Can anyone tell me or direct me to where I can find such information - How much loss in data occurs when doing a lossy compression, for different bitrates ? I am asking about MP3 and AAC.
For example,(just making up some numbers) 30% loss at 128kbps, 20% loss at 160kbps, etc...
Thanks.

It's impossible to answer this unless you define what "20% loss" is.

It sounds like he's asking for pure numerical loss. i.e. at 160kbps, truncation has reduced the spectral data to x% of its precision.

this is a relative term - on what sample(s)?

Hmm, I read here somewhere that noiseless coding increases MP3 compression efficiency by 20%, assuming that 100% = 1411kbps (standard CDDA), after compressing to 160kbps MP3 (which is 11% of 1411kbps) one could say that you discard 100% - 11% - 20% = 69% of data. The point is that most of removed data was redundant for our hearing, so one could say that it wasn't really data, and that nothing was removed.

If no data was lost and there was redundancy, than Shannon and his statistics should allow us to restore that redundancy. Unfortunately, we can't restore the information, so it wasn't really redundant in the first place.

If we consider only the lowpassing, by encoding -V2 --vbr-new (18500Hz lowpass?) you already lost 18% of your "data" (even though it's mostly noise)
Then, the transforms and approximations may reduce greatly the amount of "data" you have.

A follow-up question I have, though, is in terms of S/N ratio : Garf, do you have numbers on what the normal ATH curves for psycho-acoustic optimizations give us? I remember reading a topic here that said MP3 Signal-noise ratio was approx. 14db... Could that be correct? Or is the concept not applicable?

Imagine you have a book with text on textured paper - you can either scan it as graphics so you get a big graphics file with the text that interests you and with the paper's texture that is redundant (CDDA), or OCR it so you get tiny text file only with the text which interests you and without redundant paper's texture (transparent MP3). Hopefully you understand now what I meant by "nothing was removed" and "redundant data".

I get what you're saying.. but it's NOT about redundancy, though. I mean -- operations on entropy would be the wrong path, here (mp3 isn't working on redundancy..)

The redbook CD structure, of course, is redundant, but that's not what you copy when you rip a CD -- you copy the PCM data, which isn't redundant. It's just like bitmap data for sound : storing every pixel independantly, without making statistical analysies about sample distribution, etc.

A lossless compressor would be exploiting this redundancy to get high compression rates, but lossy encoding takes a psychoacoustic representation and removes what's invisible, uninteresting to us (in the case of the paper / message analogy, it would be the paper texture)
Analogies are never precise, though. They're not the best way for vulgarization at all, I find.

I have absolutely no idea what this means.



SNR is not really applicable in a codec. But you might expect something around 14dB "average" for typical pop/rock music, I guess.

Well, you answered anyways. Do you have numbers for classical? Up to 20 db, maybe?

Where as a CD has 96 db of SNR, always, IIRC?

let me re-phrase my question.
Lets say you compress a WAV file to MP3. Then you decompress it. The result is obviously not what you started with(wav file). You have lost some data. How much data did you loose in the compression/decompression cycle ? I was referring to that loss of data as % loss.

Your question is still just as cryptic.
When you encode, you should get the same number of samples out of your encoding as in your original. Therefore, when you convert back, you'll have a file that's 100% the size of the original.
As for binary differences between samples, it depends on the file itself.

A percentage requires a ratio of one thing to another. In general, the perceived quality of a lossy encode cannot be reduced down to one or two numbers. Almost any comparison that you can think up, that yields such a percentage, will either have a trivially useless result, or will have some sort of counterexample that gives the same numeric result but may sound much better or much worse.

Example: Compare how many samples are exactly the same as from the original WAV. For all encoders (even 320kbps) this number is very likely to be 0% or very close to it. It has no correlation with quality.

Example: Signal to noise ratio. If you define it in terms of background noise, encoders don't have any - if you feed no signal in, you will get no signal out. Perfect SNR for all encoders.

Example: THD. As was previously noted, if you run an encoder through RMAA, you're going to get extremely high THD+N results - 10% or more is not uncommon. This is simply due to the psychoacoustic model being well tuned to giving the maximum perceived quality for the lowest bitrates. Just like high THD might not matter all that much for tubed gear, it doesn't matter for encoders, and anybody who tries to optimize for minimum THD will likely wind up with reduced quality.

Example: Frequency response as a fraction of original bandwidth. Yes, all encoders have a lowpass. No, it doesn't really matter. You can take the paragraph on THD above, and replace all mention of "THD" with "frequency", and it will basically be correct.

then why is it called a lossy compression ?


can you expand on this ?
Maybe I need a little tutorial on encoding/decoding lossy compression formats.

