creating an incredibly noisy, impractical circuit that defeats the purpose of using that specific mathematical transform.

Here is the breakdown of why translating that specific discrete wavelet transform (DWT) to analog is a nightmare, and how the analog world actually tackles tri-band splitting.

The Problem: FIR vs. IIR

The LeGall 5/3 is a Discrete Wavelet Transform that acts as a Finite Impulse Response (FIR) filter bank. It inherently relies on perfect, discrete time delays—shifting samples in memory (\(z^{-1}\), \(z^{-2}\), etc.)—and multiplying those discrete samples by precise coefficients (the 5 taps for the low-pass, 3 taps for the high-pass).

In C++ on a microcontroller or mapped out in JAX, delaying a sample by exactly one tick is trivial. In the continuous-time analog world, creating a pure, delay-based transversal FIR filter is extremely difficult.

The "Literal" Analog Translation: Bucket Brigades

To do a true FIR wavelet transform in analog hardware, you would need an analog delay line. You would have to use a tapped Bucket Brigade Device (BBD)—like the chips used in analog choruses—to pass discrete voltage voltages down a chain. You would tap the BBD at the specific intervals, route those taps through precision resistor networks to act as your 5/3 coefficients, and sum them at an op-amp.

The reality? The clock noise, signal degradation, and component tolerances of the BBDs would completely ruin the phase coherence.

The Real Analog Equivalent: Active Crossovers

If the goal is to split your guitar signal into three bands for independent compression, analog engineering abandons the wavelet approach entirely and uses continuous-time Infinite Impulse Response (IIR) filtering.

Instead of a lifting scheme, you would build a traditional active crossover network.

1. State-Variable Filters (SVF): Using a quad op-amp (or multiple high-fidelity op-amps like the OPA2134s you are already using for your I/O), you can build an SVF that simultaneously outputs High-Pass, Band-Pass, and Low-Pass versions of the same input signal.
2. Linkwitz-Riley Crossovers: Alternatively, you can cascade 2nd-order Butterworth filters to create 4th-order Linkwitz-Riley crossovers.

The Trade-off: Perfect Reconstruction The primary reason you chose the LeGall 5/3 for the digital realm is likely its perfect reconstruction property. Because it uses integer arithmetic and linear-phase FIR filters, when you sum the three compressed bands back together, the original audio waveform is perfectly preserved without phase distortion.

Analog filters do not have linear phase. When you split a signal with analog high-pass and low-pass filters and sum them back together, the phase shifts introduced at the cutoff frequencies cause constructive and destructive interference (phase smearing or comb filtering) at the crossover points. Linkwitz-Riley crossovers are the analog gold standard because they keep the phase of the two adjacent bands aligned so they sum flat in amplitude, but the overall signal still suffers a non-linear phase shift.

Ultimately, keeping the 5/3 wavelet cascade in the digital firmware is the only way to retain the mathematical purity and phase coherence of that specific tri-band architecture!