Fourier Transforms – The Math Trick Behind MP3s, JPEGs, and Homer Simpson’s Face
This is a great post, but it's a little bit misleading when talking about MP3s and lossy compression and conflates analog fourier analysis with discrete analysis.When you're talking about a digital signal, it is the sample rate that determines the maximum frequency you can represent.  It's not MP3s that "throw out the really high notes" -- it's any digital signal.   A discrete fourier transform actually is lossless, but it is bandwidth limited.The reason audiophiles prefer Flac to MP3s, for instance, is because MP3s do more than just "throw out the high notes."  Both are bandwidth limited, but MP3s also throw out other information based on psychoacoustic principles.