Why do you wish to express loss as a percentage?

maybe the % of the "original data lost" can be interpreted as difference between the original and compressed waveform
i.e. substracting an encoded waveform from the source waveform and the ratio would be average amplitude of the original waveform vs. average amplitude of the difference waveform

J.M.

What good will this do? It certainly can't be used to determine quality.

The original poster should explain why such a number is desired.

Lossy encoders work mostly by reducing precision, not by removing data.

the OP wasn't asking about quality. He was asking about data loss.

(but I still think it makes no sense asking about data loss...)

Because size doesn't matter, or so they say
Seriously though, after decompression, it has the same size as the original, but its content is different - that's why it's lossy. If after decompression it were identical to the original (both size & content the same), it would be lossless.

You need a bit more than a little tutorial I'm afraid, these are basics but unfortunatelly long and boring to explain, you should do some research on your own, maybe start with wikis and terms like PCM (Pulse Code Modulation), sampling, quantization, time domain, then frequency domain, etc.

ok. I will do some homework tonight. It turned out be more deeper than I thought.
btw, by % I just meant a difference, a comparsion with the original, the amount/quantity of loss. call it anything you like.

Just thinking out loud now...
so this 'loss of quality' i.e. the difference you hear when listening to a highly compressed (like 64kps) v/s an uncompressed format(WAV) is related to the 'loss of precision'. Thats a good starting point. Rather, it seems like the precision still remains the same(16bits) even after decompression but its the value contained in that precision that has now changed as a result of the comp/decomp cycle. I have a feeling that the 'compression' ratio also depends on the value of the original sample, so the loss can be different from sample to sample and cannot be generalized.

Ok, maybe this will ring a bell a bit:
In original WAVs audio is most often stored in time domain, encoded with "physically natural" pulse code modulation - you have a number of samples per second (sample-rate), each of these samples are stored with given precision (bit depth) - they represent amplitude of sound in time. The only way to lossy compress audio with such a representation is either to reduce precision of samples (bit-depth), or amount of them (sampling-rate or lenght). It's not very effective because quality drops fast and size drops slowly that way. First thing that lossy encoders like MP3 do, is to transform audio into "psychically natural" frequency domain - then samples represent amount of signal in given frequencies. With such a representation it is more convenient to reduce precision & chop off things without losing much perceived quality (basically you filter out the highest frequencies, inteligently reduce precision of others, and then compress it losslessly). When you play back MP3s they need to be transformed back into time domain, into PCM - you're back into something that doesn't care about frequencies that you encoded with less precision or didn't encode at all, hence you get back the file of the same size as the original, but obviously with different content.
Audio is stored in WAVs & MP3s in totally different ways and you can't think about their precision in the same way.

My answer to that question is: lossy compression formats cause you to lose *all of the data*. On playback a new data stream is created that is vastly different (when doing a byte comparison of the PCM audio data), but it sounds very similar to the original (in most cases).

-brendan

No, no, no. The output from a decoder can be a 32 or 64 or 80 bit float. So by this reasoning the precision increases

The problem is that the lossy codecs store the data *entirely* differently from a WAV so this direct comparison is flawed.



Yes.

I think I can answer your question: CD audio is 1411kbps, a modern lossy codec will provide (most of the time) the same quality at 128kbps. The lossless coding in such a codec is a gain of about 20%, so the "real" bitrate would be about 154kbps. CD audio is 16 bits per sample, so a lossy codec has an equivalent precision of about 1.75 bits per sample. That's a fairly realistic number, in the sense that the actual data the codecs store is really usually only stored with 1 or 2 bits precision, on average.

Now, if you take a 16 bits WAV, and convert it to a 2 bits WAV, it will sound absolutely horrible. So, you can realize that the codecs gain their performance from reducing the precision in a domain where the loss is not relevant to the human hearing system.

Well said. I think I have a better understanding of lossy codecs now.

Short version:

You cannot compare lossless and lossy according to technical criteria. Any such comparisions will be irrelevant and misleading. In laymans terms: lossy compression is some kind of "psychological compression" - it is a psychological thing, not a technical one (like i.e. ZIP). Most lossy compressors take advantage of psychological tricks (called the psychoacoustic-model) to compress. Therefore, it is no longer possible to compare stuff on a technical level without the results becoming irrelevant(you cannot even ask a dog to compare it, because its all meant to only work for humans - let alone asking a computer to compare it).

Some hybrid-codecs do exist, which do not use any psychoacoustic model at all (i.e. WavPack Lossy) - in THAT case, you could measure quality-loss by "loss in precision / added noise". But those formats are not those which you asked about.

