Signal processing is a broad and timeless area. The term "signal" includes audio, video, speech, image, communication, geophysical, sonar, radar, medical, and more. Signal processing applies to the theory and application of filtering, coding, transmitting, estimating, detecting, analyzing, recognizing, synthesizing, recording, and reproducing signals. Handbook of Formulas and Tables for Signal Processing a must-have reference for all engineering professionals involved in signal and image processing. Collecting the most useful formulas and tables - such as integral tables, formulas of algebra, formulas of trigonometry - the text includes:Material for the deterministic and statistical signal processing areasExamples explaining the use of the given formulaNumerous definitionsMany figures that have been added to special chaptersHandbook of Formulas and Tables for Signal Processing brings together - in one textbook - all the equations necessary for signal and image processing for professionals transforming anything from a physical to a manipulated form, creating a new standard for any person starting a future in the broad, extensive area of research.

The handbook of formulas and tables for signal processing

Optimum combining for space diversity reception is studied in digital cellular mobile radio communication systems with Rayleigh fading and multiple cochannel interferers. This paper considers binary phase-shift keying (BPSK) modulation in a flat Rayleigh-fading environment when the number of interferences L is no less than the number of antenna elements N(L/spl ges/N). The approach of this paper and its main contribution is to carry out the analysis in a multivariate framework. Using this approach and with the assumption of equal-power interferers, it is shown that the probability density function of the maximum signal-to-interference ratio (SIR) at the output of the optimum combiner has a Hotelling T/sup 2/ distribution. Closed form expressions using hypergeometric functions are derived for the outage probability and the average probability of bit error. Theoretical results are demonstrated by Monte Carlo simulations.

Performance analysis of optimum combining in wireless communications with Rayleigh fading and cochannel interference

In this paper, our aim is to generalize the truncated M-fractional derivative which was recently introduced [Sousa and de 
Oliveira, A new truncated M-fractional derivative type unifying some fractional derivative types with classical properties, 
Inter. of Jour. Analy. and Appl., 16 (1), 83–96, 2018]. To do that, we used generalized M-series, which has a more general 
form than Mittag-Leffler and hypergeometric functions. We called this generalization as truncated M-series fractional 
derivative. This new derivative generalizes several fractional derivatives and satisfies important properties of the integerorder derivatives. Finally, we obtain the analytical solutions of some M-series fractional differential equations.

A generalization of truncated M-fractional derivative and applications to fractional differential equations

In this survey paper we present the natural application of certain integral inequalities such as, Chebychev's inequality for synchronous and asynchronous mappings, Holder's inequality and Gruss' and Ostrowski's inequalities for the celebrated Euler's Beta and Gamma functions. Natural applications dealing with some adaptive quadrature formulae which can be deduced from Ostrowski's inequality are also pointed out.

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Inequalities for Beta and Gamma functions via some classical and new integral inequalities.

We analyze the impact of a time-varying Rayleigh-fading channel on the performance of an Alamouti transmit-diversity scheme. We propose several optimal and suboptimal detection strategies for mitigating the effects of a time-varying channel, and derive expressions for their bit-error probability as a function of the channel correlation coefficient /spl rho/. We find that the maximum-likelihood detector that optimally compensates for the time-varying channel is very tolerant to time-varying fading, attaining full diversity order even for the extreme case of /spl rho/=0. In contrast, although lower in complexity, the suboptimal schemes suffer a diversity penalty and are thus suitable only for slowly fading channels.

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D. Gershfeld

Papers

Special functions for engineers and applied mathematicians