We have a signal which has had all the unwanted high frequencies filtered out before we performed our original sampling. Unwanted frequencies reappear due to the effect of the digital-to-analog conversion of the digitally sampled signal. The signal has discrete jumps between each data point whenever the signal amplitude changes. These discrete jumps are the source of the high frequencies that appear in the output. Recall that in order to make a discrete jump in the time domain, the signal needs all frequencies in the frequency domain. These frequencies are part of the error signal that appears in the output, which we can?t get rid of. However, if we can manipulate the frequency spectrum of the signal with the quantization error, we can move the error out of the audible range, into frequencies that are above the hearing range. We will need more than 2Khz to hold the quantization error, though. Suppose in between each sample of the signal, zeroes were to be added. The resulting zeroes would represent sample points that were not taken. Since the original signal represents the actual signal minus frequencies that have been removed, adding more data points will not gain or lose information. These data points with the new zeroes will be assigned values in between the current samples, so that they form a smooth curve between the two actual, sampled points. This new signal will have the same frequency composition as the original, but it will have a lot more data points. The result is obvious. The signal appears to have been sampled with a greater frequency than it was originally sampled. This shifts up the Nyquist frequency. 16 times oversampling means sampling the sampled signal at 16 times the original by adding 15 signal values between each existing pair of values. This corresponds to a sampling rate of 16*44.1kHz, which is 705.6kHz.This has a Nyquist frequency of 352.8 kHz. Now, a very bad filter with a shallow slope can be used, as long as the filter does not degrade the signal from zero to 20kHz. This means the filter can reduce the signal from 0dB at 20kHz to -90dB at 352kHz. This is a 332kHz range! This range is so large, that a cheap analog capacitor can be used as the output filter. When the capacitor drifts with age, the listener won?t notice, since the upper end of the range is so far above hearing level. Unfortunately, the quantization effect is not completely solved, yet. There are still some artifacts due to the quantization that result in low frequency noise, which appears to be impossible to remove. This is resolved through the use of a sigmoid-delta modulator and 1-bit D/A conversion. The sigmoid-delta modulator converts the oversampled signal into a 1-bit representation of the signal! In the process, the noise component due to quantization is shifted into the megahertz range, where the cheap filter removes it.