This sandbox was generated by Claude (Anthropic) for the DSP 101 course
materials. Every curve and every number on it is computed in your browser: the
template and its energy, seeded Gaussian noise, the full cross-correlation and its peak, the
processing gain 10·log10(N), the input and output SNR, and the analytic
ROC from P_fa = Q(tau/sigma) and P_d = Q((tau−A)/sigma). The
correlation peak you see is the sum of products the matched filter forms; nothing is
sketched.
The ROC is exact for the Gaussian model, and there is also a real Monte-Carlo run.
Switch on the empirical overlay and the page draws thousands of seeded H0/H1 draws through the
same threshold and plots the measured (P_fa, P_d) pairs — they converge onto
the analytic curve, so the two are shown agreeing rather than one being asserted.
Every relation on this page is a definition or a theorem the course itself states — the
matched filter as a cross-correlation, its output SNR, the 10·log10(N)
processing gain of coherent integration, and the Gaussian-model ROC with
P_d ≥ P_fa. Nothing here rests on a figure transcribed from a
standards document, so this page raises no “verify against the source” flag.
Chosen rather than computed, and marked where it matters: the preset template shapes,
the default amplitude, noise level, template length, threshold and seed, the offset the
template is buried at, and the Monte-Carlo trial count. The templates are normalised to unit
average power so that E_s = N and the processing gain is exactly
10·log10(N) for every shape.
Course demo — linked from the Module 10 lesson decks; the page itself is English‑only for now. Built for DSP-101 Module 10 (Correlation and Detection). Bury a known template in seeded Gaussian noise, run the matched filter — a cross-correlation of the received record with the template — and watch the correlation peak stand out at the true lag where the raw record shows nothing. The gain is 10·log10(N) for an N-sample template. Then sweep the detection threshold and read the ROC: a longer template or a higher SNR bows the ROC toward perfect detection, and at zero SNR it is the diagonal.