### Introduction to signal processing: sampled signals

#### Abstract

The article introduces the theoretical foundations of the modern method of storing, transmitting and processing signals: digital processing. It’s a way to use relatively small number of values instead of continuous real signal. For example, when transmitting information in telephony, speech is concentrated in the bandwidth up to 4 kHz. But we need doubled frequency 8 kHz sampling in digital form. This is a fundamental requirement. The reason is that the sampled signal is not just a set of quantities, but a set of short scaled pulses of large value. Resulting spectrum has multiple copies of original one infinitely duplicated on sampling frequency steps. If these copies do not overlap significant (due to the limited original useful spectrum) we could restore initial signal with filtering just one of them. That’s why doubled sampling frequency is needed. If the number of samples used is finite (as in the real cases), then we can use only an equal number of samples of the spectrum (or even a half of them). It’s enough for restoring. As in the rest parts of the series, all theoretical ideas are illustrated by mathematical rationales and Matlab programs that demonstrate the work “in life”.

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E. Tikhonov, M. Sneps-Sneppe. “Introduction to signal processing: sine wave and complex signals”, International Journal of Open Information Technologies, Vol. 7, No 3, March 2019, ISSN 2307-8162.

E. Tikhonov, M. Sneps-Sneppe. “Introduction to signal processing: spectral representation”, International Journal of Open Information Technologies, Vol. 7, No 4, April 2019, ISSN 2307-8162.

Lyons, Richard G., “Understanding digital signal processing”, 3rd ed., Library of Congress Cataloging-in-Publication Data, 1948, ISBN 0-13-702741-9

Kotelnikov VA, “On the transmission capacity of "ether" and wire in electrocommunications”, (English translation, PDF, url: http://ict.open.ac.uk/classics/1.pdf), Izd. Red. Upr. Svyazzi RKKA (1933), Reprint in Modern Sampling Theory: Mathematics and Applications, Editors: J. J. Benedetto und PJSG Ferreira, Birkhauser (Boston) 2000, ISBN 0-8176-4023-1

Robert J. Marks II, Introduction to Shannon Sampling and Interpolation Theory, Springer-Verlag, New York, 1991. Available: https://marksmannet.com/RobertMarks/REPRINTS/1999_IntroductionToShannonSamplingAndInterpolationTheory.pdf. Retrieved: May, 2019

Kharkevich A.A., “Essays on the general theory of communication” (Russian), State publishing house of technical and theoretical literature, Moscow, 1955

Ilyin V.A., Sadovnichy V.A, Sendov Bl.H. "Real Numbers // Mathematical Analysis" (Russian), 3rd ed. pererab. and add. / Ed. Tikhonov A. N., Prospect, Moscow 2006, ISBN 5-482-00445-7

Emmanuel C. Ifeachor (2011) “Digital Signal Processing A practical approach download”. Prentice Hall; 2 edition (October 7, 2001), ISBN-10: 9780201596199

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ISSN: 2307-8162