Thoughts About Software Equalizers

If a software-equalizer possesses GUI controls that correspond to approximate octaves, or repeated 1-2-5 sequences, it is entirely likely to be implemented as a set of bandpass filters acting in parallel. However, the simplistic bandpass filters I was contemplating, would also have required that the signal be multiplied by a factor of 4, to achieve unit gain where their low-pass and high-pass cutoff frequencies join, as I described in this posting.

(Edit 03/23/2017:

Actually, the parameters which define each digital filter, are non-trivial to compute, but nevertheless computable when the translation into the digital domain has been carried out correctly. And so a type of equalizer can be achieved, based on derived bandpass-filters, on the basis that each bandpass-filter has been tuned correctly.

If the filters cross over at their -6db point, then one octave lower or higher, one filter will reach its -3db point, while the other will reach its -12db point. So instead of -12db, this combination would yield -15db.

The fact that the signal which has wandered into one adjacent band is at -3db with respect to the center of that band, does not lead to a simple summation, because there is also a phase-shift between the frequency-components that wander across.

I suppose that the user should be aware, that in such a case, the gain of the adjacent bands has not dropped to zero, at the peak of the current band, so that perhaps the signal will simplify, if the corner-frequencies have been corrected. This way, a continuous curve will result from discrete settings.

Now, if the intention is to design a digital bandpass filter with greater than 6 db /Octave falloff curves, the simplistic approach would be just to put two of the previous stages in series – into a pipeline resulting in second-order filters.

Also, the only way then to preserve the accuracy of the input samples, is to convert them into floating-point format first, for use in processing, after which they can be exported to a practical audio-format again. )

(Edit 03/25/2017 :

The way simplistic high-pass filters work, they phase-shift the signal close to +90⁰ far down along the part of the frequency-response-curve, which represents their roll-off. And simplistic low-pass filters will phase-shift the signal close to -90⁰ under corresponding conditions.

OTOH, Either type of filter is supposed to phase-shift their signal ±45⁰, at their -3db point.

What this means is that if the output from several band-pass filters is taken in parallel – i.e. summed – then the center-frequency of one band will be along the roll-off part of the curve of each adjacent band, which combined with the -3db point from either its high-pass or its low-pass component. But then if the output of this one central band is set to zero, the output from the adjacent bands will be 90⁰ apart from each other. )

(Edit 03/29/2017 :

A further conclusion of this analysis would seem to be, that even to implement an equalizer with 1 slider /Octave properly, requires that each bandpass-filter be a second-order filter instead. That way, when the signals wander across to the center-frequency of the slider for the next octave, they will be at -6db relative to the output of that slider, and 180⁰ phase-shifted with respect to each other. Then, setting the center slider to its minimum position will cause the adjacent ones to form a working Notch Filter, and will thus allow any one band to be adjusted arbitrarily low.

And, halfway between the slider-center-frequencies, the gain of each will again be -3db, resulting in a phase-shift of ±90 with respect to the other one, and achieving flat frequency-response, when all sliders are in the same position.

The problem becomes, that if a 20-band equalizer is attempted, because the 1 /Octave example already required second-order bandpass-filters, the higher one will require 4th-order filters by same token, which would be a headache to program… )

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How certain signal-operations are not convolutions.

One concept that exists in signal processing, is that there could be a definition of a filter, which is based in the time-domain, and that this definition can resemble a convolution. And yet, a derived filter could no longer be expressible perfectly as a convolution.

For example, the filter in question might add reverb to a signal recursively. In the frequency-domain, the closer two frequencies are, which need to be distinguished, the longer the interval is in the time-domain, which needs to be considered before an output sample is computed.

Well, reverb that is recursive would need to be expressed as a convolution with an infinite number of samples. In the frequency-domain, this would result in sharp spikes instead of smooth curves.

I.e., If the time-constant of the reverb was 1/4 millisecond, a 4kHz sine-wave would complete within this interval, while a 2kHz sine-wave would be inverted in phase 180⁰. What this can mean is that a representation in the frequency-domain may simply have maxima and minima, that alternate every 2kHz. The task might never be undertaken to make the effect recursive.

(Last Edited on 02/23/2017 … )

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A Thought on SRS

Today, when we buy a laptop, we assume that its internal speakers offer inferior sound by themselves, but that through the use of a feature named ‘SRS’, they are enhanced, so that sound which simply comes from two speakers in front of us, seems to fill the space around us, kind of how surround-sound would work.

