Hamming spectral window - definizione. Che cos'è Hamming spectral window
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Cosa (chi) è Hamming spectral window - definizione

Hamming (7,4); Hamming code(7,4); Hamming code (7,4); Hamming code 7,4; Hamming 7,4; Hamming (7,4) code; Hamming 7,4 code
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Richard Hamming         
  • modulo]] 16, in the 16-color system.
AMERICAN MATHEMATICIAN AND INFORMATION THEORIST
Richard W. Hamming; Richard W Hamming; Richard Wesley Hamming; Hamming, Richard Wesley; Hamming, Richard; Richard Hammering; R. W. Hammering
<person> Professor Richard Wesley Hamming (1915-02-11 - 1998-01-07). An American mathematician known for his work in information theory (notably {error detection and correction}), having invented the concepts of Hamming code, Hamming distance, and Hamming window. Richard Hamming received his B.S. from the University of Chicago in 1937, his M.A. from the University of Nebraska in 1939, and his Ph.D. in mathematics from the University of Illinois at Urbana-Champaign in 1942. In 1945 Hamming joined the Manhattan Project at Los Alamos. In 1946, after World War II, Hamming joined the {Bell Telephone Laboratories} where he worked with both Shannon and John Tukey. He worked there until 1976 when he accepted a chair of computer science at the Naval Postgraduate School at Monterey, California. Hamming's fundamental paper on error-detecting and error-correcting codes ("Hamming codes") appeared in 1950. His work on the IBM 650 leading to the development in 1956 of the L2 programming language. This never displaced the workhorse language L1 devised by Michael V Wolontis. By 1958 the 650 had been elbowed aside by the 704. Although best known for error-correcting codes, Hamming was primarily a numerical analyst, working on integrating differential equations and the Hamming spectral window used for smoothing data before Fourier analysis. He wrote textbooks, propounded aphorisms ("the purpose of computing is insight, not numbers"), and was a founder of the ACM and a proponent of open-shop computing ("better to solve the right problem the wrong way than the wrong problem the right way."). In 1968 he was made a fellow of the {Institute of Electrical and Electronics Engineers} and awarded the Turing Prize from the Association for Computing Machinery. The Institute of Electrical and Electronics Engineers awarded Hamming the Emanuel R Piore Award in 1979 and a medal in 1988. http://www-gap.dcs.st-and.ac.uk/Richard Hamminghistory/Mathematicians/Hamming.html. http://zapata.seas.smu.edu/Richard Hamminggorsak/hamming.html. http://webtechniques.com/archives/1998/03/homepage/. [Richard Hamming. Coding and Information Theory. Prentice-Hall, 1980. ISBN 0-13-139139-9]. (2003-06-07)
Hamming, Richard         
  • modulo]] 16, in the 16-color system.
AMERICAN MATHEMATICIAN AND INFORMATION THEORIST
Richard W. Hamming; Richard W Hamming; Richard Wesley Hamming; Hamming, Richard Wesley; Hamming, Richard; Richard Hammering; R. W. Hammering
Window function         
  • ''t''}}&nbsp;=&nbsp;0.1}}
  • Bartlett–Hann window
  • Blackman–Harris window
  • Blackman–Nuttall window
  • Confined Gaussian window, ''σ''<sub>''t''</sub>&nbsp;=&nbsp;0.1
  • Sine window
  • DPSS window, ''α''&nbsp;=&nbsp;2
  • DPSS window, ''α''&nbsp;=&nbsp;3
  • Dolph–Chebyshev window, ''α''&nbsp;=&nbsp;5
  • Exponential window, ''τ''&nbsp;=&nbsp;(''N''/2)/(60/8.69)
  • Exponential window, ''τ''&nbsp;=&nbsp;''N''/2
  • GAP window (GAP optimized Nuttall window)
  • Gaussian window, ''σ''&nbsp;=&nbsp;0.4
  • Hamming window, ''a''<sub>0</sub>&nbsp;=&nbsp;0.53836 and ''a''<sub>1</sub>&nbsp;=&nbsp;0.46164. The original Hamming window would have ''a''<sub>0</sub>&nbsp;=&nbsp;0.54 and ''a''<sub>1</sub>&nbsp;=&nbsp;0.46.
  • Hann–Poisson window, ''α''&nbsp;=&nbsp;2
  • Kaiser window, ''α''&nbsp;=&nbsp;2
  • Kaiser window, ''α''&nbsp;=&nbsp;3
  • Sinc or Lanczos window
  • Nuttall window, continuous first derivative
  • Parzen window
  • Planck–Bessel window, ''ε''&nbsp;=&nbsp;0.1, ''α''&nbsp;=&nbsp;4.45
  • Planck-taper window, ''ε''&nbsp;=&nbsp;0.1
  • Rectangular window
  • 1=''α''&nbsp;=&nbsp;0.5}}
  • The Ultraspherical window's ''µ'' parameter determines whether its Fourier transform's side-lobe amplitudes decrease, are level, or (shown here) increase with frequency.
  • Welch window
  • Flat-top window
  • 1=''α''&nbsp;=&nbsp;0.16}}
  • Hann window
  • Triangular window (with ''L''&nbsp;=&nbsp;''N''&nbsp;+&nbsp;1)
FUNCTION USED IN SIGNAL PROCESSING
Window Function; Windowed frame; Window (signal processing); Apodization function; Rectangular window; Bartlett window; Triangular window; Bartlett-Hann window; Blackman window; Blackman-Harris window; Blackman-Nuttall window; Flat top window; Hamming window; Multiple overlap window; Triple overlapped cosine window; Gauss window; Sine window; Bessel window; Gaussian window; Bartlett function; Hamming function; Apodisation function; Hammingwindow; Windowing function; Barlett-Hann window; Windowing functions; Window functions; Tapering function; Tapering Function; Tapering (signal processing); Cosine window; De la Vallé Poussin window; De la Vallée Poussin window; Welch window; Bohman window; Boxcar window; Hann–Poisson window; Tukey window; Hann-Poisson window; DPSS window; List of window functions
In signal processing and statistics, a window function (also known as an apodization function or tapering function) is a mathematical function that is zero-valued outside of some chosen interval, normally symmetric around the middle of the interval, usually near a maximum in the middle, and usually tapering away from the middle. Mathematically, when another function or waveform/data-sequence is "multiplied" by a window function, the product is also zero-valued outside the interval: all that is left is the part where they overlap, the "view through the window".

Wikipedia

Hamming(7,4)

In coding theory, Hamming(7,4) is a linear error-correcting code that encodes four bits of data into seven bits by adding three parity bits. It is a member of a larger family of Hamming codes, but the term Hamming code often refers to this specific code that Richard W. Hamming introduced in 1950. At the time, Hamming worked at Bell Telephone Laboratories and was frustrated with the error-prone punched card reader, which is why he started working on error-correcting codes.

The Hamming code adds three additional check bits to every four data bits of the message. Hamming's (7,4) algorithm can correct any single-bit error, or detect all single-bit and two-bit errors. In other words, the minimal Hamming distance between any two correct codewords is 3, and received words can be correctly decoded if they are at a distance of at most one from the codeword that was transmitted by the sender. This means that for transmission medium situations where burst errors do not occur, Hamming's (7,4) code is effective (as the medium would have to be extremely noisy for two out of seven bits to be flipped).

In quantum information, the Hamming (7,4) is used as the base for the Steane code, a type of CSS code used for quantum error correction.