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Topic: what does 16-bit 44100 Hz mean (Read 19322 times) previous topic - next topic
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what does 16-bit 44100 Hz mean

Sorry for such a question.

I have got a book here from 1980 called Practical Stereophony, where I read that the major trend in signal processing is and is going to be a digital technology. The author states that for the perfect sound reproduction we need 60,000 values per second.

Well after reading that I went to search for the CDDA parameters and Wikipedia says it is just 44100 samples per second. Does this mean that CD is worse than perfect sound reproduction?

What is actually a sampling frequency. If it is a number of values per second how does it relate to frequency range? I am really confused here. If you play 11025 values instead of 44100, why shouldn't we get the same frequency, only in worse resolution...

what does 16-bit 44100 Hz mean

Reply #1 –
Quote from: maiki on
Sorry for such a question.

I have got a book here from 1980 called Practical Stereophony, where I read that the major trend in signal processing is and is going to be a digital technology. The author states that for the perfect sound reproduction we need 60,000 values per second.

Well after reading that I went to search for the CDDA parameters and Wikipedia says it is just 44100 samples per second. Does this mean that CD is worse than perfect sound reproduction?

What is actually a sampling frequency. If it is a number of values per second how does it relate to frequency range? I am really confused here. If you play 11025 values instead of 44100, why shouldn't we get the same frequency, only in worse resolution...


My basic understanding is that the sampling rate needs to be double the desired frequency range. So for example, if you want to accurately encode all frequencies from 20 Hz to 20 KHz, you need a sampling rate that is about 40 KHz. CD is 44.1 KHz, I think because originally the digital data was recorded to Umatic video tape.

Furthermore, although that book seems to imply that you need a sampling rate of 60 KHz, my understanding is that a modern Analog to Digital converter that uses good noise shaping should produce a transparent sound at the 44.1 KHz sampling rate.

I really don't think we need higher sampling rate formats.

what does 16-bit 44100 Hz mean

Reply #2 –
I'll give you a brief summary, and then some links so you can go do more in-depth reading.

PCM, CD-Audio:
16-bits per sample gives ~96db of dynamic range.
44100 samples per second allows reproduction of frequencies up to 22.05khz.

The author of the article you read is claiming that there are meaningful frequencies up to 30khz.

http://en.wikipedia.org/wiki/Audio_bit_depth
http://en.wikipedia.org/wiki/Nyquist%E2%80...ampling_theorem
http://en.wikipedia.org/wiki/Pulse-code_modulation
http://en.wikipedia.org/wiki/Psychoacoustics

what does 16-bit 44100 Hz mean

Reply #3 –
Wikipedia is a really good source of technical information:
http://en.wikipedia.org/wiki/PCM

Basically, the sampling frequency gives an upper limit to the highest frequency that can be represented by a PCM-coded digital audio stream (divide the sampling frequency by 2, and you have the maximim bandwidth that can be represented*)). You could look upon a CD with "theoretically perfect" A-to-D and D-to-A converters as a lowpass-filter where frequencies from 0 to 22050Hz being passed, all other frequencies being removed. You should also include in the model a non-linear clipper/distortion operating at digital full level ("0dBFS"), and a noise-source operating at something like -93dBFS.

This means that the practical question of "how high a sampling frequency do I need?" can be broken down into: 1)How high a frequency can humans perceive and 2)How much higher than the theoretical limits should we sample at to get a real-life frequency response satisfying 1)

As just about anything that interests audiophiles, this is a subject of great controversy in audiophile circles (someone always thinks that our hearing is practically unlimited, and whenever measurements and sighted listening diverts, there must be something wrong with the instruments).

It is my impression that the scientific community now pretty much agrees on 20-24kHz bandwidth free of linear and non-linear distortions as beeing enough to be "perceptually transparent" for all of us. The limit is pretty much defined by teenagers and women, as they are less prone to the degradation of high-frequency sensitivity that most male, music-interested listeners are prone to.

