Aliasing, Anti-alias Filter

The effect of an unwanted signal appearing in the wrong place is called aliasing.

Recording a steadily rising sine wave tone. At lower frequency, putting a tone through a DA converter, the tone is sampled with many points per cycle. As the tone rises in frequency, fewer and fewer sample points are available to describe it. At a frequency half of the sampling rate, only two sample points are available per cycle. Those two points are adequate, in a theoretical world, to recreate the tone after conversion back to an analog signal and putting it through a low-pass filtering to smooth it to the original wave form.

If the tone now continues to rise, the number of samples per cycle is not adequate to describe the waveform anymore. This inadequate description is even equivalent to a lower frequency tone.
In fact, the tone seems to reflect around the 24 KHz point. A 25 KHz tone becomes indistinguishable from a 23 KHz tone. A 30 KHz tone becomes an 18 KHz tone, etc.

The Nyquist Theorem defines that it is possible to successfully sample and play back frequency components up to one-half the sampling frequency.
It can be summarized as follows: to be able to reconstruct a signal, the sampling frequency must be at least twice the frequency of the signal being sampled, the highest frequency that can be represented using a sampling rate of N Hz is: ½N Hz.

When aliasing occurs, the new frequency generated will be fs - fin, where fs is the sampling frequency and fin is the frequency of the input signal.

To accomplish the Nyquist Theorem, the original analogue audio is low-pass filtered to ensure that nothing above half the sampling frequency can enter the system. This filter is called an anti-alias filter. Steep (brickwall) filters are usually put in front of an AD converter input to prevent signals above the Nyquist frequency from entering the system.

The sampling rate of the CD, 44.1kHz, is only just adequate for an audio bandwidth of 20kHz. In order to realize fully the performance potential of the system, anti-alias filters must be perfectly flat to 20kHz but attenuate signals strongly above 22.05kHz, requiring a rolloff on the order of 600dB/octave. Early generations of recording and replay equipment made a more or less good job of this with sophisticated analogue filters.