Summing And Mixing
Canonical Definition
Summing or mixing forms an output by scaling and adding two or more signals. The resulting level and spectrum depend on the coefficients and on the signals' instantaneous amplitude, polarity, phase, frequency content, and correlation.
The Coherent Worst Case
For two equal, fully correlated signals:
y = gL + gR times the original amplitude| Coefficient per input | Coherent output amplitude | Change versus one input |
|---|---|---|
| 1.000 (0 dB) | 2.000 | +6.02 dB |
| 0.707 (-3.01 dB) | 1.414 | +3.01 dB |
| 0.500 (-6.02 dB) | 1.000 | 0 dB |
Two inputs at -3 dB each are often used as a power-preserving convention for uncorrelated signals, but they do not preserve voltage for identical coherent content. Two inputs at 0.5 each preserve the amplitude of fully correlated center content. Neither convention is universally correct without naming the source, target, and margin.
Correlation Changes The Answer
- Fully correlated and same polarity: voltages add directly.
- Partially correlated: the result falls between coherent and uncorrelated cases and varies with time and frequency.
- Uncorrelated: average powers add; two equal sources increase average level by about 3 dB.
- Opposite polarity or opposing phase: content can cancel partially or completely.
A stereo music file contains different correlation at different moments and frequencies. Test tones prove specific cases; representative program material reveals others.
Stereo-To-Mono Is Not Lossless
An L+R sum emphasizes center-correlated content and can reduce or remove elements that are opposite between channels. Some recordings, effects, factory differential signals, and noise-cancellation paths contain intentional side or anti-phase information. Listen and measure the sum rather than assuming all stereo content survives.
When factory channels have different EQ, delay, all-pass filtering, limiting, or crossover bands, summing them can create a response that changes with level and frequency.
Where To Meter
Input meters cannot show the sum. Place or identify a meter:
- on each contributing input
- at the completed summing node
- after post-sum EQ or gain
- before the DAC or physical output
Keep enough margin for the maximum expected coherent condition, not only the average music condition seen during setup.
Verification Signals
- left-only and right-only tones
- identical mono tone in both channels
- one channel polarity-inverted
- uncorrelated noise in each channel
- representative stereo music with wide and centered elements
- factory-source measurements across volume and source modes
Practical Mono-Sub Starting Point
For two normal stereo inputs, 0.5 L + 0.5 R is a conservative starting coefficient set for preserving fully correlated center content at one-input voltage. Then verify:
- the actual source correlation and frequency response
- the post-sum meter and physical output voltage
- loss of anti-phase content
- the downstream crossover, EQ, limiter, and amplifier sensitivity
- the required subwoofer level after acoustic calibration