### Abstract

The Hartley transform, using yet another set of orthogonal functions, is purely real and fully equivalent to the well-known Fourier transform. It is an offshoot of the Fourier transform with the same physical significance as that of its progenitor. The fact that the Fourier and Hartley transforms contain the same information at each frequency combined with that these two transforms yield identical amplitude and phase paves the way for phrasing them to be a mathematical twin. The Hartley transform has some computational advantages over the Fourier transform and therefore can be an ideal alternative to the Fourier transform for all its applications. Some salient features of this transform which is emerging as an important tool in the field of digital signal processing are incorporated herein.

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

Pages (from-to) | 1361-1365 |

Number of pages | 5 |

Journal | Indian Journal of Pure and Applied Mathematics |

Volume | 28 |

Issue number | 10 |

Publication status | Published - Oct 1997 |

### Fingerprint

### Keywords

- Fourier transforms
- Hartley transforms
- Orthogonal functions

### ASJC Scopus subject areas

- Mathematics(all)

### Cite this

*Indian Journal of Pure and Applied Mathematics*,

*28*(10), 1361-1365.

**Fourier and Hartley transforms - A mathematical twin.** / Sundararajan, N.

Research output: Contribution to journal › Article

*Indian Journal of Pure and Applied Mathematics*, vol. 28, no. 10, pp. 1361-1365.

}

TY - JOUR

T1 - Fourier and Hartley transforms - A mathematical twin

AU - Sundararajan, N.

PY - 1997/10

Y1 - 1997/10

N2 - The Hartley transform, using yet another set of orthogonal functions, is purely real and fully equivalent to the well-known Fourier transform. It is an offshoot of the Fourier transform with the same physical significance as that of its progenitor. The fact that the Fourier and Hartley transforms contain the same information at each frequency combined with that these two transforms yield identical amplitude and phase paves the way for phrasing them to be a mathematical twin. The Hartley transform has some computational advantages over the Fourier transform and therefore can be an ideal alternative to the Fourier transform for all its applications. Some salient features of this transform which is emerging as an important tool in the field of digital signal processing are incorporated herein.

AB - The Hartley transform, using yet another set of orthogonal functions, is purely real and fully equivalent to the well-known Fourier transform. It is an offshoot of the Fourier transform with the same physical significance as that of its progenitor. The fact that the Fourier and Hartley transforms contain the same information at each frequency combined with that these two transforms yield identical amplitude and phase paves the way for phrasing them to be a mathematical twin. The Hartley transform has some computational advantages over the Fourier transform and therefore can be an ideal alternative to the Fourier transform for all its applications. Some salient features of this transform which is emerging as an important tool in the field of digital signal processing are incorporated herein.

KW - Fourier transforms

KW - Hartley transforms

KW - Orthogonal functions

UR - http://www.scopus.com/inward/record.url?scp=0031330433&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0031330433&partnerID=8YFLogxK

M3 - Article

VL - 28

SP - 1361

EP - 1365

JO - Indian Journal of Pure and Applied Mathematics

JF - Indian Journal of Pure and Applied Mathematics

SN - 0019-5588

IS - 10

ER -