Title :
Multiresolution of the Fourier transform
Author :
Grigoryan, Artyom M. ; Dursun, Serkan
Author_Institution :
Dept. of Electr. Eng., Texas Univ., San Antonio, TX, USA
Abstract :
In this paper, the integral Fourier transform is described as a specific wavelet-like transform with a fully scalable modulated window, but not all possible translations. The transform is defined by sinusoidal waves of half periods. A geometrical locus of frequency-time points for the proposed wavelet-like transform is derived and the function coverage is described and compared with the short-time Fourier transform as well as with the wavelet transform.
Keywords :
Fourier transforms; signal representation; time-frequency analysis; wavelet transforms; Fourier transform multiresolution; frequency-time point geometrical locus; half period sinusoidal waves; integral Fourier transform; joint time-frequency signal representation; multiresolution signal processing; scalable modulated window; short-time Fourier transform; transform translations; wavelet-like transform function coverage; Fourier transforms; Frequency; Image analysis; Image processing; Image resolution; Signal analysis; Signal processing; Signal resolution; Wavelet analysis; Wavelet transforms;
Conference_Titel :
Acoustics, Speech, and Signal Processing, 2005. Proceedings. (ICASSP '05). IEEE International Conference on
Print_ISBN :
0-7803-8874-7
DOI :
10.1109/ICASSP.2005.1416074
