Digital Signal Processing (DSP) with Python Programming
eBook - ePub

Digital Signal Processing (DSP) with Python Programming

  1. English
  2. ePUB (mobile friendly)
  3. Available on iOS & Android
eBook - ePub

Digital Signal Processing (DSP) with Python Programming

About this book

The parameter estimation and hypothesis testing are the basic tools in statistical inference. These techniques occur in many applications of data processing., and methods of Monte Carlo have become an essential tool to assess performance. For pedagogical purposes the book includes several computational problems and exercices. To prevent students from getting stuck on exercises, detailed corrections are provided.

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Yes, you can access Digital Signal Processing (DSP) with Python Programming by Maurice Charbit in PDF and/or ePUB format, as well as other popular books in Technology & Engineering & Signals & Signal Processing. We have over one million books available in our catalogue for you to explore.

1
Useful Maths

1.1. Basic concepts on probability

Without describing in detail the formalism of the probability theory, we simply remind the reader of useful concepts. However, we advise the reader to consult some of the many books with authority on the subject [BIL 12].
In probability theory, we consider a sample space Ω, which is the set of all possible outcomes ω, and a collection
images
of its subsets with a structure of σ-algebra, the elements of which are called the events.
DEFINITION 1.1 (Random variable).– A real random variable X is a (measurable) application from the Ω to
images
:
[1.1]
Numbered equation
DEFINITION 1.2 (Discrete random variable).– A random variable X is said to be discrete if it takes its values in a subset of
images
, at the most countable. If {a0, …, an, …}, where n
images
, denotes this set of values, the probability distribution of X is characterized by the sequence:
[1.2]
Numbered equation
representing the probability that X is equal to the element an. These values are such that 0 ≤ pX(n) ≤ 1 and
images
.
This leads us to the probability for the random variable X to belong to the interval ]a, b]. It is...

Table of contents

  1. Cover
  2. Table of Contents
  3. Title
  4. Copyright
  5. Preface
  6. Notations and Abbreviations
  7. A Few Functions of Python®
  8. 1 Useful Maths
  9. 2 Statistical Inferences
  10. 3 Inferences on HMM
  11. 4 Monte-Carlo Methods
  12. 5 Hints and Solutions
  13. Bibliography
  14. Index
  15. End User License Agreement