# Analog and Digital Conversion/Nyquist Sampling Rate

## Aliasing

[edit | edit source]If a sampler is only reading in values at particular times, it can become confused if the input frequency is too fast. The resulting problem is called **Aliasing**, and is a major factor in Sampler design.

- Aliasing
- When the input signal frequency is faster than half the sampling frequency, the sampled result will appear to be a low-frequency wave.

In the image above, the black dots are the sampling points, and the red sinusoid is the input waveform. Notice that since the sampler is sampling so slowly, the output appears to be the blue waveform, which is slower.

## Nyquist Sampling Rate

[edit | edit source]To avoid the problem of aliasing, the **Nyquist Sampling Rate** should be considered the slowest possible sampling rate. Any slower then the nyquist sampling rate, and the sampler is in danger of producing an aliased signal.

- Nyquist Sampling Rate
- The nyquist sampling rate is two times the highest frequency of the input signal.

For instance, if the input signal has a high-frequency component of 1 kHz, then the sampler must sample *at least* 2 kHz, or the signal might alias. However, if the sampler happens to sample the waveform exactly at the places where it crosses the zero line, it will appear like there is zero signal. Therefore, the nyquist sampling rate is a bare minimum, and it is recommended that samplers sample much faster than the minimum. For instance, one common guideline recommends sampling at least 10 times faster than the input signal.

When designing a system, there are 2 ways to prevent ultrasonic sounds (or other unwanted high-frequency noise) from aliasing to a lower frequency, becoming audible noise:

- Adjust the capacitors or other components of the anti-aliasing filter so it blocks all frequencies more than half the sampling rate.
- Adjust the sampling rate to more than twice the frequency of the highest frequency passed by the anti-aliasing filter.