Hi. Welcome back, and happy new year.
This one is prompted by a question I recently saw on social media
about the phase shift in minimum phase EQs such as ReaEQ,
and specifically how to interpret the phase response curve
that you can choose to show if you want.
Predictability many people answered this question by saying that the EQ delays certain frequencies,
which results in phase shift.
But this answer is problematic. If you've watched one of my previous videos you'll know
that a minimum phase EQ can cancel itself out, if you run equal and opposite settings,
and that this doesn't only cancel out the boosts and cuts, but also the phase shifts.
If the phase shift is caused by delay, how does a zero latency EQ plug that requires
no plugin delay compensation manage to cancel itself out?
This implies that it can see into the future and apply a negative delay...
So here's my little demonstration: I've a burst of sine wave at 100Hz which I simply
rendered out of the provided JS tone generator plugin,
and I’ve created three copies.
Interestingly the JS tone generator always starts high at full positive excursion,
but thats ok, doesn’t matter.
Now lets unmute the first copy, right click… and invert the phase to quite literally turn
the waveform upside down. Now its starts low,
and for every peak in the original there’s a trough in the copy.
Now when I press play… we get silence as you’d expect:
they cancel out perfectly.
Ok lets move onto the next one,
and this time I’ll bring up the nudge dialog.
Now, this being a 100Hz sine wave, logically one full cycle must take 10ms,
so if I nudge this clip to the right by 5ms… we should have shifted it by half a cycle…
and sure enough the peaks and troughs now line up with the inverted copy above.
If I play this back… we get a blip at the start where the copy comes in later,
and a blip at the end where the original stops sooner,
but in between the two signals cancel perfectly again.
So lets think about that for a moment: we’ve achieved a 180 degree phase reversal
in two different ways. Here we’ve done it with 5ms of delay.
But up here we’ve done it without any delay.
Another difference: if this was a 200Hz sine wave, then inverting the polarity would still
cause a 180 degree phase reversal.
But delaying a 200Hz signal by 5 ms will actually shift it by a full cycle.
It will be shifted 360 degrees and end up back in phase with the original.
This is why mixing delayed signals with the original results in comb filtering of course.
But anyway, there’s the proof: delaying the signal always means phase shift.
But we can achieve 180 degrees of phase shift just by turning the signal upside down with no delay.
Ok, now you’re saying that inverting the polarity is a special case, and doesn’t
help us to consider phase shift from EQ.
And yes, I’ll accept that.
So lets try another method.
Here’s the final copy,
and I’ve added an instance of ReaEQ to the track.
Lets delete all but a single band…
and switch that to an All Pass filter.
This is an interesting filter type that doesn’t affect the frequency response at all:
if i adjust he Gain slider, nothing happens, the frequency response just remains flat.
But if we tick “show phase” we can see that this filter causes a 180 degree phase shift at the target frequency,
which then returns gradually to zero phase either side.
So lets set this to exactly 100Hz…
and see what happens to our null.
At first this seems very similar to the delay:
we get a blip at the start and end,
but in between there’s a perfect null.
The first clue that its not the same lies in the sound:
lets listen to the delayed version again…
that blip doesn’t sound the same as this one…
Lets render that out again so we can see whats happening to the waveform...
and look how interesting this is:
there’s the original underneath,
and here’s the verion thats passed through our allpass filter
Don't be fooled by the little ramp before the start
Reaper simply joins the dots with straight lines when zoomed in this tight, so this does
indeed represent all zeroes until the original waveform suddenly starts high…
and the processed version also starts high, so it seems there’s no phase shift yet.
But look how quickly it reverses direction…
and by the time the delayed copy comes in its already reversed its polarity to match..
In fact it seems to anticipate the delayed copy, and start to shift much earlier in the cycle.
So it can’t be just delay, right?
Otherwise the sine wave would start 5ms later, just like my delayed copy.
But there’s another interesting difference: notice that this cycle here…
although already shifted in phase… is not quite yet at full amplitude.
This peak clearly peaks higher than that one.
This I believe is filter ringing, which might sound a bit strange…
but lets take a look at the end of the test tone, because interesting things happen there too.
Notice how the processed version continues beyond the end of the original wave… and
also continues beyond the delayed copy as well… the filter rings on for longer.
In fact all filters ring. Linear phase filters have equal ringing both before and after the
original impulse. But minimum phase filters like these only ring after the impulse.
And actually in theory they continue to ring infinitely as they use feedback loops,
but thats not relevant here.
The important point is, any system that takes time to stop resonating at a certain frequency
is also going to need some time to start resonating at that frequency,
so ringing after the impulse is also matched by a kind of ramp up at the start of the impulse…
which is I believe what we’re seeing at the start of the tone.
Lets have another look at the end, because there’s another interesting phenomenon you may have noticed:
whats going on with that huge downward spike where the original waveform stops?
So, lets consider the original waveform, and where it suddenly stops,
plunging instantly from full excursion down to zero.
That sudden downwards spike is in fact a short burst of all frequencies.
If we consider that spike separately from the 100Hz test tone
its suddenly easy to see that the sine wave has shifted in phase,
while the spike has remained mostly intact.
But instead of going from a positive value down to zero,
that spike now goes from a negative value to an even more negative value,
and by the look of it almost doubles the peak level of the wave.
So this actually answers another common social media question:
How come an EQ cut makes my track louder?
Which in fact should really be: how come phase shift can make my peak levels higher?
But that might be a topic for another day.
Thats all for now, thanks for watching.