Completely cut frequencies below a certain threshold

Question

I'm warming up to Ableton Live by attempting to manipulate songs into how various animals would hear them.

For example, idealized bats hear roughly between octave 7, starting at 1.28kHz, to octave 13, ending at about 164kHz. Just like us, their sensitivity to sounds in their hearing range drops off toward the edges (they hear 20kHz really well, but 2kHz & 150kHz would be really quiet).

Ok, so, I load a song into a Live clip, and I add an EQ device, and I cut off low frequencies below about 1.28kHz. However, this is what the frequency visualization shows me:

Far from ending the frequencies at 1.28 and rounding them in above that, it seems that many frequencies, the whole way down to 50Hz, are still in this audio. And indeed, the human vocal range ends at about 1100Hz (though Jeff Mangum's seems to be centered around 610 in this song), but the singing can still be heard very clearly with this EQ in effect (& it doesn't just sound like overtones).

So I could "eye it up" to ensure that I don't, in this particular song, see any frequencies leaking in below my cutoff. But that feels incredibly unscientific. Is there a better way to EQ or limit my audio to get the (admittedly strange) effect I want?

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Related: Why's the EQ visual end at just above 11k? That leaves more than half an octave of human hearing out! (I know, I know, it's all just air, but still.) It would actually be kinda nice to be able to see some higher pitches in my visual, just to have some sense of what my bat might hear. Bonus points if you know a way to do this! (Above 44kHz would all just be digital noise, I realize, since that's the sampling rate of this track, but that could still be interesting, since I think a bat would indeed hear that digital mess.)

Answer 1

Using a higher order filter will give you a greater roll-off slope in the filters stop-band. So a 1st order filter has a roll-off slope of -6db/octave, 2nd order filter has a roll-off slope of -12db/octave, 3rd order filter has a roll-off slope of -18db/octave, 4th order filter has a roll-off slope of -24db/octave, etc. This means the filter does not act like a brick wall and some frequency content beyond the cut-off will be present, but at a corresponding reduced level. Also remember that the cut-off frequency is the point the filter has reduced the level by -3dB (also know as the half-power point or the signal level has been reduced by 0.707).

Most audio filters have a fairly low order as we normal want to hear frequencies being reduced in a fairly slow way. Most common are 2nd order, -12db/octave or 4th order, -24db/octave, but sometimes 3rd order also pops up. Typically, it is rare to see much higher order filters implemented. However, you can achieve an accumulative result by using filters is series, that is feeding your audio into one filter and then the resulting audio into a second filter. So if you used 2nd order filters the accumulative result would be -48db/octave reduction.

With this knowledge you should be able to choose appropriate settings to get the result that you are after. Again though you might want to look at the actual frequency response of these animals as it would seem unlikely that their hearing is linear.

Answer 2

Those combined EQ + spectroscopes can seem a bit misleading. The curve on your EQ isn't always what's actually happening, and similarly metering is only an averaging of the signal because audio is a much faster rate than your monitor. With a regular eq it's really more about using your ears to find something that works. You might be better off using an FFT filter for this, you will have more accurate control of individual frequencies which may be better for you.

This is the one in Audition, you can draw any shape you like here and the result is surgically accurate:

Answer 3

This is not possible by traditional, analogue means. As said by Bit Depth, such filters have a property called the order. What that means: the response of a filter of order n can be written as

              ( a_n ⋅ ωⁿ + a_n-1 ⋅ ω^n-1 + ... + a₂ ⋅ ω² + a₁ ⋅ ω + a₀ )
A(ω) =  ———————————————————————
              ( b_n ⋅ ωⁿ + b_n-1 ⋅ ω^n-1 + ... + b₂ ⋅ ω² + b₁ ⋅ ω + b₀ )

For this to be exactly zero, the numerator must be zero. That's a polynomial. As we know, a polynomial can only be zero at single, discrete points¹: so you can perfectly filter away a single frequency with a notch filter, but you can't completely "kill" an entire band, only attenuate it. In particular, to get a roll-off, the best you can do is use the denominator. If that grows towards infinity, then the response goes to zero; but it can't grow faster than ωⁿ, so even at high frequencies there's always some signal left.

Well, except of course, if you use an infinite order filter! This doesn't exists in the analogue realm, and since most EQs are at least modelled after analogue circuits you usually won't find it there either; but it can actually be approximated pretty well by digital means: by convolution. Because the convolution kernel is a sinus cardinalis function, such a filter is called sinc filter.

Convolution is mathematically infeasible if you do it directly, so these filters are usually implemented with some fourier-transform trick. Hence, the plugins are often called something like "FFT EQ", but strictly speaking the correct name is FIR filter. That's indeed the name of that plugin in Reaper, you can try it out: ReaFIR.

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¹Unless you simply make all coefficients zero... but then you've simply switched the entire signal off.

Answer 4

Nothing definite since I can't play around with it first hand, but what might have happened here is that you put the EQ as an effect on top of the audio file, but didn't render it to permanently change the audio file itself. So, when you go to view the waveform, it's still showing you the original, un-eq'd waveform.

I'm not that familiar with ableton, but I know with pro tools you have the option of either putting an EQ in the plug in chain (which doesn't actually change the source sound, just the output of the chain), or setting one and then applying it and having it rerender your file (which does change the file).

Additionally, EQ's can vary on what they're actually cutting off. Some will completely cut off the sound below the bottom point, while others only attenuate what's there.

For your related section, I'm on the fence on whether it's actually getting cut off here. In pro tools that one bar from 11k to the next actually covers the range up to 20k.

Hope this helps.

Answer 5

Theres really more to the limitations , phase will destroy you if u cut so steep, you will have 2 ugly bells at the spots you cut steep which will not be real.

cause when you don't hear a frequency it's not like it's EQed out of your brain or nature or something, u just dont hear it. But if you do this process by equalizing you will get ugly phase problems that will not reflect what the animal really hears. Maybe use a linear EQ which doesn't produce bells.