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Occam's Razor: The Signal to Noise Ratio

Occam's Razor can be paraphrased as "the best explanation is the simplest one". In the case of audio, I suggest the best "explanation" for the best sound is the highest signal to noise ratio. We commonly pursue this with equipment topology, vibration isolation for turntables, electronics and speakers, electrical isolation with dedicated circuits, component isolation, cable hygiene and all our other efforts to eliminate noise pollution. I believe it extends well beyond this, culminating not in what comes out of the speaker, where I think many folks stop, but rather what finally hits our ears. This means wave interference in the listening room is one of our largest noise contributors.

 

I have been fortunate in having the time and means to curate a nice system, but I recognized that it would never deliver the best SNR if the signal that leaves the speaker is corrupted by the noise created as it careens throughout the room before it reaches my ear. Over the last few months, I have added room treatments that together cost more than any one single component in my system.  I initially paid attention to first reflections, creating what I call the “circle of silence” with absorption on the walls, ceiling and floor. I also directed my efforts towards speaker boundary interference response with appropriate placement of the speakers and listening position. Bass traps and a distributed bass array deal with uneven lower bass response. Not wanting to dull the room with overabsorption, I added pure diffusion or a combination of diffusion and absorption.

 

What I now have is a system that not only provides a very accurate signal, but one that is not muddied by all of the other signals (noise) bouncing off the room surfaces.  Instruments and voices are clear with an obvious start and stop. While the system always had decent width and height, they are greater now.  The most significant contribution is that the soundstage now extends in front of and far behind the speakers. On a good rock recording, I can place the drum set, the bass, the keyboard, the vocalists and the guitars three-dimensionally. Classical and jazz are even more remarkable. It is stunning and at times, even startling.

 

I recognize that not everyone has a room they can devote to their audio pursuits, but within your means and what you and yours find socially acceptable, you should do everything you can to attend to the noise your room adds to your pure and pristine signal. Fuses, power cords, cables, amplifier design, speaker type, etc., all pale in comparison. No matter how your particular equipment tastes run, if you were to put your system in my room, it would likely sound better.

 

Bottom line, defend and protect your hard won signal from all the noise throughout the entire reproduction process. Everything counts, especially the room.

 

tcutter
Post removed 
mahgister's avatar
mahgister
13,102 posts
 

A timbre experience is a subjective perception which come from a multidimensional set of interacting parameters and cannot be reduced to SNR concept and to a physical waveform...

Audio is not so much about the gear but about psychoacoustics...

Occam razor is a philosophical concept not an acoustical concept...It is a general methodological concept that cannot be used to justify the reduction of a complex concept and experience as "timbre" to be just a SNR simply measured factor..
 
In fact the definition of timbre in acoustics EXCLUDE a simple SNR definition based only on the physical waveform spectral distributions ...
 
«Helmholtz was the first scholar to link timbre (a perceptual aspect of sound waves) to spectral distribution (a physical aspect of sound waves). He specifically focused on the spectral distribution of the steady state portion of sound signals (defined below). This approach overlooked several acoustical aspects of sound signals, such as attack (onset transients) and signal/spectral time variance, both of which have been proven important to timbre perception.»
 
 
«At this point, the signal can be regarded as having a very high acoustic SNR since there is no acoustic noise (distorted waveform) yet associated with the signal/waveform. (This may be the reason headphones are enjoyed by many.) Once it leaves the speaker, this waveform, the original signal, makes a beeline to our ears but it also travels to every corner of our room, where it is reflected and after a while, makes it to our ears as well. If these waveform reflections that are relatively loud hit our ears within the window during which we cannot distinguish their arrival time from the incoming original waveform, they become the noise that competes with the original signal/waveform and consequently lowers the signal to noise ratio. Reducing these competing waveforms in number or amplitude through absorption or diffusion will increase your SNR. You do want to retain some reflections for a sense of space and ambiance so pure absorption is not indicated. You just want fewer or softer competing waveforms (noise) so the original waveform (signal) predominates.»
 
