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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.
In this example, f s is the sampling rate, and 0.5 cycle/sample × f s is the corresponding Nyquist frequency. The black dot plotted at 0.6 f s represents the amplitude and frequency of a sinusoidal function whose frequency is 60% of the sample rate. The other three dots indicate the frequencies and amplitudes of three other sinusoids that ...
The sampling frequency or sampling rate, , is the average number of samples obtained in one second, thus = /, with the unit samples per second, sometimes referred to as hertz, for example 48 kHz is 48,000 samples per second.
The samples (sometimes called frequency bins) are numbered consecutively, corresponding to a frequency normalization by . [2]: p.56 eq.(16) [3] The normalized Nyquist frequency is with the unit 1 / N th cycle/sample. Angular frequency, denoted by and with the unit radians per second, can be similarly normalized.
This factor multiplies the sampling interval or, equivalently, divides the sampling rate. For example, if compact disc audio at 44,100 samples/second is decimated by a factor of 5/4, the resulting sample rate is 35,280. A system component that performs decimation is called a decimator.
The sampling theorem states that sampling frequency would have to be greater than 200 Hz. Sampling at four times that rate requires a sampling frequency of 800 Hz. This gives the anti-aliasing filter a transition band of 300 Hz ((f s /2) − B = (800 Hz/2) − 100 Hz = 300 Hz) instead of 0 Hz if the sampling frequency was 200 Hz. Achieving an ...
In method 1, a slow pre-computation (such as the Remez algorithm) can be used to obtain an optimal (per application requirements) filter design. Method 2 will work in more general cases, e.g. where the ratio of sample rates is not rational, or two real-time streams must be accommodated, or the sample rates are time-varying.
The sampling theorem introduces the concept of a sample rate that is sufficient for perfect fidelity for the class of functions that are band-limited to a given bandwidth, such that no actual information is lost in the sampling process. It expresses the sufficient sample rate in terms of the bandwidth for the class of functions.