7 accepted papers
Efficient computation of the Discrete Fourier Transform (DFT) for signals with structured frequency support remains a significant challenge in signal processing. The traditional Fast Fourier Transform (FFT) algorithm achieves O(NlogN) complexity, but substantial improvements are possible for signals…
In this paper, we investigate the intriguing connection between the Discrete Cosine Transform (DCT) and integral graphs, contributing to the field of signal processing on graphs. Throughout our investigation, we discover two types of novel integral graphs based on DCT. The first type emerges as a re…
In this paper, we present a novel operator designed to handle the shifting of multiple periodic signals. By exploiting the unique properties of the companion matrix and the elegant structure of cyclotomic polynomials, we have developed an efficient and versatile tool for signal processing applicatio…
We investigate the reconstruction of a binary image from its sparse 2D discrete Fourier transform (2D-DFT) coefficients. Specifically, we focus on the case where the image height is equal to its width and is a prime number. We derive a lower bound on the number of coefficients required for perfect i…
Unseen data, which are not samples from the distribution of training data and are difficult to collect, have exhibited importance in numerous applications, ({\em e.g.,} novelty detection, semi-supervised learning, and adversarial training). In this paper, we introduce a general framework called \t…
In this paper, we propose an adaptive STFT (ASTFT) with adaptive chirp-modulated Gaussian window. The window is obtained from rotating Gaussian function in time-frequency plane by fractional Fourier transform (FRFT). It is completely adaptive where the two parameters, FRFT rotation angle and Gaussia…
Linear canonical transform (LCT) is an attractive and useful tool in optics and signal processing. In previous work, a generalization of the LCT with two extra parameters, called offset LCT (OLCT), has been developed. In this paper, a different definition of OLCT is proposed, which has a more concis…