In this paper, we employ the concept of the Generalized Discrete Fourier Transform, which in turn relies on the Hasse derivative of polynomials, to give a general construction of Reed-Solomon codes over Galois fields of characteristic not necessarily co-prime with the length of the code. The constructed linear codes  enjoy nice algebraic properties just as the classic one.

AA-LP Anti-aliasing lowpass AC3 Adaptive transform coder 3 ACR Absolute-category rating ADC Analog-to-digital converter ADPCM Adaptive differential pulse-code modulation AEC Acoustic echo cancellation / caneller AIR Acoustic impulse response ALP Adaptive lattice predictor ANC Active noise control or adaptive noise canceller AP Affine projection APC Adaptive predictive coding AR Auto-regressive ...

Hadamard transform is an important tool in discrete signal processing. In this paper, we define the discrete fractional Hadamard transform which is a generalized one. The development of discrete fractional Hadamard is based upon the same spirit of discrete fractional Fourier transform.

the aim of this paper is to prove new quantitative uncertainty principle for the generalized fourier transform connected with a dunkl type operator on the real line. more precisely we prove an lp-lq-version of morgan's theorem.

The discrete evolutionary transform is applied to signals in a blind–way without any signal parameters. For this reason, discrete evolutionary transform is not optimal and needs an improvement by using some information about the signal. In this paper, we propose an improvement for the discrete evolutionary transform. We redefine the generalized timebandwidth product optimal short–time Fourier t...