# How lossless is my lossless music?

I have ripped an audio CD using iTunes and saved it in Apple Lossless format. I used Spek to draw a specrtogram and here is the result:

My first question is, why doesn't it go all the way up to 22 kHz? Does this mean that they sell audio CDs recorded from lossy formats?

Another thing I want to ask is about converting this file to a lossy format. I used iTunes to convert this file to AAC (iTunes Plus) format. The specrtogram now reaches 22kHz at some points. So how is this possible? Here is the image (I converted the aac file to wav for compatibilty with other programs, but this should not have any effect):

I'm new to analyzing specrtograms, so I hope you can help me understand them.

Audio sampled at 44.1 kHz (like normal audio CDs) can in theory contain content up to the Nyquist limit of 22.05kHz. However, you need a filter to remove all content above that limit, otherwise it folds back into the hearable range: you hear this as aliasing.

A perfect, theoretical filter would remove all content above 22.05kHz and leave everything else unaffected. This would be an infinitely steep low-pass filter.

In practice, such a filter doesn't exist, so a very steep low-pass filter is set at about 20 kHz, so that the attenuation is sufficient at 22.05kHz to make the aliasing inaudible.

Besides, a perfect human being hears frequency content up to 20kHz. Most, if not all are not perfect, so depending on age and other factors they don't hear anything above 16/17/18 kHz. This means this practical filtering is not a problem for everyday listening.

A lossy format, like mp3 or aac, analyses the audio and manipulates it in such a way that it can be saved using less data, while minimising the audible effects this has. This could also mean that certain peaks are saved unfiltered, because the algorithm knows the super-high-frequency content which is that quiet will be masked by the rest of the audio, or even be completely inaudible to the human ear. The peaks in your spectrogram could also result from the decoding algorithm performing insufficient filtering for the peaks to show up in the analysis. This doesn't automatically mean that the filtering is bad: do you hear these spikes? Probably not.

• This is correct, though there's a trend to have the ADCs running at much higher rates with only smooth filtering, and do the proper band-limiting with digital brickwalls either right at recording, or after the mix. In that scenario there's no reason why frequencies between 20 and 22.05 kHz would be strongly attenuated. – leftaroundabout Sep 15 '14 at 14:41
• @leftaroundabout you left out the filtering happening at the output, after each DAC. These are analog filters necessary to remove the harmonics above thhe nyquist frequency by the DAC: en.wikipedia.org/wiki/Reconstruction_filter – EMV Sep 15 '14 at 19:23
• ...So at the output of a DAC running at 44.1kHz, content present between 20 and 22 kHz is removed. If the output DAC runs above 44.1kHz, it might stay intact. Then again, if the content is present and the output filtering is done badly, aliasing can be audible. So someone creating a piece of audio can choose to filter from 20 kHz to be sure no aliasing turns up in the output chain he has no control over. – EMV Sep 15 '14 at 19:31