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When did we decide to sample telephone at $8$ kHz? Has this always been the case? Why did we do that? Is it because higher bit rates can't be transferred as quick? And do these reasons still count? And if not, why isn't there a new standard yet? Is it true that $8$ kHz is the lowest possible sampling rate to transfer understandable speech?

I'm trying to find sources for this, but there doesn't seem to be much information about it.

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    $\begingroup$ It hasn't always been the case, because telephone lines used to be totally analogue. $\endgroup$ – Simon B Mar 16 '15 at 11:31
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    $\begingroup$ in fact, they might still be totally analog for local calls within the same exchange. but i dunno. but even when they were analog, there were bandwidth limitations and "voice quality" was the sufficient criterion. $\endgroup$ – robert bristow-johnson Mar 17 '15 at 18:03
  • $\begingroup$ Just so we don't get confused ...and a refresher Baud rate and bit rate are not the same .. Baud is "Bits at Unit Density". Baud is the signalling rate , Bits are the information rate. so if your BAUD rate is 1200 baud and you are passing 4 bits per clock cycle you are running 4800 bits per second .. We had DSP modems which were capable of passing 150Kb/s down an analog phone line but the modulation technique was very sophisticated and used anywhere from 256 to 512 audio tones to move data down the pipe.. as well as equalize the line and remove the delay.. I do recall seeing some modems that w $\endgroup$ – Keith Mar 6 at 20:32
  • $\begingroup$ Ah found it... US Robotics made a 2400 BAUD Modem called the Sportster HST v92. it was 2400 Baud but passed 21,600 bits per second. So there were 2400 BAUD modems in the marketplace in the mid 90's $\endgroup$ – Keith Mar 6 at 20:43
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If anyone cares to dig I think they will find that before Bell Telephone started multiplexing voice lines they did a lot of research on the frequency content of the human voice. They originally used test groups to develop the bel audio unit and the power distribution of the voice as well as the sensitivity of the human ear to various frequencies. They developed a band pass characteristic that peaked around 2.1 KHz and rolled off below 300 and over 3000 HZ. That gave a good human sounding voice when done correctly. All that was analog.
AM radio expanded that to 5 KHz to include music that was acceptable to most folks when we were young and had good ears. Television flyback transformers were designed to run at ~17.5 KHz because there was a magic number for picture reproduction and most folks could not hear the whine. Single sideband radio was commercialized in the 1960's and needed very sharp cutoff frequencies. I used radios with filters at 2.1 and 3.1 KHz. 2.1 had some Donald Duck characteristics. 3.1 sounded fine, again with young ears. Audio bandpass was increased to 20 KHZ or better with FM because the higher carrier frequencies could handle higher bandwidth for better music reproduction. Stack up some xylophones or bells or other high pitched instruments and they can get enough harmonic energy into the higher frequencies. OTOH, as was state, most folks cannot hear it.

The bottom line is that anyone claiming they need 20 KHz bandwidth for voice is not paying attention. 3 KHz will do it, 5 will give you some margin. If it does not sound right then something other than the bandwidth is the issue.

When digital signaling was being developed folks who know figured out that no matter how weird a waveform looked it could be broken down into a set of sine waves. The harmonic mixing of those waves produced the typical spikey pattern of voice or music. Lastly, Nyquist did research on the digital sampling rate needed to reproduce a sine wave at a given frequency. It turns out that it takes 2 samples to make a sine wave so the highest frequency that will be reproduced is half the sample rate. You want 5 KHz of audio then sample at 10 KHz. Fine for voice. You want higher fidelity music than most folks can hear then sample at 40 KHz or so to get 20+ KHz.

One more tidbit is sampling vs bitrate. If you sample at a given frequency then multiply that by the word length you will get the minimum bitrate needed to produce the desired signal. Reduce bitrate and the size of the sample word will get cut to meet the new bit rate at a given sample rate. That is all "lossless" encoding. This is all from memory and trying to find current data. It's there if somebody looks for cites. I'm not going to bother as I am getting too old to care. I just got tired of wading through a lot of obvious mythical issues when I got interested in doing some audio capture.

