MATH 262/CME 372: Applied Fourier Analysis and
Winter 2014
Elements of Modern Signal Processing
Lecture 4 January 13, 2014
Prof. Emmanuel Candes
Scribe: Carlos A. Sing-Long
1
Outline
Agenda:
Uncertainty Principle
1. Weyl-Heisenberg Uncertainty Principle
2
MATH 262/CME 372: Applied Fourier Analysis and
Winter 2014
Elements of Modern Signal Processing
Lecture 7 January 29, 2014
Prof. Emmanuel Candes
Scribe: Carlos A. Sing-Long
1
Outline
Agenda:
The trapezoidal rule and the discrete Fourier transform.
1. Nume
Math 262 / CME 372
Winter 2014
Homework 1
Due January 22
1. Gibbs Phenomenon. Gibbs phenomenon has to do with how poorly Fourier series converge in the
vicinity of a jump or discontinuity of a signal f . This fact was pointed out by Gibbs in a letter to N
Math 262 / CME 372
Winter 2014
Homework 2
Due February 7, 2014
1. Aliasing. Suppose we sample the function f (t) = cos(0 t) every T seconds collecting f (nT ). What is
Shannons interpolation formula computed with the assumption that f is bandlimited to [/
MATH 262/CME 372: Applied Fourier Analysis and
Winter 2014
Elements of Modern Signal Processing
Lecture 6 January 27, 2014
Prof. Emmanuel Candes
Scribe: Carlos A. Sing-Long
1
Outline
Agenda:
Fourier series
1. Discrete convolutions
2. Fourier series
3. A d
MATH 262/CME 372: Applied Fourier Analysis and
Winter 2014
Elements of Modern Signal Processing
Lecture 5 January 15, 2014
Prof. Emmanuel Candes
Scribe: Carlos A. Sing-Long
1
Outline
Agenda:
Poisson summation formula and sampling
1. Poisson summation form
MATH 262/CME 372: Applied Fourier Analysis and
Winter 2014
Elements of Modern Signal Processing
Lecture 1 January 6, 2014
Prof. Emmanuel Candes
Scribe: Carlos A. Sing-Long
1
Outline
Agenda:
Fourier Integrals
1. Time-invariant operators
2. Convolutions
3.
MATH 262/CME 372: Applied Fourier Analysis and
Winter 2014
Elements of Modern Signal Processing
Lecture 2 January 8, 2014
Prof. Emmanuel Candes
Scribe: Carlos A. Sing-Long
1
Outline
Agenda:
Fourier Integrals (continued)
1. Fourier inversion formula
2. Con
MATH 262/CME 372: Applied Fourier Analysis and
Winter 2014
Elements of Modern Signal Processing
Lecture 3 January 10, 2014
Prof. Emmanuel Candes
Scribe: Carlos A. Sing-Long
1
Outline
Agenda:
Fourier Integrals (continued)
1. Parseval-Plancherel theorem
2.
Math 262 / CME 372
Winter 2014
Homework 1
Due January 22
1. Gibbs Phenomenon. Gibbs phenomenon has to do with how poorly Fourier series converge in the
vicinity of a jump or discontinuity of a signal f . This fact was pointed out by Gibbs in a letter to N