The immediate problem with Linux computers is, that they do not offer this enhancement. However, technophiles have known for a long time that this problem can be solved.

The underlying assumption here is, that the stereo being sent to the speakers should act as if each channel was sent to one ear in an isolated way, as if we were using headphones.

The sound that leaves the left speaker, reaches our right ear with a slightly longer time-delay, than the time-delay with which it reaches our left ear, and a converse truth exists for the right speaker.

It has always been possible to time-delay and attenuate the sound that came from the left speaker in total, before subtracting the result from the right speaker-output, and vice-verso. That way, the added signal that reaches the left ear from the left speaker, cancels with the sound that reached it from the right speaker…

The main problem with that effect, is that it will mainly seem to work when the listener is positioned in front of the speakers, in exactly one position.

I have just represented a hypothetical setup in the time-domain. There can exist a corresponding representation in the frequency-domain. The only problem is, that this effect cannot truly be achieved just with one graphical equalizer setting, because it affects (L+R) differently from how it affects (L-R). (L+R) would be receiving some recursive, negative reverb, while (L-R) would be receiving some recursive, positive reverb. But reverb can also be expressed by a frequency-response curve, as long as that has sufficiently fine resolution.

This effect will also work well with MP3-compressed stereo, because with Joint Stereo, an MP3 stream is spectrally complex in its reproduction of the (L-R) component.

I expect that when companies package SRS, they do something similar, except that they may tweak the actual frequency-response curves into something simpler, and they may also incorporate a compensation, for the inferior way the speakers reproduce frequencies.

Simplifying the curves would allow the effect to break down less, when the listener is not perfectly positioned.

We do not have it under Linux.

(Edit 02/24/2017 : A related effect is possible, by which 2 or more speakers are converted into an effectively-directional speaker-system. I.e., the intent could be, that sound which reaches our filter as the (L) channel, should predominantly leave the speaker-set at one angle, while sound which reaches our filter as the (R) channel, should leave the speaker-set at an opposing angle.

In fact, if we have an entire array of speakers – i.e. a speaker-bar – then we can apply the same sort of logic to them, as we would apply to a phased-array radar system.

The main difference with such a system, as opposed to one based on the Inter-Aural Delay, is that this one would absolutely require we know the distance between the speakers. And then we would use that distance, as the basis for our time-delays… )

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HBS-750 Equalizer Function Actually Useful

The shape of my ears has generally been a problem, for ear-pieces to fit, in my past. Mine are narrow, so that I need the most narrow inserts already. But then it can happen to me, that my facial muscles tense differently, at different times of day, which I believe causes a subtle change in the shape of my ears. Do not laugh. And so simply because I may be cracking a smile, I will also be cracking a non-airtight gap between ear-pieces that just fit, and my ears, which results in a sudden loss of deep bass.

The LG HBS-750 Headphones have an equalizer function, that switches between three modes:

 

  1. Bass boost (the default),
  2. Flat,
  3. Treble boost.

 

When I try these settings indoors, at first the difference seems so slight, I tend to think, ‘What a waste of an equalizer.’ But when I am walking outdoors, I now find that switching from mode (2) above back to mode (1), gives me back exactly what I lost, because the ear-pieces are no longer airtight in my ears.

I tend to find that mode (3) is less useful, because it emphasizes the aspects of aptX -compressed sounds, that are more scratchy. But then again, maybe somebody else appreciates the treble boost feature of this headset.

Now, one way to tell whether a product is a forgery or not, is by the fact for example, that the equalizer on the HBS-730 I was playing with before, did not kick in. But in reality the logic is more confuted than that. The manual of the HBS-730 clearly states, that the equalizer settings cannot be changed, if that unit is in aptX mode.

The manual for the HBS-750, which I am using now, clearly states that its equalizer settings are available, when this unit is in aptX mode.

Further, today, when testing the HBS-750, I did listen to music for 7 hours straight. It was my initial intention, to run the batteries all the way down, just so that I could recharge them once, and allow them to live up to full capacity ‘in the field’, later. But after about 6 hours of my own music, I grew too sick of that. I could not force myself to listen to more than 7 hours of music, at which time the battery-level announcement still told me that the batteries were at “medium” level.

They then needed 70 minutes of charging time, to come back up to full.

With the HBS-730, I could not listen for more than 135 minutes, before they were dead. And to recharge the supposed HBS-730 only took 35 minutes, cycle after cycle.

Dirk