Understanding HPFs and LPFs

In yesterday’s post, we talked about the phase response of LPFs and HPFs, and how that can sometimes be a reason to use shelving EQ instead.

But this doesn’t mean that HPFs and LPFs don’t have their place! They do, and I use them frequently. I particularly like them in situations where it’s helpful to blur the line a bit between what is and isn’t being filtered.

I realized as I was thinking about HPFs and LPFs, though, that I’m pretty sure a lot of us start off with a misconception about how they actually work. Like, what do the numbers mean? What precisely does it mean when you have a HPF with a corner frequency of, say, 100 Hz?

I know that, for the longest time, I assumed that what that meant was that the downward curve started at precisely 100 Hz. Everything above 100 Hz is untouched, and everything below 100 Hz is being filtered.

But that’s not correct! The way this is measured is a little bit unintuitive; the corner frequency doesn’t measure the point where the line departs from 0, but rather the point at which the curve results in the output being -3 dB down — i.e., 50% quieter.

What’s more, this -3 dB measurement is irrespective of the steepness of the filter. So, if the HPF is 24 dB/oct, then the -3 dB “corner frequency” point is going to be pretty close to the point at which the curve departs from 0, because 24 dB/oct is pretty steep. But if the HPF is a much gentler 6 dB/oct, then the -3 dB point is going to be a full half-octave below the nominal frequency!

So you might in your mind be putting a gentle 6 dB/oct HPF at 100 Hz, thinking that all the frequencies above that 100 Hz corner-frequency number are being left untouched — but, in actuality, that downward descent is starting at more like 150 Hz, give or take.

And this is valuable information! Being able to visualize your curve accurately can help guide your ears to hear what it’s doing.

I told you there was going to be some math — jamie