Understanding Audio Frequency Response & Psychoacoustics (Video)

[dorirod]

Thank you Amir, great video, for myself the best one so far! I am not sure I understand if there actually is an ERB adaptive smoothing filter out there? Does REW have one? Does NFS have one for the graphs it can produce? Is there a standard formula that is agreed upon?

Also, when producing PEQ filters, do you have a guideline as to what min/max Q would be audible in each region of freq?

Thank you

 

[Andrej]

Hey Vini darko, the graph is logarithmic. Here's a link that should help explain it:
https://en.wikipedia.org/wiki/Logarithmic_scale

Edit: I should say it's semi logarithmic ie logarithmic only on one axis

It is logarithmic on both axes. dB is a measure of ratios, thus inherently logarithmic/exponential. Every linear increase in deciBells magnifies the observed value by multiplying it by a constant factor.

 

[Robbo99999]

For some of you this is old news but for many, I thought it would be good to do a tutorial on frequency response. No, not the trivial aspects of it but digging into psychoacoustics so that you can properly analyze headphone, speaker and room measurements and determine audibility of deviations from neutral.

Article Referenced:
Perceptual Effects of Room Reflections: https://www.audiosciencereview.com/...ds/perceptual-effects-of-room-reflections.13/

Thanks for the revelations re ERB's in terms of how their wideness increases with frequency and the fact that we "average" the sound power of the response within an ERB....your EQ testing procedure at 18:40 was something that I could do in the future when testing EQ's of my speakers & headphones. In fact I can incorporate some of this newfound knowledge with a renewed Room EQ attempt on my speakers that I have been planning to do anyway using the MMM method which is new to me (vs multiple static microphone measurements that I was doing before). I'm thinking this new awareness of the ERB situation could save me a few filters which would be particularly useful when using my miniDSP 2x4 that "only" has 12 filters available, and I'll be wanting to combine an Anechoic EQ of my 308p's with Room EQ to fit within those 12 filters......so knowledge of the ERB situation means I'm more likely be able to fit both Room EQ & Anechoic EQ within the limitations of my miniDSP. When I'm using Equaliser APO with it's unlimited number of filters then I suppose this is less critical and I may not be able to stop myself striving for greater objective perfection, but I can certainly bare all this in mind when EQ'ing using my miniDSP!

EDIT: re ERB's, does REW's Var Smoothing option directly take into account ERB's increasing wideness as you go up the frequency range......it seems like it does?

 

[MRC01]

... I have a question about the way the frequency graph is laid out. Why do the box sizes vary like they do? They start wide , go narrow then wide then narrow ect. It doesn't seem to correlate with any aspect of pshcoacoustics that I've heard discussed.
...

This is a logarithmic X scale. It matches the psychoacoustics of how we perceive frequency. Perceptually, the difference between 50 Hz and 100 Hz is the same as 5000 Hz to 10000 Hz. We perceive each as 1 octave even though the actual difference is only 50 Hz in the first case and 5000 Hz in the second. The ratio is the same, and that is how we perceive frequency differences.

PS: Another example can help clarify: consider the notes in a scale (like a piano). 12 notes in an octave, so the ratio of each note to the next is the 12th root of 2, which is about 1.059. So each musical note is about 5.9% difference in pitch. That is, if A = 440 Hz, then A# / Bb = 440 * 1.059 = 466 Hz. And 2 octaves higher, A = 1760 Hz and A# / Bb = 1864 Hz. The difference sounds the same, because it's the same ratio, even though in absolute arithmetic terms, the higher frequencies are further apart.

That (log scale) is why the vertical divisions of the X axis have uneven spacing.

 

[dougrus]

Ive been mixing music for 20 years and never really took auditory filter bandwidth into consideration on my filters. A lot of those little high-mid bumps were doing a lot less than I thought, more than likely. Thank you so much for this informative video.

