This paper concerns the issue of wavelet analysis of signals by continuous and discrete wavelet transforms (CWT – Continous Wavelet Transform, DWT – Discrete Wavelet Transform). The main goal of our work was to develop a program which, through the CWT and the DWT analyses, would obtain graph of time-scale changes and would transform it into the spectrum, that is a graph of frequency changes. In...

Bird calls range from simple tones to rich dynamic multi-harmonic structures. The more complex calls are very poorly understood at present, such as those of the scientifically important corvid family (jackdaws, crows, ravens, etc.). Individual birds can recognise familiar individuals from calls, but where in the signal is this identity encoded? We studied the question by applying a combination ...

We present the concept that for uniformly rotated images, the optimal approximation of the images can be obtained by computing the basis vectors for the discrete cosine transform (DCT) of the original image in polar coordinates, and that the images can be represented as linear combinations of the basis vectors.

Multirate filterbanks have found applications in speech processing, image processing, communications, and in the development of new sampling theorems. This paper explores the relationship between sampling theorems and multirate filterbanks in the linear canonical transform (LCT) domain. The sampling identity and the interpolation identity for bandlimited signals in the LCT domain are discussed ...

Phase retrieval problems occur in a wide range of applications in physics and engineering. Usually, these problems consist in the recovery of an unknown signal from the magnitudes of its Fourier transform. In some applications, however, the given intensity arises from a different transformation such as the Fresnel or fractional Fourier transform. More generally, we here consider the phase retri...

Piecewise-linear models constitute an attractive alternative to construct a function whose graph fits a finite set of discrete points. These models are preferably selected over other approximation strategies like polynomials or splines. Although there are several piecewise-linear models reported in literature, the so-called High Level Canonical has the remarkable advantage of emerging from a we...

Starting with the Iwasawa-type decomposition of a first-order optical system (or ABCD system) as a cascade of a lens, a magnifier, and an orthosymplectic system (a system that is both symplectic and orthogonal), a further decomposition of the orthosymplectic system in the form of a separable fractional Fourier transformer embedded between two spatial-coordinate rotators is proposed. The resulti...

The uncertainty principle plays an important role in mathematics, physics, signal processing, and so on. Firstly, based on definition of the linear canonical transform (LCT) and the traditional Pitt’s inequality, one novel Pitt’s inequality in the LCT domains is obtained, which is connected with the LCT parameters a and b. Then one novel logarithmic uncertainty principle is derived from this no...