A key observation in digital audio theory is that the entire waveform is represented by the sampling points, but a reconstruction process still needs to occur in order to recreate the waveform represented. One cannot simply “connect the dots” between sample points and yield the original waveform.A waveform can be represented in multiple ways during the process of sampling, display and reconstruction.The process of recreating the original waveform from the sampled waveform involves a filter called a reconstruction filter. This filter removes all content above the Nyquist frequency (half the sample rate). The range below the Nyquist frequency defines the “legal” range of allowed frequencies as frequencies in this range can be accurately reproduced. All frequencies above the Nyquist frequency do not adhere to Nyquist or Shannon’s theorems regarding allowable frequencies, cannot be reproduced and are therefore considered “illegal” frequencies. Because of mathematical realities observed by Fourier in the 1800’s and subsequently by Shannon in 1948, when a waveform has all frequencies removed above the Nyquist frequency, the resulting waveform will be the original waveform that was sampled.This process is significantly more involved than simply “connecting the dots” between sample points. Today it involves extremely sophisticated means of reconstructing the waveform, using filters that are highly complex mathematical systems utilizing “oversampling,” “upsampling,” “linear phase, equiripple FIR” designs and much more.Oversampling creates a more accurate digital representation of an analog signal by sampling some number of times per second (frequency) and converting into digital form. Oversampling requires at least twice the bandwidth of the frequency being sampled. For example, a consumer CD player using 2x oversampling is processing information at 88.2 kHz.The result is that today’s digital to analog converters get closer to the original than ever before, making music played on systems today as accurate as possible. Even today’s inexpensive components such as off-the-shelf CD players have drastically improved filters and thus better reconstruction abilities than in years past.