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To avoid aliasing, the sampling rate must be no less than the Nyquist rate of the signal; that is, the Nyquist rate of the signal must be under double the Nyquist frequency of the sampling. In signal processing , the Nyquist frequency (or folding frequency ), named after Harry Nyquist , is a characteristic of a sampler , which converts a ...
The Nyquist–Shannon sampling theorem is an essential principle for digital signal processing linking the frequency range of a signal and the sample rate required to avoid a type of distortion called aliasing.
If a piece of music is sampled at 32,000 samples per second (Hz), any frequency components at or above 16,000 Hz (the Nyquist frequency for this sampling rate) will cause aliasing when the music is reproduced by a digital-to-analog converter (DAC). The high frequencies in the analog signal will appear as lower frequencies (wrong alias) in the ...
Fig 1: Typical example of Nyquist frequency and rate. They are rarely equal, because that would require over-sampling by a factor of 2 (i.e. 4 times the bandwidth). In signal processing , the Nyquist rate , named after Harry Nyquist , is a value equal to twice the highest frequency ( bandwidth ) of a given function or signal.
The corresponding frequency limit, in cycles per second , is cycle/sample × samples/second = /, known as the Nyquist frequency of the sampler. Therefore, s ( t ) {\displaystyle s(t)} is usually the output of a low-pass filter , functionally known as an anti-aliasing filter .
An anti-aliasing filter (AAF) is a filter used before a signal sampler to restrict the bandwidth of a signal to satisfy the Nyquist–Shannon sampling theorem over the band of interest. Since the theorem states that unambiguous reconstruction of the signal from its samples is possible when the power of frequencies above the Nyquist frequency is ...
Important signals of this sort include a radio's intermediate-frequency (IF), radio-frequency (RF) signal, and the individual channels of a filter bank. If n > 1, then the conditions result in what is sometimes referred to as undersampling, bandpass sampling, or using a sampling rate less than the Nyquist rate (2f H). For the case of a given ...
The Nyquist rate is defined as twice the bandwidth of the signal. Oversampling is capable of improving resolution and signal-to-noise ratio, and can be helpful in avoiding aliasing and phase distortion by relaxing anti-aliasing filter performance requirements. A signal is said to be oversampled by a factor of N if it is sampled at N times the ...