Interpreting the Phase Trace

Interpreting the Phase Trace

We start with a common topic of confusion: what the heck is this “phase” response trace telling us? Well, it tells us a lot of things, but one aspect of it is something like asking the question “What point in its cycle was this frequency at when the measurement was taken?” For a single frequency, this tells us just about nothing, but when observed over a frequency range, we can glean a lot of useful information for us. We need to look for trends.
 
Here is a very basic rule of thumb that covers a LOT of the common phase trace questions:
 
  • The steeper the phase trace slope, the more time offset exists.
  • If the slope is descending left to right, the arrival is late. If the slope is ascending left to right, the arrival is early.
 
Let me be clear: the phase trace indicates lots of different things, but this simple concept will get you some clarity in a lot of situations.
 
 
 
Let’s see some examples:
 
Here is a trace taken during the benchtesting of a system processor. Note that I personally choose to view magnitude response on top and phase response on the bottom. This is the opposite of the default view in Smaart, so just be aware of that.
 
There’s a few things to point out here:
 
  • The phase trace is descending left to right, so it’s indicating a late arrival, as I mentioned above. In this particular case, I simply hadn’t yet added delay to the analyzer to compensate for the device’s latency. The trace gets steeper with frequency because the same amount of time offset will cause more phase offset at higher frequencies because those cycles happen faster. This is linear – we have twice as much phase offset at 1k as we do at 500 Hz, because the cycle takes half the time. The slope appears to be increasing because of the log frequency axis. If you were to view the phase trace on a linear frequency axis, it would be a constant slope. If you have REW (which you should, because it’s free), give it a try.
  • Looking at the magnitude display, we see that the coherence (the red line across the top) drops above 10 kHz, and the associated frequency response data is no bueno. This is because the time delay is so much that at these frequencies, the information comes back outside the time window and therefore is not considered to correlate with the reference signal. Think about an echo that takes a week to come back – it no longer correlates with what we yelled to cause the echo, and so it’s now “noise.” That’s what the coherence trace shows us – how confident it is in the answer it’s giving. Put another way, is the frequency response this way because it’s related to the reference signal? Or is there just noise in the room that has nothing to do with our test signal? How do we tell HVAC from LF pink noise? The analyzer will do the same calculation a bunch of times and average the result over successive measurements. Returning the same answer over and over is high coherence. If it’s wandering around, or what the mic is picking up doesn’t seem to be related to the signal we’re sending out, coherence drops.
 
We can actually figure out how much delay we’re dealing with by doing a little math. The first wraparound passes through 0 again at just about 1 kHz, so we’ve gone 360° (one cycle) back over a 1000 Hz range. 1/1000 = 1 ms. 
 
So let’s look at how we might actually use this knowledge in the wild.
 
This image shows measurements taken of two speakers (Left and Right) in a small home audio listening room (with nasty acoustics, but that’s another topic).
We have a few problems here but direct your attention to the phase trace. At the listening position, where this measurement was taken, one of the speakers is arriving earlier (because it’s closer). Which one? That would be the thicker teal trace, because it has a steeper slope (more time offset) and it’s ascending from left to right (early arrival). We have to look at the HF here because the LF has the normal descending trend associated with LF drivers AND we’ve got some bad modal issues interfering. We do a whole wrap (whole cycle) between 2k and 3k so let’s add a millisecond delay to that channel in the DSP.
Much better. In a large venue situation (larger than one listener) this is close enough for show business, because moving over one seat will result in a completely different result. But this is a listening room and we know exactly where the listener is going to be sitting so let’s get closer.
 
We’re about 90 degrees off at 8 kHz. A full cycle at 8 kHz is .125 ms, so we don’t need much delay to fix this. In fact, a quarter cycle (90°) would be 31 microseconds (heh) so let’s change our delay to .95 ms and see if we miss it the other way.
We do indeed. The final solution ended up being 0.954ms:
I could have actually locked in all the way up to 16 kHz given a DSP with sufficient delay resolution, but the distance between the listener’s ears is multiple wavelengths at these frequencies so drilling down any further is arguably pointless since both ears can’t even perceive the benefit, plus I was ready for my lunch break at that point.

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