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In signal processing, sampling is the reduction of a continuous-time signal to a discrete-time signal. A common example is the conversion of a sound wave to a sequence of "samples". A sample is a value of the signal at a point in time and/or space; this definition differs from the term's usage in statistics, which refers to a set of such values ...
In digital signal processing (DSP), a normalized frequency is a ratio of a variable frequency and a constant frequency associated with a system (such as a sampling rate, ). Some software applications require normalized inputs and produce normalized outputs, which can be re-scaled to physical units when necessary.
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. The theorem states that the sample rate must be at least twice the bandwidth of the signal to avoid aliasing.
Early uses of the term Nyquist frequency, such as those cited above, are all consistent with the definition presented in this article.Some later publications, including some respectable textbooks, call twice the signal bandwidth the Nyquist frequency; [6] [7] this is a distinctly minority usage, and the frequency at twice the signal bandwidth is otherwise commonly referred to as the Nyquist rate.
Sampling rate conversion systems are used to change the sampling rate of a signal. The process of sampling rate decrease is called decimation, and the process of sampling rate increase is called interpolation. T. Schilcher. RF applications in digital signal processing//" Digital signal processing".
The sinc function as audio, at 2000 Hz (±1.5 seconds around zero) In mathematics, the historical unnormalized sinc function is defined for x ≠ 0 by = .. Alternatively, the unnormalized sinc function is often called the sampling function, indicated as Sa(x).
It has important applications in signal processing, [1] magnetic resonance imaging, [2] and the numerical solution of partial differential equations. [3] As a generalized approach for nonuniform sampling, the NUDFT allows one to obtain frequency domain information of a finite length signal at any frequency. One of the reasons to adopt the NUDFT ...
An analog-to-digital converter (ADC) can be modeled as two processes: sampling and quantization. Sampling converts a time-varying voltage signal into a discrete-time signal, a sequence of real numbers. Quantization replaces each real number with an approximation from a finite set of discrete values.