## The Origins of the Sampling Theorem

Citations: | 3 - 0 self |

### BibTeX

@MISC{Lüke_theorigins,

author = {Hans Dieter Lüke},

title = {The Origins of the Sampling Theorem},

year = {}

}

### OpenURL

### Abstract

the two revolutionary papers in which he founded the information theory [1, 2]. In [1] the sampling theorem is formulated as “Theorem 13”: Let f(t) contain no frequencies over W. Then ∞ sin π ( 2Wt−n) f() t = ∑ Xn

### Citations

584 |
Communication in the presence of noise
- Shannon
- 1949
(Show Context)
Citation Context ... the Sampling Theorem Hans Dieter Lüke, Aachen University of Technology ABSTRACT I n 1948 and 1949, Claude E. Shannon published the two revolutionary papers in which he founded the information theory =-=[1, 2]-=-. In [1] the sampling theorem is formulated as “Theorem 13”: Let f(t) contain no frequencies over W. Then ∞ sin π( 2Wt−n) f() t = ∑ Xn −∞ π( 2 Wt−n) where n Xn = f W ⎛ ⎞ . ⎝2 ⎠ Fifty years ago the pub... |

159 |
A mathematical theory of communication,” Bell Sys
- Shannon
- 1948
(Show Context)
Citation Context ... the Sampling Theorem Hans Dieter Lüke, Aachen University of Technology ABSTRACT I n 1948 and 1949, Claude E. Shannon published the two revolutionary papers in which he founded the information theory =-=[1, 2]-=-. In [1] the sampling theorem is formulated as “Theorem 13”: Let f(t) contain no frequencies over W. Then ∞ sin π( 2Wt−n) f() t = ∑ Xn −∞ π( 2 Wt−n) where n Xn = f W ⎛ ⎞ . ⎝2 ⎠ Fifty years ago the pub... |

81 |
The Shannon Sampling Theorem - Its Various Extensions and Applications: A Tutorial Review
- Jerri
- 1977
(Show Context)
Citation Context ...efers to this book in [2]. By way of conclusion, it should be mentioned that an extensive tutorial review of the development of the sampling theorem after Shannon was published by A. J. Jerri in 1977 =-=[14]-=-. CONCLUSION The sampling theorem for lowpass functions plays an important role in communication engineering as a connecting link between continuous-time and discrete-time signals. The numerous differ... |

69 |
On the functions which are represented by the expansion of the interpolation theory
- Whittaker
- 1915
(Show Context)
Citation Context ... functions which are represented by the expansions of the interpolation theory” in 1915 must therefore be regarded as the first work ever to address the sampling theorem for all bandlimited functions =-=[12]-=-. Whittaker addresses the problem of achieving the smoothest possible interpolation without singularities and without “rapid oscillations” for given tabular values of a function f(x). In order to fulf... |

45 |
The intelligibility of interrupted speech
- Miller, Licklider
- 1950
(Show Context)
Citation Context ...ible to reduce the sampling rate and still achieve the same word intelligibility. This dependency was examined quantitatively by G. A. Miller and J. C. R. Licklider; their results are shown in Fig. 3 =-=[8]-=-. According to these results, word intelligibility with a dropping sampling rate is only reduced monotonely for very short sampling impulses (up to a relative width of approximately 6 percent of the s... |

26 |
Interpolatory Function Theory
- WHITTAKER
(Show Context)
Citation Context ...rs this important invariance property of the sampling theorem as “consistency.” Subsequent publications on the cardinal function are cited by J. M. Whittaker (not to be confused with E. T. Whittaker) =-=[13]-=-. Shannon then refers to this book in [2]. By way of conclusion, it should be mentioned that an extensive tutorial review of the development of the sampling theorem after Shannon was published by A. J... |

10 |
Cattermole, Principles of Pulse Code Modulation
- W
- 1969
(Show Context)
Citation Context ... Figure 1. Circuit diagram. 106 0163-6804/99/$10.00 © 1999 IEEE IEEE Communications Magazine • April 1999In the 1930s several TDM systems for telephony were developed. However, as Cattermole remarks =-=[7]-=-: The situation about 1936, then, was that sampling and TDM telephony were known empirically though the theory was rudimentary .... Some authors, such as M. Marro in 1938, appear to give toolow sampli... |

4 |
Untersuchungen an der wechselzeitigen Mehrfachübertragung (Multiplexübertragung), Elektr. Nachr. 16
- Raabe
- 1939
(Show Context)
Citation Context ... of the sampling theorem in the literature of communication engineering came about independent of one another. Thus, H. Raabe deduced the sampling theorem in his Ph.D. thesis and published it in 1939 =-=[10]-=-. This publication is especially relevant to the practical application of the sampling theorem, since it is here that the influence of sampling impulses of finite duration is taken into account in the... |

2 |
Time division multiplex systems,” Bell Sys
- Bennett
- 1941
(Show Context)
Citation Context ...ty by time division multiplex transmission. This work also contains a special sampling theorem for bandpass signals. Raabe’s work is cited in a related publication by W. R. Bennett from the year 1941 =-=[11]-=-, and Bennett’s work is in turn cited by Shannon in [2] as one of the sources of the sampling theorem. Lastly, it should be mentioned that the sampling theorem is also treated in 1949 in the Japanese ... |

1 |
Geschichte der elektrischen Telegraphie
- Zetzsche
(Show Context)
Citation Context ...8), A. V. Newton (1851), and M. B. Farmer (1853). Technically more accomplished methods were then developed by B. Meyer (1870), J. M. E. Baudot (to 1874), as well as P. Lacour and P. B. Delany (1878) =-=[3, 4]-=-. It is significant not only that methods were used in which complete telegraphic signals from different transmitters were placed in chronological order (e.g., Baudot), but that certain systems were a... |

1 |
Die Mehrfach-Telegraphie auf einem Drahte
- Granfeld
(Show Context)
Citation Context ...8), A. V. Newton (1851), and M. B. Farmer (1853). Technically more accomplished methods were then developed by B. Meyer (1870), J. M. E. Baudot (to 1874), as well as P. Lacour and P. B. Delany (1878) =-=[3, 4]-=-. It is significant not only that methods were used in which complete telegraphic signals from different transmitters were placed in chronological order (e.g., Baudot), but that certain systems were a... |

1 |
Recent developments in multiplex-telephony,” Elec
- Miner
- 1903
(Show Context)
Citation Context ...first demonstration of TDM of telephone signals. The inventor’s name was Willard M. Miner. He had his method patented in 1903 following many years of preliminary experiments [5]. Figures 1 and 2 from =-=[6]-=- show the circuit diagram and the “Patten Distributor” which was used. Miner determined the required sampling rate experimentally [6]: It will be understood, then, that the apparatus devised by Mr. Mi... |

1 |
O propusknoj sposobnosti ‘efira’ i provoloki v elektrosvjazi,” (“On the transmission capacity of ‘ether’ and wire
- Kotelnikov
(Show Context)
Citation Context ...ov. In his work “On the transmission capacity of ‘ether’ and wire in electrical communications,” published in 1933, he proves the sampling theorems for lowpass signals as well as for bandpass signals =-=[9]-=-. He uses these theorems in the course of his work to show that the bandwidth of an analog signal cannot be reduced by modulation methods. The lowpass sampling theorem is formulated as follows: THEORE... |