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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.
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]
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 ...
Reduce high-frequency signal components with a digital lowpass filter. Decimate the filtered signal by M; that is, keep only every M th sample. Step 2 alone creates undesirable aliasing (i.e. high-frequency signal components will copy into the lower frequency band and be mistaken for lower frequencies). Step 1, when necessary, suppresses ...
An early breakthrough in signal processing was the Nyquist–Shannon sampling theorem. It states that if a real signal's highest frequency is less than half of the sampling rate, then the signal can be reconstructed perfectly by means of sinc interpolation. The main idea is that with prior knowledge about constraints on the signal's frequencies ...
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.
In both cases, the dominant component is at the signal frequency: = / =. Also visible in Fig 2 is the spectral leakage pattern of the = rectangular window. The illusion in Fig 3 is a result of sampling the DTFT at just its zero-crossings. Rather than the DTFT of a finite-length sequence, it gives the impression of an infinitely long sinusoidal ...
In digital signal processing, upsampling, expansion, and interpolation are terms associated with the process of resampling in a multi-rate digital signal processing system. Upsampling can be synonymous with expansion, or it can describe an entire process of expansion and filtering (interpolation).