Search results
Results From The WOW.Com Content Network
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.
A typical choice of characteristic frequency is the sampling rate that is used to create the digital signal from a continuous one. The normalized quantity, f ′ = f f s , {\displaystyle f'={\tfrac {f}{f_{s}}},} has the unit cycle per sample regardless of whether the original signal is a function of time or distance.
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 ...
[1] [2] When the process is performed on a sequence of samples of a signal or a continuous function, it produces an approximation of the sequence that would have been obtained by sampling the signal at a lower rate (or density, as in the case of a photograph). Decimation is a term that historically means the removal of every tenth one.
This Fourier series (in frequency) is a continuous periodic function, whose periodicity is the sampling frequency /. The subscript 1 / T {\displaystyle 1/T} distinguishes it from the continuous Fourier transform S ( f ) {\displaystyle S(f)} , and from the angular frequency form of the DTFT.
Instead, the sampling of the signal should be made in a short enough interval that it can represent the instantaneous value of the signal with the highest frequency. This means that in the FM radio example above, the sampling circuit must be able to capture a signal with a frequency of 108 MHz, not 43.2 MHz.
Fig 2: The first triangle of the first graph represents the Fourier transform X(f) of a continuous function x(t). The entirety of the first graph depicts the discrete-time Fourier transform of a sequence x[n] formed by sampling the continuous function x(t) at a low-rate of 1/T. The second graph depicts the application of a lowpass filter at a ...
If the ratio of the two sample rates is (or can be approximated by) [A] [4] a fixed rational number L/M: generate an intermediate signal by inserting L − 1 zeros between each of the original samples. Low-pass filter this signal at half of the lower of the two rates. Select every M-th sample from the filtered output, to obtain the result. [5]