Lock-In Correlation Sign Three-Row Scan - Signals and Noise in Physics Measurements Step by Step

A lock-in correlation multiplies each signal sample by a reference sample, then sums the signed products. The scan makes the sign visible: a matching reference accepts, a flat cancellation gives zero, and an opposite reference turns the same pattern negative. The three rows give correlations 4, 0, and -4 against a positive-sign threshold, yielding accepted bits 1, 0, and 0 for the stated toy product ledger. Real lock-in measurements still have reference phase error, baseline drift, harmonic content, and noise-floor uncertainty.

Lock-in acceptance is scanned through positive, zero, and negative correlation. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.

highlighted = computed this step

A matching reference gives positive correlation

Four positive products make correlation four, so the lock-in row is accepted.

4>0\Rightarrow1

Zero correlation is not accepted

A flat reference cancels the signed products exactly to zero.

0\not>0\Rightarrow0

An inverted reference makes the sum negative

The final row is below the same threshold, not just mismatched by name.

\begin{array}{c|c}\text{corr}&\text{accepted}\\4&1\\0&0\\\mathbin{-}4&0\\\end{array}