Then the problem with your description is if the recorded acoustics parameters picked by the sound engineer in this album you listen to can be reduced to SNR total sum of the gear system by contrast the experience you will have from it in your room with your ears/brain specific characteristics cannot be reduced to a SNR . Timbre is a subjective very complex experiencve which cannot be understood and controlled with the SNR concept. Our ears/brain /room condition create the sound experience, they do not convey it in a passive way as a cable or even an amplifier will do adding only some noise level to the signal. Then you description is not even wrong , it is a simplistic reductive reduction of a complex acoustic phenomenon to a set of linear signals on a channel. But the ears/brain dont work linearly in the linear Fourier time domain. Then the SNR concept capture only a part of the audio problem, not the acoustic more important part . All these metaphors Using the SNR concept are not enough to understand timbre experience in a room ... the simplest metaphor are not always the good one , Occam razor or not.... Then you are not even wrong in your description reducing all audio aspects to SNR ...
 
The reason for such metaphors with SNR is the audiophile focus on gear design more than on acoustics itself...
 
 

 

 

tcutter OP
108 posts
 

All timbre information is contained within the original waveform.

From Britannica.com: "timbre, quality of auditory sensations produced by the tone of a sound wave."  

From DSP Guide.com: "The perception of a continuous sound, such as a note from a musical instrument, is often divided into three parts: loudness, pitch, and timbre (pronounced "timber").  Loudness is a measure of sound wave intensity, as previously described.  Pitch is the frequency of the fundamental component in the sound, that is, the frequency with which the waveform repeats itself. While there are subtle effects in both these perceptions, they are a straightforward match with easily characterized physical quantities.Timbre is more complicated, being determined by the harmonic content of the signal." 

"Harmonic content of the signal."  I don't know where harmonic content would reside other than in the waveform.

Again, it's all about the waveform and its purity. Psychoacoustics doesn't start until the waveforms have hit your eardrum. By then, damage done.

mahgister's avatar
mahgister
13,102 posts
 

All timbre information is contained within the original waveform.

You forgot to observe the way our ears-brain-room will modify a recorded timbre and will transform it in an experienced timbre in a specific way for each different room and ears/brain.

Timbre is not reducible to a SNR analysis...

From Britannica.com: "timbre, quality of auditory sensations produced by the tone of a sound wave."

From DSP Guide.com: "The perception of a continuous sound, such as a note from a musical instrument, is often divided into three parts: loudness, pitch, and timbre (pronounced "timber"). Loudness is a measure of sound wave intensity, as previously described. Pitch is the frequency of the fundamental component in the sound, that is, the frequency with which the waveform repeats itself. While there are subtle effects in both these perceptions, they are a straightforward match with easily characterized physical quantities.Timbre is more complicated, being determined by the harmonic content of the signal."

Instead of these too simplistic definition read the article i suggested on psychoacoustics

http://acousticslab.org/psychoacoustics/PMFiles/Module06.htm

Timbre is not only determined by the harmonic content of the waveforms but by his time envelope and timing dimensions of the room also by the dynamic of the sound...

  1. signal time variance (envelope)

  2. degree of attack and decay synchrony of the sine components;

  3. presence or absence of high-frequency inharmonic energy in the attack portion of a signal;

  4. spectral energy distribution (frequency, amplitude and phase values of the sine components of a complex signal - may change with changes in intensity and register, even for a given instrument); and

  5. spectral energy distribution time-variance (spectral flux or "jitter").

 

Your sentence here resume all your misunderstanding:

Again, it’s all about the waveform and its purity. Psychoacoustics doesn’t start until the waveforms have hit your eardrum. By then, damage done.

For sure you are right ...But the physical waveform in the room is an acoustic translation of the recorded waveform not a mere deformation or a perturbation or a mere loss from a so called pure signal but an acoustic positive-negative trade-off transformation which cannot be explained by only a SNR metaphor... For example crosstalk effect result in a loss of spatial information in all stereo system and had no direct relation to only measured SNR of the gear but resulted from physical stereo disposition and physiological conditions.