There might be situations where suboptimal equipment shows different performance for different samplerates, but I think that is an argument for hiring better R&D engineers, not for wasting bits in the transmission :-)

-k

*)A CD does not have to represent the frequency range of 0 to <22050Hz. It could just as easily represent the range of 100.000Hz to <122050Hz as long as the bandwith is <22050, and the proper arrangements are made in the filtering in AD and DA converters.

what does 16-bit 44100 Hz mean

Reply #4 –
This is what I do not get: 44100 samples per second allows reproduction of frequencies up to 22.05khz

Why is the frequency dependent on the number of samples per second?

what does 16-bit 44100 Hz mean

Reply #5 –
Quote from: maiki on
This is what I do not get: 44100 samples per second allows reproduction of frequencies up to 22.05khz

Why is the frequency dependent on the number of samples per second?

I think that the graphics on wikipedia explains this quite well.

If you want to measure something that changes often, you have to measure it often. If you measure it to seldomly, you wont capture the rapid variations. If you do election polls once a month, but the opinion of the people change every week, then you wont be able to see that variation.

Harry Nyquist figured out in the 1920s that the absolute maximum highest frequency baseband signal that could be sampled at discrete points in time, then flawlessly reconstructed was just less than one half the sampling frequency.

-k

what does 16-bit 44100 Hz mean

Reply #6 –
Quote from: maiki on
Why is the frequency dependent on the number of samples per second?

Translate your question to the domain of digital images : the more pixels you have in an image, the more details you have in that image. Same thing for audio: could you imagine a sound with only one sample per second? How much details would you get? Not much...

So the higher the sampling frequency, the more "details" you get.

- Daniel

what does 16-bit 44100 Hz mean

Reply #7 –
Quote from: maiki on
This is what I do not get: 44100 samples per second allows reproduction of frequencies up to 22.05khz

Why is the frequency dependent on the number of samples per second?


Frequency, as defined in the dictionary:
Code: [Select]
frequency
6 dictionary results for: frequency
Dictionary.com Unabridged (v 1.1) - Cite This Source - Share This
fre·quen·cy       /?frikw?nsi/ Pronunciation Key - Show Spelled Pronunciation[free-kwuhn-see] Pronunciation Key - Show IPA Pronunciation
–noun, plural -cies.
1.    Also, frequence. the state or fact of being frequent; frequent occurrence: We are alarmed by the frequency of fires in the neighborhood.
2.    rate of occurrence: The doctor has increased the frequency of his visits.
3.    Physics.
a.    the number of periods or regularly occurring events of any given kind in unit of time, usually in one second.
b.    the number of cycles or completed alternations per unit time of a wave or oscillation. Symbol: F; Abbreviation: freq.
4.    Mathematics. the number of times a value recurs in a unit change of the independent variable of a given function.
5.    Statistics. the number of items occurring in a given category.


Frequency being the number of completed cycles of a wave, usually expressed in terms of cycles per second.  The Shannon/Nyquist sampling theorem defined the minimum number of digital samples needed to accurately reproduce a given signal - slightly more than double the frequency to be duplicated.

For a more in-depth discussion of this, please read the link I provided concerning the Nyquist Sampling Theorem.
http://en.wikipedia.org/wiki/Nyquist%E2%80...ampling_theorem

what does 16-bit 44100 Hz mean

Reply #8 –
Quote from: maiki on
Why is the frequency dependent on the number of samples per second?

Frequency (Hz) is the number of events/cycles occurring per second.
Thus to capture high frequencies (many cycles per second) you need a high sample rate (many samples per second). And as others have pointed out you need something like twice the number of samples for the frequency, so to capture 20,000 Hz (cycles per second) you need 40,000 samples (snapshots) per second.

C.

[EDIT: a little late]
PC = TAK + LossyWAV  ::  Portable = Opus (130)

what does 16-bit 44100 Hz mean

Reply #9 –
Thanks. I might get it now. For the 10 kHz I would need a volume value at least 10,000 times per second. And 8-bit or 16-bit would mean either 256 or 65536 volume levels?

what does 16-bit 44100 Hz mean

Reply #10 –
Quote from: maiki on
Thanks. I might get it now. For the 10 kHz I would need a volume value at least 10,000 times per second. And 8-bit or 16-bit would mean either 256 or 65536 volume levels?


For 10 khz you would need 20,000 samples per second.

what does 16-bit 44100 Hz mean

Reply #12 –
Bandwidth-limited signals can be described or approximated by sums of sinusoidal components.

