### Abstract

In a broader scope, a transformation in mathematics can broadly be defined as the operation which takes its input and “represents” it in a different form. Such a definition immediately implies preserving the essential characteristics of the input through several conservation rules or laws. In order to outline the complete input-output relationship in an abstract transformation, the input and output of the transformation should be characterized as well. Therefore, mathematically speaking, a transformation can be viewed as a special function (or a correspondence) whose input and output can be a single value or another function. In this context, signals are considered to be both input and output functions of the transformation of interest.

Original language | English |
---|---|

Title of host publication | Mathematical Foundations for Signal Processing, Communications, and Networking |

Publisher | CRC Press |

Pages | 5-33 |

Number of pages | 29 |

ISBN (Electronic) | 9781439855140 |

ISBN (Print) | 9781138072169 |

DOIs | |

Publication status | Published - 1 Jan 2017 |

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### ASJC Scopus subject areas

- Computer Science(all)
- Mathematics(all)
- Engineering(all)

### Cite this

*Mathematical Foundations for Signal Processing, Communications, and Networking*(pp. 5-33). CRC Press. https://doi.org/10.1201/9781351105668

**Signal processing transforms.** / Yarkan, Serhan; Qaraqe, Khalid.

Research output: Chapter in Book/Report/Conference proceeding › Chapter

*Mathematical Foundations for Signal Processing, Communications, and Networking.*CRC Press, pp. 5-33. https://doi.org/10.1201/9781351105668

}

TY - CHAP

T1 - Signal processing transforms

AU - Yarkan, Serhan

AU - Qaraqe, Khalid

PY - 2017/1/1

Y1 - 2017/1/1

N2 - In a broader scope, a transformation in mathematics can broadly be defined as the operation which takes its input and “represents” it in a different form. Such a definition immediately implies preserving the essential characteristics of the input through several conservation rules or laws. In order to outline the complete input-output relationship in an abstract transformation, the input and output of the transformation should be characterized as well. Therefore, mathematically speaking, a transformation can be viewed as a special function (or a correspondence) whose input and output can be a single value or another function. In this context, signals are considered to be both input and output functions of the transformation of interest.

AB - In a broader scope, a transformation in mathematics can broadly be defined as the operation which takes its input and “represents” it in a different form. Such a definition immediately implies preserving the essential characteristics of the input through several conservation rules or laws. In order to outline the complete input-output relationship in an abstract transformation, the input and output of the transformation should be characterized as well. Therefore, mathematically speaking, a transformation can be viewed as a special function (or a correspondence) whose input and output can be a single value or another function. In this context, signals are considered to be both input and output functions of the transformation of interest.

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U2 - 10.1201/9781351105668

DO - 10.1201/9781351105668

M3 - Chapter

AN - SCOPUS:85051612904

SN - 9781138072169

SP - 5

EP - 33

BT - Mathematical Foundations for Signal Processing, Communications, and Networking

PB - CRC Press

ER -