Search results
Results From The WOW.Com Content Network
The term Nyquist Sampling Theorem (capitalized thus) appeared as early as 1959 in a book from his former employer, Bell Labs, [22] and appeared again in 1963, [23] and not capitalized in 1965. [24] It had been called the Shannon Sampling Theorem as early as 1954, [25] but also just the sampling theorem by several other books in the early 1950s.
For a given sampling rate (samples per second), the Nyquist frequency (cycles per second) is the frequency whose cycle-length (or period) is twice the interval between samples, thus 0.5 cycle/sample. For example, audio CDs have a sampling rate of 44100 samples/second. At 0.5 cycle/sample, the corresponding Nyquist frequency is 22050 cycles/second .
The Shannon sampling theory for non-uniform sampling states that a band-limited signal can be perfectly reconstructed from its samples if the average sampling rate satisfies the Nyquist condition. [1] Therefore, although uniformly spaced samples may result in easier reconstruction algorithms, it is not a necessary condition for perfect ...
In our example, the vector space of sampled signals is n-dimensional complex space. Any proposed inverse R of F ( reconstruction formula , in the lingo) would have to map C n {\displaystyle \mathbb {C} ^{n}} to some subset of L 2 {\displaystyle L^{2}} .
As with the Nyquist–Shannon sampling theorem, this theorem also assumes an idealization of any real-world situation, as it only applies to functions that are sampled over an infinitude of points. Perfect reconstruction is mathematically possible for the idealized model but only an approximation for real-world functions and sampling techniques ...
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 ...
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 ...
Download as PDF; Printable version; ... move to sidebar hide. sampling theory may mean: Nyquist–Shannon sampling theorem, digital signal ... Fourier sampling