But you can compare lossy codecs on a psychological basis - "how it sounds like" compared to the original - so DBT. In this case, there as well is no answer to your question, because it depends on the kind of music. Some music needs more bits, some needs less bits - thats why VBR is better than CBR.

This has been facinating. I'd like to add a question to the mix. Is this psychological compression of MP3s in any way related to the equal loudness curves, or am I off base?

http://en.wikipedia.org/wiki/Equal_loudness_curve

It's one of the standard factors in any psychoacoustic model, but only one of many.

Quite a while ago I remember reading a thread with responses to someone asking similar questions. That guy was talking about difference patterns from subtracting wavforms (original wave - decoded mp3). There was some good discussion of how the quietest difference is not always the most transparent. That might be a good one to look at for more info on the distinction between information and hearing transparency.

The easiest explanation by way of analogy is JPEG compression.

Take a picture, scan it, save as TIF & JPEG. The JPEG-encoded pic will be vastly smaller. But if you view it on screen, can you discern the difference? Unless you are using too big a compression coefficient, usually the answer is: No.

Is there any loss of data, in terms of pixel size? No.

Is there any reduction in saved file size? Definitely.

Is there a pixel-by-pixel difference between the TIFF and the JPEG file? Yes.

So, the "lossy" term comes from the nature of compression, i.e. when you decompress, it will not give bit-by-bit identical data to the uncompressed data. But, performed properly and not excessively, lossy compression should not give discernible degradation, or there is degradation but still acceptable.

I don't know if what I am going to say next even makes sense or if it has been done before or not but here goes...

Is it possible by any means to do a spectral analysis (FFT) of a lossy format file (MP3, AAC,..) ? (Probably not, but I thought I'd ask anyway). In that case is there anything available to convert a lossy format back to WAV ?

I am wondering if anyone has done a spectral analysis comparison of an original WAV file and a WAV file recreated back from the compressed (MP3, AAC) file of the original. The WAV file doesn't have to be music. To keep things simple it could be just a high frequency tone signal of reasonable amplitude. Maybe even a mixed signal of a couple or more fixed tones.

Would be interesting to see what type and amount of distortion (or "loss") it would reveal for different bitrate compression.

Spectral analysis is extremely easy to do on lossy formats. But the general concensus here is that it's counterproductive for comparison purposes.

can you suggest a free(or trial) PC based spectrum analyser (like RMAA) that will take an MP3 file ?

counterproductive as in it will show losses that dont seem to exist in listening tests ?

The problem with spectral analysis is that it tells you virtually nothing about how good the file will sound. You can make a file that looks nice on a spectral graph, but sounds horrible.

sure. just like an amplifier's measurements doesn't really tell anything about how it sounds.
I dont want to use a FFT to find out how it sounds. I am just interested in knowing what the spectral difference is between the original and compressed.

Can't audacity do that?

Hi, I have a similar question but couldnt find an exact answer so I post it here.

I have an original audio data, which is a stream of numbers. I developed a lossy compression algorithm which gives me another stream of numbers after decompression and compression. So:

Original data: a stream of numbers.
Data after compresison: another stream of numbers.

How could I measure the quality of decompressed data "technically" ? After reading this thread, I know it's hard to differentiate between the "technical" or "psycological" point of views, but I'm asked to write some kind of scientific measurement of my algorithm and I have no idea now. Please give me some suggestions.

Thanks
hixhix

An ABX test.

Just a thought -

Would the difference in the FFT analysis of the original with that of the compressed signal be a valid "technical" difference ? Then you could write an algorithm that spits out this difference.

you could see a greater difference with higher frequencies at higher amplitudes so you'd have to factor that in too in your selection of the original signal.

Back in the day when it was free, CoolEdit was the obvious choice for this.

It's trivial to decode lossy back to .wav in foobar2k.

It's easy to inverse mix paste the decoded over the original to get the difference in many audio editors.

It's trivial to FFT the difference signal to see what's there, and even to play it back to hear what's there.

But please see the FAQ for reasons why this is only useful for inquisitive people who want to know what the codec is doing, rather than how well it is working!

Cheers,
David.

Listen to the original WAV file from cd and the compressed mp3. The amount of difference you hear is the amount of data lost in the process.

All the other differences between the "raw" data (such as, a hex file compare) of the two waveforms are redundant.

2Bdecided,


yes I understand that and the only reason I mentioned that is because I didn't know it was possible to do a spectrum analysis from a compressed file directly. I assumed a wav is needed.


yes I also understand that listening to a difference signal or looking at its FFT is useless, but a measure of the amount of difference could give the comparison a quantitative side that hixhix is looking for ?


edit: although I still believe that looking at the two FFT's seperately (and not the fft of the difference signal) would give a good visual presentation of what the decoder is doing to your original signal.