The spectrum of a signal is like a snapshot of the frequency content it bears, showing the distribution of signal power among different frequencies.

The range between the lowest and highest frequency observed in the signal is known as the bandwidth of the signal.

Theoretically an analog signal would take infinite samples of infinite resolution in order to reproduce faithfully, which translates into an infinite amount of bytes to store a digital representation thereof.

Thankfully, it has been proven that a signal can be faithfully reproduced if you take samples every Ts seconds. The Ts value is the so-called sampling period, or time difference between two successive samples. Mathematics have shown that by sampling a signal, it's spectrum is copied to higher and lower frequencies, which can be filtered out, so that we keep only the frequency range of the original signal.

However, if those copies are too close to one another, there may be overlapping, so when you filter, you can't be sure if you're keeping original signal, or also frequencies from the adjacent spectra. This problem is known as aliasing. It has been shown that the corresponding sampling frequency fs ( = 1/Ts ) in order for this not to happen has to be at least twice that of the signal bandwidth.

Humans can hear sounds with frequencies from 20 Hz to 20000 Hz theoretically, although a large percentage cannot hear much above 16000-17000 KHz. For practical purposes it can be said that the bandwidth of signals perceivable by man is 20000 Hz (20 KHz). For audio recording, additional headroom has been added, and the bandwidth measures 22050 Hz.

Based on the law of sampling, we need a sampling frequency of 2 x 22050 = 44100 Hz in order to reproduce sounds/music perceivable by man faithfully. That's where the 44,1 KHz value comes from.

Now, I haven't heard of 60000 Hz sampling, even though sampling rates of 48 KHz, 96 KHz, even 192 KHz are in use, despite the practical lack of benefit over 44,1 KHz.

As for the resolution, it concerns how close each individual sample is to it's original analogue source. Since we cannot store analog values in digital systems, we have to settle for a value close to the original. This is called quantization. The difference between the original sample and it's quantized value is called the quantization error. The target is to keep quantization errors as low as possible in order not to have the signal quality degrade audibly by quantization noise.

This is done by trying to make sure that the quantization levels within a range of signal voltage (amplitude) are as close to each other as possible. This way the quantization values are more likely to be close to the value to be quantized, therefore the error will be small. For human ears, 65536 levels have proved sufficient for music listening. Usually the amount of levels are chosen to be a power of two. 65536 values require 16-bit binary words to be coded.

So 44100 samples of 16-bit resolution per second per channel, there ya go.
Wanna buy a monkey?

what does 16-bit 44100 Hz mean

Reply #13 –
Quote from: maiki on
Quote from: Tahnru on

For 10 khz you would need 20,000 samples per second.


Why not 10,000?

btw what do you mean by "samples"?

Lets talk about opinion polls. You know, where a company calls citizens and asks them what political party they will vote for.

Lets say that doing one such poll at one day is a "sample". It is an approximation to the "opinion" of the people at that time. It does not say much about what the people will feel next year or last year, only what the think today (I am sure that one could make jokes about the unpredictability of voters right here).

If I was interested in fluctuations or oscillations in the opinion of the people I would have to "sample" their opinion multiple times.

Now, lets imagine that the opinion of the people oscillate like a sine-wave where the period is one month. Within that month, there will be a maximum and a minimum. If I "sampled" only at one point that month, I wouldnt know if I had hit the maximum or the minimum, and I would be left clueless.

Now, on the other hand, if I "sampled" at two times that month, the beauty of Nyquist is that he guarantees that I can reconstruct the "true" waveform as long as it does not contain frequencies at or above 2x the sampling frequency.


The plot shows a sine-wave (green) that is sampled at to low a rate (black dots). Note that although the sampling frequency is higher than the frequency we put into the A/D-converter, it is not 2x higher. Therefore, we miss having a positive and negative sample of each period, and when we try to reconstruct the waveform, we actually "guess" at a wrong, lower frequency (red).

-k

what does 16-bit 44100 Hz mean

Reply #14 –
Quote from: yourtallness on
For practical purposes it can be said that the bandwidth of signals perceivable by man is 20000 Hz (10 KHz).

I'm assuming that's a typo.

