Nyquist frequency


Nyquist frequency - Definition

The sampling frequency or sampling rate defines the number of samples per second taken from a continuous signal to make a discrete signal. The inverse of the sampling frequency is the sampling period or sampling time, which is the time between samples.

The sampling frequency can only be applied to samplers in which each sample is periodically taken. There is no rule that limits a sampler from taking a sample at a non-periodic rate.

Contents

Sampling theorem

The Nyquist-Shannon sampling theorem states that the sampling frequency has to be twice the bandwidth of the signal being sampled.

Oversampling

In some cases, it is desirable to have a sampling frequency more than twice the bandwidth so that a digital filter can be used in exchange for a weaker analog anti-aliasing filter. This process is known as oversampling.

Audio

In digital audio, common sampling rates are:

8,000 Hz - telephone, adequate for human speech
11,025 Hz
22,050 Hz - radio
44,100 Hz - compact disc
48,000 Hz - digital sound used for films and professional audio
96,000 or 192,400 Hz - DVD Audio

Video

In digital video, which uses a CCD as the sensor, the sampling rate is defined the frame/field rate, rather than the notional pixel clock. All modern TV cameras use CCDs, and the image sampling frequency is the repetition rate of the CCD integration period.

50 Hz - PAL video
60 / 1.001 Hz - NTSC video

When analogue video is converted to digital video, a different sampling process occurs, this time at the pixel frequency. Some common pixel sampling rates are:

13.5 MHz - CCIR 601, D1 video

The Nyquist frequency, named after the Nyquist-Shannon sampling theorem, is half the sampling frequency and is sometimes called the critical frequency. In keeping consistent with the sampling theorem, the nyquist frequency is the same as the bandwidth of the signal being sampled. If the signal is a baseband signal, then the Nyquist frequency corresponds to the maximum frequency in the signal.

As an example, audio CDs have a sampling frequency of 44,100 Hz. The Nyquist frequency is then 22,050 Hz, which represents the highest frequency the data can produce.

It should be noted that the nyquist frequency itself should not be contained within the signal. If the signal contains a frequency at the Nyquist frequency then the phase between the signal and the sampler will determine the level of the frequency contained within the discrete signal.