Yes, but if you sample the frequency to create a step wave, then neglect to filter the results, you will end up reproducing tons of high frequencies. That is why we need to filter the output for signals >20KHz...to remove these harmonics that result from reproducing the square wave.
Of course, filters aren't perfect, and result in phase shift and roll-off. So we over-sample the signal to create a signal with a much higher frequency than 20KHz, so that the filtering occurs well outside the audible band, allowing us to filter out all of these harmonics without affecting the desired signal.
Basically, the end result is that by sampling the signal, you are introducing high frequency content that must be removed prior to playback. This high frequency content is one of the reasons old CD players from the 80s and 90s cause "listener fatigue", although I have no sources to back up that last statement.
Yup... people need to get very clear in their heads the difference between the recording/sampling/mixing/mastering stages, where high bitrate/width/gear/knowledge is helpful, and playback, which is a completely different thing.
(not for eatmyshorts -you get this I gather) - everyone gets that "upsampling" can't add detail to a recording right? You can't get more than you've got.... no matter what you do. There is no magic. You upsample so you drive harmonics generated in the digital-to-analog process during playback further up in the spectrum so when you get to the analog stage you can use a nice gentle analog filter to filter them out. Without the upsampling, you need a nasty steep analog filter to filter them out, and that can have audible side-effects (or at least measurable) in the audible spectrum.
eatmyshorts - correct me if I mis-stated any of that please....
You got it 100% correct. You upsample simply to move the frequency of the analog filter higher, with a gentle rolloff (and ideally a 1st order filter, so you introduce no phase effects) to get your final signal.
Of course, filters aren't perfect, and result in phase shift and roll-off. So we over-sample the signal to create a signal with a much higher frequency than 20KHz, so that the filtering occurs well outside the audible band, allowing us to filter out all of these harmonics without affecting the desired signal.
Basically, the end result is that by sampling the signal, you are introducing high frequency content that must be removed prior to playback. This high frequency content is one of the reasons old CD players from the 80s and 90s cause "listener fatigue", although I have no sources to back up that last statement.