Coherence Averaging Calculator for Measurements

There is a nice smooth transfer function trace on your screen. Phase are handled and magnitude response is flat. You look at the EQ moves and everything looks clean. But something doesn’t feel right, maybe the measurement isn’t to be trusted. Did some room noise get into it? Was microphone moved while taking the sweep?

In that situation, more than what the curve says, amount of coherence say if data is real signal or merely statistical noise. That’s where magnitude squared coherence comes into play. This is how much of measurement was actualy your source vs. It is random stuff interfering with your test.

What Is Coherence?

Many people often use averaging as a way to fix poor data. When you put in your rejection rate and number of frame into the calculator above, it do the math for you. This keeps us from assuming that more is always better in terms of averages. Adding more frames merely stabilizes an incorrect answer if microphone has shifted or system itself has drifted off tune. Knowing how many frames makes sense only if you know what constitutes an effective average.

Choices like windows and overlap will decreases the independence between each frame. For example, a 50% overlapped Hann window provides nice-looking displays but severely reduces number of independent data points different than no-overlap. That is part of tradeoff required for real-time monitoring, but it loses some statistical power when trying to find a specific crossover frequency.

Signal-to-noise ratio and coherence are easily understood as well. Adding uncorrelated energy to the mix decrease coherence. Decent signal dominance would be represented by a coherence value around point nine. Getting into the nineties takes quite a bit more signal compared to noise level. As you see in the reference table on the page, random numbers generates very deceptive coherence results because low averages can produce very high coherence levels. Setting a reasonable confidence limit makes all the difference.

What if your measured coherence number fall below this random number limit? The trace is statistically worthless. There’s no such thing as an EQ’d ghost. These inputs deserve attention because practical measurement scenarios show their need.

Low frequency coherence is one such area where room equalization can struggle. Traffic noise or HVAC rumble will inflate the noise floor without providing significant energy within signal itself. Here, a larger FFT size will serve to reduce the bandwidth of each bin, so it increase the signal-to-noise ratio per bin and improves coherence as a naturaly side effect.

Another challenge is subwoofer alignment, in which case long decay times smears the impulse response, killing coherence in higher frequencies. The trick here is to realize that you’re not battling the software settings; you’re fighting physics of the room. Good measurements are destroyed by source stability. No amount of averaging would of recover from a wobbling mic stand or a vibrating speaker cabinet.

Frame rejection is a feature, not a bug. Let your analyzer throw away bad frames. Thirty clean averages is worth more than sixty contaminated ones. You’ll just end up diluting your signal with non-linear artifacts.

Look at the results and concentrate on the bands you’re going to spend your time listening to. Don’t waste your time chasing perfect numbers out in ultrasonic range where nobody cares. Keep in mind, trust your setup more than your display. In a noisy situation a trace may appear too good to be true; it most likely is.

The guardrails of coherence prevent this from becoming phantom data. After confirming that the coherence holds for the effective averages and within the confidence limits, begin adjusting filters. A pretty curve without coherence is simply colorful noise, ready to spoil system tuning. Control the environment, keep the geometry constant and let the statistics do the work before you rely on any one point on the graph.