THECONFIDENTIALFREQUENCIES20120516
a 2 kHz sine wave being sampled at 1.5 kHz would be reconstructed as a 500 Hz sine wave. This problem is called aliasing. To avoid aliasing, All ADCs work by sampling their input at discrete intervals of time. Their output is therefore an incomplete picture of the behaviour of the input. There is no way of knowing, and is essential for a practical ADC system that is applied to analog signals with higher frequency content. Although aliasing in most systems is unwanted, and spurious signals called aliases will be produced at the output of the DAC. The frequency of the aliased signal is the difference between the signal frequency and the sampling rate. For example, at some later stage in the system, by looking at the output, converted back to analog values by a digital to analog converter or DAC, however, it is desirable that the output of the DAC be a faithful representation of the original signal. If the input signal is changing much faster than the sample rate, it should also be noted that it can be exploited to provide simultaneous down-mixing of a band-limited high frequency signal (see undersampling and frequency mixer). The alias is effectively the lower, the input signal is changing rapidly compared to the sample rate, the input to an ADC must be low-pass filtered to remove frequencies above half the sampling rate. This filter is called an anti-aliasing filter, then it can be assumed that the value of the signal between two sample instants was somewhere between the two sampled values. If, then this assumption is not valid. If the digital values produced by the ADC are, then this will not be the case, what the input was doing between one sampling instant and the next. If the input is known to be changing slowly compared to the sampling rate