C.
PC = TAK + LossyWAV  ::  Portable = Opus (130)

what does 16-bit 44100 Hz mean

Reply #17 –
Quote from: yourtallness on
The spectrum of a signal is like a snapshot of the frequency content it bears, showing the distribution of signal power among different frequencies.

Mathematics have shown that by sampling a signal, it's spectrum is copied to higher and lower frequencies, which can be filtered out, so that we keep only the frequency range of the original signal.

However, if those copies are too close to one another, there may be overlapping, so when you filter, you can't be sure if you're keeping original signal, or also frequencies from the adjacent spectra. This problem is known as aliasing. It has been shown that the corresponding sampling frequency fs ( = 1/Ts ) in order for this not to happen has to be at least twice that of the signal bandwidth.


For human ears, 65536 levels have proved sufficient for music listening.


So, we might call a sample to be "an instant value representing the signal power"?

As for the frequency range... by sampling an analogue signal we get some unwanted frequencies that we want to get rid of? That's why we filter? So we use twice the number of positions to avoid overlapping of the values then?

65536 signal power levels... if we used 256 how the sound would be downgraded?

what does 16-bit 44100 Hz mean

Reply #18 –
Quote from: maiki on
65536 signal power levels... if we used 256 how the sound would be downgraded?

Use of 8 bits instead of 16 adds significant noise. Instead of 96 dB of signal-to-noise ratio you only have 48 dB, which is 256 times more noise.

what does 16-bit 44100 Hz mean

Reply #19 –
If you want to hear 16 bit-> 8 bit degradation foobar player can do it. (ctrl+p -> playback -> output 8-bit)

what does 16-bit 44100 Hz mean

Reply #20 –
Quote from: maiki on
Quote from: yourtallness on

The spectrum of a signal is like a snapshot of the frequency content it bears, showing the distribution of signal power among different frequencies.

Mathematics have shown that by sampling a signal, it's spectrum is copied to higher and lower frequencies, which can be filtered out, so that we keep only the frequency range of the original signal.

However, if those copies are too close to one another, there may be overlapping, so when you filter, you can't be sure if you're keeping original signal, or also frequencies from the adjacent spectra. This problem is known as aliasing. It has been shown that the corresponding sampling frequency fs ( = 1/Ts ) in order for this not to happen has to be at least twice that of the signal bandwidth.


For human ears, 65536 levels have proved sufficient for music listening.


So, we might call a sample to be "an instant value representing the signal power"?

As for the frequency range... by sampling an analogue signal we get some unwanted frequencies that we want to get rid of? That's why we filter? So we use twice the number of positions to avoid overlapping of the values then?

65536 signal power levels... if we used 256 how the sound would be downgraded?


More like a value representing instant voltage (positive or negative, relative to 0 or to the mean).
Power is proportional to square voltage, therefore always positive.

As for the filtering, that's the logic more or less. Note that usually the analogue signal is filtered before sampling as well, so that you can be sure it's bandwidth-limited.

Each additional bit of resolution doubles the available quantization levels and improves the SNR (or SQNR) rate by approximately 6 dB, for a normalized signal.

The ratio of the peak to the lowest amplitude in a signal is referred to as dynamic range. Reducing the available levels used to approximate values within that range leads to reduced fidelity, because chances are you're not rounding to values as close to the original as you can with more levels.

It's like being forced to count time in 15-minute units, you wouldn't be a very precise clock, would you?
Wanna buy a monkey?

what does 16-bit 44100 Hz mean

Reply #22 –
Quote
So, we might call a sample to be "an instant value representing the signal power"?
  Sort-of...  Technically, it's the instantaneous amplitude ("height") of the "wave".  Power (i.e. Watts) is proportional to the square of the amplitude (so it's always positive, even for the negative-half of the waveform), and it depends on the particular amplification. 

(I hate to overload you another link...  But there is a simple introduction to digital audio on the Audacity website.)

Quote
As for the frequency range... by sampling an analogue signal we get some unwanted frequencies that we want to get rid of? That's why we filter? So we use twice the number of positions to avoid overlapping of the values then?
Right.  If you don't filter-out frequencies above the Nyquist limit (half the sample rate), you can get false (alias) frequencies when you reproduce the wave.  This filtering has to be done before sampling (and before downsampling).  A properly designed soundcard/driver will always apply the required filtering, but not all soundcards are "properly designed".