Recitation 17
Convolution
After studying this chapter, you should be able to:
switch between the functional for a system (or the system function) and the signal representation;
sketch the convolution of two signals; and
compute the convolution of two s
Recitation 14
Bode plots
After studying this chapter, you should be able to:
sketch a Bode plot given a system function H(s);
deduce a system function from a Bode plot.
Here is the magnitude sketch of the low-pass, second-order, high-Q system from the l
Recitation 18
Fourier series and ltering
After studying this chapter, you should be able to:
explain the analogy between Fourier coefcients and coordinates in a vector space;
nd the Fourier coefcients of a periodic signal; and
analyze a system by how i
Recitation 20
Fourier series as rotations
After studying this chapter, you should be able to:
explain how converting to and from the Fourier representation is a rotation;
deduce properties of Fourier series based on this geometric interpretation; and
a
Recitation 9
Image processing using operators
The goals of this chapter are:
to analyze spatial signals using functionals (or operators);
to look in slow motion at how to invert blurring operations;
to notice non-idealities, such as quantization error,
Recitation 19
Fourier transform
After studying this chapter, you should be able to:
derive the analysis and synthesis equations for Fourier transforms from their counterparts for relations for Fourier series;
simplify convolution problems by using the f
Recitation 22
Sampling and reconstruction
After studying this chapter, you should be able to:
reconstruct bandlimited signals from their samples, if the samples are frequent enough;
and
explain the factor of 2 in the sampling theorem.
Unless you believe
Recitation 23
Interpolation as reconstruction
After studying this chapter, you should be able to:
explain bandlimited, piece constant, and piecewise linear reconstruction using either the
time or frequency representations; and
write a program that uses
Recitation 21
A tour of Fourier representations
After studying this chapter, you should be able to:
explain the connection between Fourier series and transforms in terms of sampling the
frequency representation; and
explain the connection between discre
Pattern Recognition
and Machine Learning
Summary Week 14
Lecturer: Matthias Seeger
Assistants: Nikolaos Arvanitopoulos, Young Jun Ko, Carlos Stein, Friedemann Zenke
Tuesday
Convergence proof for K-means algorithm
Energy function (t, )
It is possible fo
Pattern Recognition
and Machine Learning
Summary Week 11
Lecturer: Matthias Seeger
Assistants: Nikolaos Arvanitopoulos, Young Jun Ko, Carlos Stein, Friedemann Zenke
Tuesday
KKT optimality conditions for SVM dual problem
Support vector (essential and bou
Pattern Recognition
and Machine Learning
Summary Week 10
Lecturer: Matthias Seeger
Assistants: Nikolaos Arvanitopoulos, Young Jun Ko, Carlos Stein, Friedemann Zenke
Tuesday
Recap of representer theorem
Kernel functions
Derivation as inner product for s
Recitation 16
Multiple representations of resonance
After studying this chapter, you should be able to:
Find Q given a system function, and write a system function with a given Q;
Find Q given the poles, and nd the poles given Q;
Find Q from how amplit
Recitation 15
Feedback and control
After studying this chapter, you should be able to:
sketch Bode plots for complicated systems by making plots for simpler subsystems and
combining these plots; and
use Bode plots to analyze feedback control.
We illustr
Recitation 13
Eigenfunctions and frequency response
After studying this chapter, you should be able to:
nd the system function H(s) for a system characterized by a second-order linear,
constant-coefcient differential equations;
explain the analogy betwe
Recitation 6
The perfect (sine) wave
The goals of this chapter are:
to analyze several methods for discretizing a continuous-time system; and
to illustrate complex poles and the signicance of the unit circle.
How can you compute a sine wave if your prog
Recitation 2
Difference equations and modularity
The goals of this chapter are:
to illustrate modularity and to describe systems in a modular way;
to translate problems from their representation as a verbal description into their representation as discr
Recitation 3
Block diagrams and operators:
Two new representations
The goals of this chapter are:
to introduce two representations for discrete-time systems: block diagrams and operators;
to introduce the whole-signal abstraction and to exhort you to us