Wav is needed. If your program takes an MP3, it first converts to WAV (or rather PCM) and then runs the FFT o that. The input to an FFT must be PCM or similar.




An FFT is just another way of expressing the same information in a WAV. So its no more and no less quantitative then the source WAV file is. However, it also doesn't tell you anything else either because it IS the same information as the source WAV.

It sounds to me that you want a single number that tells how good a compression format is. There is no such thing. The only valid test of goodness for compression is the ABX test, and you won't get a single number out of that. The problem is more complex then you're hoping.




No better then looking at the WAV files separately. The only striking difference between the two will be the lowpass filter, and thats relatively unimportant. You could disable it on some formats and lose even that difference.

Why would looking at the WAV be the same as looking at the FFT ?

WAV doesn't show the frequency content - or rather harmonic content - of the signal. WAV shows just a waveform envelope which is formed by combination of frequencies, but FFT also shows you those frequencies individually that make up that waveform also - the harmonics.

I guess what I am really hoping to see is the change or difference in the harmonic content in the compressed file.

Let me explain by example. Some pictures might help and I will get them as soon as I do my little mad scientist experiment, but I will just try to explain in words -

Take a wav file with a simple signal that has some harmonics and do an FFT on it. Lets say the fundamental is 1Khz with odd and even order harmonics at 2,3,4,5Khz etc.. in varying but decreasing amplitude. Just a simple classic frequency with some harmonics.

Now compress the wav into a mp3 or your favorite format. Use a bitrate at which you can easily hear the difference.

Then do an FFT again on that compressed format. (obviously after converting it to wav/pcm so the analyzer can work).

I am sure (or I should say I am hoping) that the harmonic content (order and amount) would be different than the original. Otherwise why would it sound different ?!

Because both are useless.



You'll see the lowpass filter settings anyway. Not much else.



The FFT doesn't contain any information that wasn't in the time domain PCM. You seem to realize that looking at the time domain PCM is useless. Why do you think looking at the same information in the frequency domain is going to work any better?

Also, why do you care about individual harmonics? You're unlikely to spot many of those in actual music, so it seems an odd choice for a test thats supposed to evaluate audio quality.

because any audible change in the original signal will be a result of the change in its harmonics - aka distortion. And like I mentioned earlier a time domain PCM view (waveform) will not show you that distortion, only an FFT will.

As for the choice of type of a signal - that's for the sake of simplicity. A music signal would be very difficult to evaluate.

1. First, imagine a "codec" that just delay every sample by 1000 samples, producing a 1000-sample longer file.

The time-domain difference, as well as the frequency domain difference could be considerable. If the high-frequency content was large enough, it could be a full 16bits (96dB) of difference at times. Still, no listener could discern any perceptual difference.

2. Second, imagine a 16bit->8bit->16bit truncation. The difference would be quite small. At all times the error would be less than -48dBFS. Still, most listeners would immidiately identify an irritating "buzzing" distortion.

3. Third, imagine a top-notch audio codec at low bitrates that both distorts, delays and mis-shapes the waveform in any conceivable way so as to keep it sounding as similar as possible to the original, while throwing away as many bits as possible. It could contain any proportion of case One and Two, and throw in any number of other cases. Any measurement would be utterly useless unless you know exactly what to look for, how the codec functions, and consequently how human perception works.

-k

Any audible change will result in exactly equal amounts of change to both time domain, and fourier domain versions. You realize that the time domain version doesn't tell you anything, so why do you think the fourier domain one will?



If you can't apply this idea of yours to real music, then what use is it in evaluating audio quality?

I am talking about the presentation of the fact, not the actual fact! I am not saying time domain does not have the information. It does! but there is no way of representing it. Fourier will represent it for you.


I wasn't quite expecting that. Well, real music is a complex combination of such "simple" signals, and lets just leave it at that.

I did a quick and dirty test now and I am sure I can prove it to you what I am trying to say. In the meantime just to explain my side of the argument about the Time/Freq domain issue I'd like to draw your attention to this old thread where I demonstrated how bad the soundcard's or the window's mixer is and how good SSRC resampler is.
http://www.hydrogenaudio.org/forums/index....c=44925&hl=

(just noticed you have posted in that thread too so it might ring a bell!)

Could I "hear" a difference between the crappy resampler and SSRC ? No!
Could I "see" a difference between the crappy resampler and SSRC in the time domain (recorded wav/pcm file) ? No!
Could I "see" a difference with FFT analysis ? You Bet!!

this is EXACTLY what I am talking about - http://www.jensign.com/RMAA/ZenXtra/Comparison.htm

scroll down to the THD and IMD charts.