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Note for Digital Signal Processing - DSP By Dipankar Mahato

  • Digital Signal Processing - DSP
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Digital Signal Processing with Python Programming

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Digital Signal Processing with Python Programming Maurice Charbit

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First published 2017 in Great Britain and the United States by ISTE Ltd and John Wiley & Sons, Inc. Apart from any fair dealing for the purposes of research or private study, or criticism or review, as permitted under the Copyright, Designs and Patents Act 1988, this publication may only be reproduced, stored or transmitted, in any form or by any means, with the prior permission in writing of the publishers, or in the case of reprographic reproduction in accordance with the terms and licenses issued by the CLA. Enquiries concerning reproduction outside these terms should be sent to the publishers at the undermentioned address: ISTE Ltd 27-37 St George’s Road London SW19 4EU UK John Wiley & Sons, Inc. 111 River Street Hoboken, NJ 07030 USA www.iste.co.uk www.wiley.com © ISTE Ltd 2017 The rights of Maurice Charbit to be identified as the author of this work have been asserted by him in accordance with the Copyright, Designs and Patents Act 1988. Library of Congress Control Number: 2016955620 British Library Cataloguing-in-Publication Data A CIP record for this book is available from the British Library ISBN 978-1-78630-126-0

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Contents Preface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ix Notations and Abbreviations . . . . . . . . . . . . . . . . . . . . . . . . . . xi A Few Functions of Python® . . . . . . . . . . . . . . . . . . . . . . . . . . xiii Chapter 1. Useful Maths . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.1. Basic concepts on probability . . . . . . . . 1.2. Conditional expectation . . . . . . . . . . . . 1.3. Projection theorem . . . . . . . . . . . . . . . 1.3.1. Conditional expectation . . . . . . . . . . 1.4. Gaussianity . . . . . . . . . . . . . . . . . . . 1.4.1. Gaussian random variable . . . . . . . . 1.4.2. Gaussian random vectors . . . . . . . . . 1.4.3. Gaussian conditional distribution . . . . 1.5. Random variable transformation . . . . . . . 1.5.1. General expression . . . . . . . . . . . . 1.5.2. Law of the sum of two random variables 1.5.3. δ-method . . . . . . . . . . . . . . . . . . 1.6. Fundamental theorems of statistics . . . . . 1.7. A few probability distributions . . . . . . . . Chapter 2. Statistical Inferences . . . . . . . . . . . . . . 1 10 11 14 14 14 15 16 18 18 19 20 22 24 . . . . . . . . . . . . . . . . . . . . . . . 29 2.1. First step: visualizing data . . . . . 2.1.1. Scatter plot . . . . . . . . . . . . 2.1.2. Histogram/boxplot . . . . . . . . 2.1.3. Q-Q plot . . . . . . . . . . . . . 2.2. Reduction of dataset dimensionality . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29 29 30 32 34

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