are you joking? yes, CDs are compressed. the sound waves are interpolated, compressed, etc. they are certainly not lossless when compared to the original waves.
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completely wrong. compared to the original recordings, the audio waves pressed onto CDs are certainly compressed. a trained ear can hear the difference; or you can look at the waves. CDs are interpolated.
The term "compression" usually refers to "data compression", that means that by several mathematical tricks (huffmann coding, fourier analysis and synthesis, stereo signal processing, reduction of sampling rate to name some) the size of these files are reduced while trying to keep the audible quality the same. There are a lot of variations of this kind of processing.
What I think you are trying to say is that the data on a CD is digitalized or quantized. That is an inevitable part of the processing and every digital data is quantized. That is just how the technology works. However at 44100 Hz/16 bit this is considered to be not audible. The Nyquist-Shannon sampling theorem explains why that is the case: At 44100 Hz sampling frequency the highest possible frequency is 22050 Hz. Human hearing capabilities are limited to hearing up to 20 kHz (and that is certainly not the case any longer if you are older than, say 20 years). The "vertical" quantization (16 bit) results in a very subtle noise in the background. Most people can't hear this at volumes considered normal.
You also compared the recording to the original sound waves. That is pretty much senseless. You can never achieve a recording that sounds flawlessly like the original waves, as they always are just a (carefully and consciously chosen) excerpt of all the information in the real sound waves. In the signal path you have a microphone, you have a microphone amp, you have an A/D-converter, you have mixing software and at home you have a D/A-Converter, an amp and most important you have loudspeakers. Loudspeakers and Microphones are most likely the bottlenecks of this signal path. The processing in between is pretty much (please forgive me audiophiles) working perfectly nowadays (considering decent quality). The software processing in between is also very important. You see, audio recordings do not claim to be a perfect image of real sounds. Audio recordings do not try to fool you into thinking there is a real band sitting behind your speakers. The tweaking of the sound in the post processing is considered part of the artistic work.
There are recording of live performances as well, but believe me, you
certainly don't need to have trained ears to be able to tell that the sounds coming from your loudspeakers are not "real". So thinking about that, I have absolutely no idea what your problem is.