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Digital Signal ProcessingAbout the TutorialDigital Signal Processing is an important branch of Electronics and Telecommunicationengineering that deals with the improvisation of reliability and accuracy of the digitalcommunication by employing multiple techniques. This tutorial explains the basic conceptsof digital signal processing in a simple and easy-to-understand manner.AudienceThis tutorial is meant for the students of E&TC, Electrical and Computer Scienceengineering. In addition, it should be useful for any enthusiastic reader who would like tounderstand more about various signals, systems, and the methods to process a digitalsignal.PrerequisitesDigital signal processing deals with the signal phenomenon. Along with it, in this tutorial,we have shown the filter design using the concept of DSP. This tutorial has a good balancebetween theory and mathematical rigor. Before proceeding with this tutorial, the readersare expected to have a basic understanding of discrete mathematical structures.Disclaimer & Copyright Copyright 2015 by Tutorials Point (I) Pvt. Ltd.All the content and graphics published in this e-book are the property of Tutorials Point (I)Pvt. Ltd. The user of this e-book is prohibited to reuse, retain, copy, distribute, or republishany contents or a part of contents of this e-book in any manner without written consentof the publisher.We strive to update the contents of our website and tutorials as timely and as precisely aspossible, however, the contents may contain inaccuracies or errors. Tutorials Point (I) Pvt.Ltd. provides no guarantee regarding the accuracy, timeliness, or completeness of ourwebsite or its contents including this tutorial. If you discover any errors on our website orin this tutorial, please notify us at contact@tutorialspoint.comi
Digital Signal ProcessingTable of ContentsAbout the Tutorial . iAudience . iPrerequisites . iDisclaimer & Copyright . iTable of Contents . iiPART 1 – INTRODUCTION TO SIGNALS . 11.Signals – Definition . 2Definition . 2Continuous Time Signals. 2Discrete Time signals . 22.Basic CT Signals . 4Unit Impulse or Delta Function . 4Unit Step Signal . 4Ramp Signal . 5Parabolic Signal. 5Signum Function . 6Sinc Function . 6Sinusoidal Signal . 7Rectangular Function. 7Triangular Pulse Signal . 83.Basic DT Signals. 9Unit Impulse Sequence . 9Unit Step Signal . 9Unit Ramp Function . 9Parabolic Function . 10Sinusoidal Signal . 104.Classification of CT Signals . 12Even and Odd Signals . 12Periodic and Non- Periodic Signals . 14Energy and Power Signals . 15Solved Examples . 165.Classification of DT Signals . 18Even and Odd Signals . 18Periodic and Non-Periodic Signals . 19Energy and Power Signals . 196.Miscellaneous Signals . 21Conjugate Signals . 21Conjugate Anti-Symmetric Signals. 21Half Wave Symmetric Signals . 22Orthogonal Signal . 22ii
Digital Signal ProcessingPART 2 – OPERATIONS ON SIGNALS . 247.Shifting . 25Time Shifting . 25Amplitude Shifting . 268.Scaling . 28Time Scaling . 28Amplitude Scaling . 299.Reversal . 31Time Reversal . 31Amplitude Reversal . 3110. Differentiation . 32Differentiation . 3211. Integration . 3412. Convolution . 35Steps for convolution . 35Properties of Convolution . 36Solved Examples . 37PART 3: BASIC SYSTEM PROPERTIES . 3913. Static Systems . 4014. Dynamic Systems . 4115. Causal Systems . 4216. Non-Causal Systems . 4317. Anti-Causal Systems . 4418. Linear Systems . 4519. Non-Linear Systems . 4720. Time-Invariant Systems. 4821. Time-Variant Systems . 4922. Stable Systems . 5023. Unstable Systems. 5124. Solved Examples . 52iii
Digital Signal ProcessingPART 4 – Z-TRANSFORM . 5325. Introduction . 54Region of Convergence . 54Signals and their ROC . 5526. Properties of Z-Transform . 56Linearity . 56Time Shifting . 56Time Scaling .
Digital Signal Processing i About the Tutorial Digital Signal Processing is an important branch of Electronics and Telecommunication engineering that deals with the improvisation of reliability and accuracy of the digital communication by employing multiple techniques. This tutorial explains the basic concepts of digital signal processing in a simple and easy-to-understand manner. Audience
