List of Figures
List of Tables
Listings
Preface
1
Analog and Digital Signals
2
Transforms and Signal Representation
3
Analog and Digital Systems
4
Spectral Estimation Techniques
A
Useful Mathematics
A.1
Euler’s equation
A.2
Trigonometry
A.3
Manipulating complex numbers and rational functions
A.4
Manipulating complex exponentials
A.5
Q function
A.6
Matched filter and Cauchy-Schwarz’s inequality
A.7
Geometric series
A.8
Sum of squares
A.9
Summations and integrals
A.10
Partial fraction decomposition
A.11
Calculus
A.12
Sinc Function
A.13
Rectangular Integration to Define Normalization Factors for Functions
A.14
Linear Algebra
A.15
Gram-Schmidt orthonormalization procedure
A.16
Principal component analysis (PCA)
A.17
Fourier Analysis: Properties
A.18
Fourier Analysis: Pairs
A.19
Probability and Stochastic Processes
A.20
Stochastic Processes
A.21
Estimation Theory
A.22
One-dimensional linear prediction over time
A.23
Vector prediction exploring spatial correlation
A.24
Decibel (dB) and Related Definitions
A.25
Insertion loss and insertion frequency response
A.26
Discrete and Continuous-Time Impulses
A.27
System Properties
A.28
Fixed and Floating-Point Number Representations
B
Useful Softwares and Programming Tricks
Glossary
Bibliography
Index
Digital Signal Processing with Python, Matlab or Octave
GitHub
PDF
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A.8
Sum of squares
The sum of the squares of the first
N
integers is
∑
n
=
1
N
n
2
=
N
(
N
+
1
)
(
2
N
+
1
)
6
,
(A.21)
which can be proved by induction [
urlBMson
].
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