Then you are not wrong you forgot half of the story... Timbre is experienced in a room and with some ears... Then it is not only about electronic reproduction it is about acoustic translation ...Then it is more than just SNR meassures...

Psychoacoustics begins before the waveform has hit your eardrums. 😁It begins in the design of the gear itself , for example in the Dr. Choueiri design of his filters to erase the effect of crosstalk . This is way more than SNR physical measures, it is psychoacoustics design .

Psychoacoustics is the root and the canopy of the audio tree...Gear design resulted from this science at the end. It is way more than just SNR measures...Your are not even wrong and this is my point... I added only the part of the acoustic story you inconsciously  put under the SNR rug metaphor...

Audiophile experience is more than buying gear design with good measured SNR, it is also acoustics and psychoacoustics varying parameters in the TRANSLATION of acoustic recorded waveform for your room/ears/brain in another perceived experience which will differ from the recorded waveform by acoustic definition..

No audio system is perfect high fidelity reproduction ... They all translate in a relative way some experience, timbre and spatial acoustic qualities, which are not reducible at all to signal noise ratio on a line

 

 

tcutter OP
108 posts
 

The title of your link is “Perceptual attributes of acoustic waves – Timbre”. I believe you make my point right there but I will expand further.

 

You cite the following factors:

  1. signal time variance (envelope) 
  2. degree of attack and decay synchrony of the sine components;
  3. presence or absence of high-frequency inharmonic energy in the attack portion of a signal;
  4. spectral energy distribution (frequency, amplitude and phase values of the sine components of a complex signal - may change with changes in intensity and register, even for a given instrument); and 
  5. spectral energy distribution time-variance (spectral flux or "jitter").

Where in the article does it refer to something other than a waveform?

a. The “signal” is a waveform

b. “Sine components” are only found in a wave

c. “inharmonic energy” refers to waves

d. “Frequency amplitude and phase changes of the sine components” refer to waves

e.  and from the article itself: “Helmholtz was the first scholar to link timbre (a perceptual aspect of sound waves) to spectral distribution (a physical aspect of sound waves). He specifically focused on the spectral distribution of the steady state portion of sound signals (defined below). This approach overlooked several acoustical aspects of sound signals, such as attack (onset transients) and signal/spectral time variance, both of which have been proven important to timbre perception.” 

Where do you think onset transients or signal/spectral time variances are found, if not during the delivery of waves? These are not created in one’s head. 

 

Regarding crosstalk, it is defined by Wikipedia as “usually caused by undesired capacitive, inductive, or conductive coupling from one circuit or channel to another.”

Meaning that the electromagnetic waves created in one wire impact the electromagnetic waves in an adjacent wire, thereby making it different from the original signal. Crosstalk is an example of electromagnetic interference.  Waves again.

 

Referring to psychoacoustics, Ansys.com states: “Psychoacoustics is the study of how humans perceive sound. It’s a relatively young field that began in the late 1800s to help aid in the development of communications. Psychoacoustics combines the physiology of sound — how our bodies receive sound — with the psychology of sound, or how our brains interpret sound.”

 

Our stereo systems can only address what sounds (waveforms/signals) our body receives. As I said earlier, once it hits the brain, the damage is done. Your brain cannot repair what was missing from or added to the original signal. It can interpret it, but it cannot change it.  That has to happen before it gets to the eardrum.

 

You finish with: “No audio system is perfect high fidelity reproduction ... They all translate in a relative way some experience, timbre and spatial acoustic qualities, which are not reducible at all to signal noise ratio on a line”.

 

First of all, they are reducible, but only in part. The other influence is the speaker’s interaction with the room and that is why I continue to emphasize that to get the best signal/waveform to your ears, you need to address the signal in the room as well as in your electronics. What happens to the signals in your head is your problem and yours alone.

 

 

 

 

 

 

 

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