The Spectrum Sliding Analysis (SSA) is a dynamic spectrum analysis in which the next analysis interval differs from the previous one by including the next signal sample and excluding the first one from the previous analysis interval. Such a spectrum analysis is necessary for time-frequency localization of analyzed signals with given peculiarities. Using the well-known Fast Fourier Transform (FF...

It is well known that a quadratic function defined on a finite field of odd degree is almost bent (AB) if and only if it is almost perfect nonlinear (APN). For the even degree case there is no apparent relationship between the values in the Fourier spectrum of a function and the APN property. In this article we compute the Fourier spectrum of the quadranomial family of APN functions from [5]. W...

The use of different kinds of nonlinear filtering in a joint transform correlator are studied and compared. The study is divided into two parts, one corresponding to object space and the second to the Fourier domain of the joint power spectrum. In the first part, phase and inverse filters are computed; their inverse Fourier transforms are also computed, thereby becoming the reference in the obj...

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...

The slow light effects of an amplitude modulated Gaussian (AMG) pulse in a cesium atomic vapor are presented. In a single-Λ type electromagnetically induced transparency (EIT) medium, more severe distortion is observed for an AMG pulse than a Gaussian one. Using Fourier spectrum analysis, we find that the distortion, as well as the loss, is dominantly caused by linear absorption than dispersion...

A classical way to reduce a radar’s data is to compute the spectrum using FFT and then to identify the different peak contributions. But in case an overlapping between the different echoes (atmospheric echo, clutter, hydrometeor echo. . . ) exists, Fourier-like techniques provide poor frequency resolution and then sophisticated peak-identification may not be able to detect the different echoes....

We present a range of new results for testing properties of Boolean functions that are defined in terms of the Fourier spectrum. Broadly speaking, our results show that the property of a Boolean function having a concise Fourier representation is locally testable. We give the first efficient algorithms for testing whether a Boolean function has a sparse Fourier spectrum (small number of nonzero...