 

[Andrej]

Looking at the article quoted at the beginning of the review, quoting here:
"As an example, at 300 Hz source frequency (horizontal axis), the ear’s sensitivity or discrimination is a narrow 60 Hz (vertical axis). At the other extreme, for a source frequency of 10 KHz, the level climbs way up to 1.1 KHz. This readily shows that we are far less sensitive to frequency variations at 10 KHz than we are at 300 Hz."
The correct interpretation is the exact opposite. At 300Hz the sensitivity is 1/5th of the center frequency, but at 10 kHz it is approx 1/10 of the center frequency, so we are twice as sensitive at 10 kHz. An octave is essentially based on the "ratio" of bandwidth and center frequency, and it should apply here too.

 

[jaakkopasanen]

There seems to be some confusion here nobody has addressed yet. The key point in the video is how the equvalent rectangular bandwidth (ERB) grows as frequency grows which means that two sounds in high frequencies need to be further apart (in Hertz) than in lower frequencies for humans to be able to discriminate the sounds. However when we look at bandwidth in octaves, we'll see that the bandwidth decreases as frequency goes up. Combine this with the fact that frequency response graphs typically have logarithmic x-axis and the conclusion is that a peak or a dip in the frequency response graph of the same width will be more audible in high frequencies than in low frequencies. So the opposite of @amirm 's statement.

Here's the plot of ERB in octaves vs frequency

Moreover, Room Eq Wizard has an ERB smoothing function where the high frequencies are smoothed with narrower smoothing window than low frequencies: https://www.roomeqwizard.com/help/help_en-GB/html/graph.html

 

[ck42]

Also enjoyed this one the most....so far.
Also had the question....is there a smoothing filter that can apply smoothing while taking ERB's into consideration? ('ERB-smoothing') Seems super obvious that this is what we should all want after watching this!

 

[Vini darko]

Hey Vini darko, the graph is logarithmic. Here's a link that should help explain it:
https://en.wikipedia.org/wiki/Logarithmic_scale

Edit: I should say it's semi logarithmic ie logarithmic only on one axis

Thanks the link helped. Turns out logarithmic means a slightly different thing than I thought I had it confused with linear

 

[Andrej]

There seems to be some confusion here nobody has addressed yet. The key point in the video is how the equvalent rectangular bandwidth (ERB) grows as frequency grows which means that two sounds in high frequencies need to be further apart (in Hertz) than in lower frequencies for humans to be able to discriminate the sounds. However when we look at bandwidth in octaves, we'll see that the bandwidth decreases as frequency goes up. Combine this with the fact that frequency response graphs typically have logarithmic x-axis and the conclusion is that a peak or a dip in the frequency response graph of the same width will be more audible in high frequencies than in low frequencies. So the opposite of @amirm 's statement.

Here's the plot of ERB in octaves vs frequency
View attachment 125657
Moreover, Room Eq Wizard has an ERB smoothing function where the high frequencies are smoothed with narrower smoothing window than low frequencies: https://www.roomeqwizard.com/help/help_en-GB/html/graph.html[/QUOTE
You are absolutely correct. Perhaps a simpler rule of thumb (also used in speech modeling) is to think about it this way:
Below 1kHz, as you go down in frequency you should widen the window when looking for meaningful anomalies in frequency response, and above 1kHz, keep the window constant, as we are less sensitive as you go down in frequency blow about 1kHz. Not exact, but good enough.

 

[jaakkopasanen]

@Andrej looks like you were faster so "nobody has addressed yet" wasn't entirely correct.

 

[Robbo99999]

There seems to be some confusion here nobody has addressed yet. The key point in the video is how the equvalent rectangular bandwidth (ERB) grows as frequency grows which means that two sounds in high frequencies need to be further apart (in Hertz) than in lower frequencies for humans to be able to discriminate the sounds. However when we look at bandwidth in octaves, we'll see that the bandwidth decreases as frequency goes up. Combine this with the fact that frequency response graphs typically have logarithmic x-axis and the conclusion is that a peak or a dip in the frequency response graph of the same width will be more audible in high frequencies than in low frequencies. So the opposite of @amirm 's statement.

