Logarithmic frequency representation plays an important role in many audio and acoustic signal processing applications. This article presents a methodology for frequency-warped signal processing where the frequency representation is logarithmic above a certain limit frequency. It is demonstrated how this approach can be used with FFT or linear prediction to perform non-parametric, or parametric...

We show that a stationary signal concept such as the Fourier transform (FT) can be linked to a time-varying (TV) concept such as linear TV filtering. In particular, we give a continuous-time and discrete-time linear TV filter interpretation to continuous-time FT and discrete Fourier transform (DFT), respectively. As a consequence, important variants such as warped DFT, DCT, DST also can be view...

The fractional Fourier transform is a mathematical operation that generalizes the well-known Fourier transform. This operation has been shown to have physical and optical fundamental meanings, and it has been experimentally implemented by relatively simple optical setups. Based on the fractional Fourier-transform operation, a new space-frequency chart definition is introduced. By the applicatio...

A new design of laser warning system is proposed. This novel system is composed of an optical antenna based on fiber bundle and a spatially modulated stationary Michelson interferometer as Fourier transform device. The interferometer has no moving parts, which can distinguish laser from background noise and from other non-coherent radiation such as flares, sunlight, and lighting. Based on Fouri...

Image processing is a recent trend that is grabbing attention in almost all areas like space, medical, defence, authentication systems etc. ,. Discrete Fourier Transforms is one of the most used transforms in image processing. Discrete Fourier Transform helps to transform the signal from spatial domain to frequency domain which is often used for filtering, correlation analysis and spectrum anal...

In this paper, we introduce a novel algorithm to perform multi-scale Fourier transform analysis of piecewise stationary signals with application to automatic speech recognition. Such signals are composed of quasi-stationary segments of variable lengths. Therefore, in the proposed algorithm, signals are analyzed with multiple-sized windows. Resulting power spectra are then normalized such that t...

This paper presents a novel method for classifying an image into one of predeened classes in a data bank by applying mutual information to a representation of the Fourier amplitude domain. Template and test images are made translation and rotation invariant through the Fourier-Mellin transform. While mutual information could be employed here, we choose instead to apply it to the lower dimension...

A new method to generate synthetic online signatures is presented. The algorithm uses a parametrical model to generate the synthetic Discrete Fourier Transform (DFT) of the trajectory signals, which are then refined in the time domain and completed with a synthetic pressure function. Multiple samples of each signature are created so that synthetic databases may be produced. Quantitative and qua...

This article describes an application the author developed in order to compare analysis and synthesis of musical audio signals through Short Time Fourier transform (STFT), Constant Q and Sliding Discrete Fourier Transform (SDFT). This software is the basis for applications of SDFT and Constant Q to other consolidated synthesis techniques. By itself, it is a stand alone instrument for calculatin...

This paper describes a novel structure for a hardwired fast Fourier transform (FFT) signal processor that promises to permit digital spectrum analysis to achieve throughput rates consistent with extremely wide-band radars. The technique is based on the use of serial storage for data and intermediate results and multiple arithmetic units each of which carries out a sparse Fourier transform. Deta...