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It was thought to provide a good trade-off between quality and bandwidth. Actually a single voice signal occupies 8 kHz, not 8 kbps, of bandwidth. Each sample is quantized into 8 bits, yielding a rate of 64 kbps which is used universally.

Further reading:

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    $\begingroup$ When the voice signal is sampled at 8 khz, its bandwidth is assumed to be less than 4khz not 8khz. Also the resulting raw PCM 64 kbps bitrate may be lowered by DPCM and ADPCM techniques down to 32kbps or 16 kbps whenever efficiency is required. $\endgroup$ – Fat32 Mar 18 '15 at 12:44
  • $\begingroup$ That is true. Not only that, it is guaranteed to occupy less than 4 kHz through low-pass filtering. Otherwise aliasing occurs. $\endgroup$ – Emre Mar 18 '15 at 17:58
  • $\begingroup$ then I guess you should review your answer saying "Actually a single voice signal occupies 8 kHz, not 8 kbps, of bandwidth". A voice signal can occupy the full spectrum of 20-20 khz, but only the first 4khz is taken in transmission. $\endgroup$ – Fat32 Mar 19 '15 at 14:40
  • $\begingroup$ I think you meant to say the human ear can discern frequencies in that range? That's a different issue. $\endgroup$ – Emre Mar 19 '15 at 17:01
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Another reason is that, before digital signal transmission, telephone audio used to be analog modulated into a narrow-band channel so that multiple phone calls could be sent down a single analog link (RF and microwave tower relays, etc.) The audio thus had to be first be low-pass filtered to narrow the bandwidth required for each channel so as to pack the largest number of channels down one analog pipe (but even then, on a bad day, one could hear some of any adjacent phone call as background noise). Since people got used to long distance calls lacking frequencies higher than 3.5 kHz or so, this bandwidth became commercially acceptable even for local calls.

However, even narrower bandwidths were used for early space exploration communications, so 3.5 kHz may not be the minimum for understandable speech.

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As others have said 4kHz is standard, because it naturally where human voice is source1 source2. I did find this one article that mentions fundamental frequencies are much lower 85Hz-300Hz article. Whether or not this works in practice, I can't say for sure. but worth a try

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The analogue telephone system had a brick wall filter at 3.9 KHz. This passed all necessary info for intelligible speech and allowed bandwidth packing. Many people have been brainwashed in their thinking about necessary bandwidths. Bandwidths of 20-20,000 Hz are great for music, but completely unnecessary to reproduce human speech.

Will somebody please ask Nyquist how we sent 56 KBaud fax signals over analog lines with 3.9 KHz brick wall filters. Does anybody remember fax machines?

The highest note on a piano is 4186 Hz. The frequency range of human voices is less than around 1000 Hz. Middle C on a piano is about 262 Hz, just to put some perspective on things.

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To clear up a whole lot of misconceptions.

First, there has never been a 56k “baud” modem. Baud is about state change, and was maxed out at 1200 baud. Anything beyond that required more sophisticated encoding.

Second, human hearing perceives not only the fundamental tones, but also many orders of harmonic content far above and beyond the fundamental. When that harmonic content is removed, the audio sounds less natural and pleasing. Higher (than 8Khz) resolution audio is both more intelligible and more pleasing to the ear.

Third, Nyquist works within a fixed time domain. If you begin sampling at the exact moment of a peak or trough, then you only need 2x the sample rate to the frequency. However, in the real world your sample points can occur at any random offset in time to the peak or trough, therefore requiring a higher sampling rate. For example, if you sample a sine wave and your sample moment occurs at precisely 90 degrees offset from the start of the wave, your data will suggest a straight line rather than a wave. For fundamental tones this is critical. For harmonic content, it is more of a nice to have, with diminishing returns near the top end of the audible range. Nyquist applied to audio processing is one of the most poorly interpreted theorems out there.

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  • $\begingroup$ Do you have a reference for the claim of no modems being above 1200 baud? I believe the claim is incorrect. Also, for what it's worth, the paragraph on sampling is wrong. When sampling a sine wave, any sampling rate larger than twice the sine's frequency is enough, regardless of the phase. $\endgroup$ – MBaz Nov 17 '18 at 23:30

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