Here's the plot of ERB in octaves vs frequency
View attachment 125657
Moreover, Room Eq Wizard has an ERB smoothing function where the high frequencies are smoothed with narrower smoothing window than low frequencies: https://www.roomeqwizard.com/help/help_en-GB/html/graph.html

Thanks for the tip about ERB smoothing function in REW, I didn't know about that. How come Var Smoothing is recommended at that link for EQ purposes and not the ERB smoothing function......is there much difference?

 

[ernestcarl]

Also enjoyed this one the most....so far.
Also had the question....is there a smoothing filter that can apply smoothing while taking ERB's into consideration? ('ERB-smoothing') Seems super obvious that this is what we should all want after watching this!

There really isn't much difference between ERB smoothing and psychoacoustic smoothing. One could also apply frequency dependent windowing which takes into account the time domain information as another comparison curve. Add to that the anechoic curves Amir already provides as another reference when one is EQ'ing...

 

[ck42]

There seems to be some confusion here nobody has addressed yet. The key point in the video is how the equvalent rectangular bandwidth (ERB) grows as frequency grows which means that two sounds in high frequencies need to be further apart (in Hertz) than in lower frequencies for humans to be able to discriminate the sounds. However when we look at bandwidth in octaves, we'll see that the bandwidth decreases as frequency goes up. Combine this with the fact that frequency response graphs typically have logarithmic x-axis and the conclusion is that a peak or a dip in the frequency response graph of the same width will be more audible in high frequencies than in low frequencies. So the opposite of @amirm 's statement.

Here's the plot of ERB in octaves vs frequency

Moreover, Room Eq Wizard has an ERB smoothing function where the high frequencies are smoothed with narrower smoothing window than low frequencies: https://www.roomeqwizard.com/help/help_en-GB/html/graph.html

Regarding your very last statement....shouldn't the smoothing be done on a -wider- frequency range at higher frequencies, and lower frequencies smoothed using -narrower- frequency widths? Or did I just completely misunderstand Amir's discussion on ERB?

 

[Midwest Blade]

Hope we don't have to start taking exams with all the teaching... I always hated taking exams.

This was another really good video!

 

[Omar Cumming]

I thought I understood frequency response until I saw this, turns out I didn't. See my tagline below.

Superb teaching video. Thanks Amir!

Cheers

 

[ck42]

REW:

ERB smoothing

uses a variable smoothing bandwidth that corresponds to the ear's Equivalent Rectangular Bandwidth, which is (107.77f + 24.673) Hz, where f is in kHz. At low frequencies this gives heavy smoothing, about 1 octave at 50Hz, 1/2 octave at 100 Hz, 1/3 octave at 200 Hz then levelling out to approximately 1/6 octave above 1 kHz.

So there we go. This is going to be my new default smoothing in REW

 

[ernestcarl]

Thanks for the tip about ERB smoothing function in REW, I didn't know about that. How come Var Smoothing is recommended at that link for EQ purposes and not the ERB smoothing function......is there much difference?

I only use variable smoothing with single point measurements...

 

[ernestcarl]

Take a spatial average of, say, 20+ -- or better yet -- 50+ measurements and there really is not much point smoothing it further down more -- although I do still tend to use psychoacoustic on top sometimes. MMM is a way quicker alternative.

 

[Robbo99999]

Take a spatial average of, say, 20+ -- or better yet -- 50+ measurements and there really is not much point smoothing it further down more -- although I do still tend to use psychoacoustic on top sometimes. MMM is a way quicker alternative.

I can see how many different measurements would provide their own smoothing when you average them....I'll be giving MMM a go when I feel like having another stab at room EQ, then I'll take a look at the averaged results and make a decision re if & what smoothing to apply. To be honest I'm only gonna be EQ'ing it below the transition zone in terms of any measurements I make, and I'll do an Anechoic EQ above the transition zone.