◬ MIMZY · instrument № 12 · the analog–quantum suite · SOFTWARE
The Kernel Lab
A convolution kernel is analog software: a small shape you slide along a signal. An RC filter is analog hardware: a resistor and a capacitor. This lab runs your signal through both at once — the software kernel and the simulated circuit — overlays the outputs, and measures their disagreement live. They are the same machine.
⊙ EDUCATIONAL & SIMULATION — y = x ∗ k (software) vs dv/dt = (x−v)/RC (hardware), agreement measured live
signal source (the folders of the lab)
kernel (each one has a hardware twin)
Input signal x(t)
Output — software kernel vs hardware circuit
software: convolution y = x ∗ khardware: circuit simulation
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The kernel k(t)
The hardware twin
How real is this? Entirely. An RC low-pass filter's impulse response is exactly the decaying exponential kernel (1/τ)e^(−t/τ) — convolving with that kernel and integrating the circuit equation dv/dt = (x−v)/RC are two descriptions of one machine, and the live deviation readout shows them agreeing to numerical precision (the residue is discretization, shrinking with step size). The boxcar's twin is an ideal integrate-and-dump; the Gaussian's twin is a cascade of RC stages (by the central limit theorem, many RCs → Gaussian); the differencer's twin is a CR high-pass in its small-τ limit. This identity — kernel = circuit, software = hardware — is the working heart of analog computing, and of every DSP chip that replaced one.