Continuous-time Fourier Series Prof. Siripong Potisuk.

Slides:

Advertisements

Similar presentations

For more ppt’s, visit Fourier Series For more ppt’s, visit

Advertisements

Signals and Systems Fall 2003 Lecture #5 18 September Complex Exponentials as Eigenfunctions of LTI Systems 2. Fourier Series representation of.

Fourier Series & Transforms

Fourier Series 主講者：虞台文.

Lecture 8: Fourier Series and Fourier Transform

Signals, Fourier Series

Continuous-Time Fourier Methods

Discrete-Time Fourier Methods

Signals and Systems Discrete Time Fourier Series.

The Discrete Fourier Series

1 Prof. Nizamettin AYDIN Digital Signal Processing.

Fourier Series Motivation (Time Domain Representation) (Frequency Domain Representation)

CH#3 Fourier Series and Transform

3.0 Fourier Series Representation of Periodic Signals

Chapter 15 Fourier Series and Fourier Transform

Leo Lam © Signals and Systems EE235 Lecture 23.

Function approximation: Fourier, Chebyshev, Lagrange

The z-Transform Prof. Siripong Potisuk. LTI System description Previous basis function: unit sample or DT impulse  The input sequence is represented.

Orthogonal Functions Numerical Methods in Geophysics Function Approximation The Problem we are trying to approximate a function f(x) by another function.

CISE315 SaS, L171/16 Lecture 8: Basis Functions & Fourier Series 3. Basis functions: Concept of basis function. Fourier series representation of time functions.

12.1 The Dirichlet conditions: Chapter 12 Fourier series Advantages: (1)describes functions that are not everywhere continuous and/or differentiable. (2)represent.

Signals and Systems Lecture 7

Basic signals Why use complex exponentials? – Because they are useful building blocks which can be used to represent large and useful classes of signals.

1 Review of Continuous-Time Fourier Series. 2 Example 3.5 T/2 T1T1 -T/2 -T 1 This periodic signal x(t) repeats every T seconds. x(t)=1, for |t|

Discrete Fourier Transform Prof. Siripong Potisuk.

Fourier TheoryModern Seismology – Data processing and inversion 1 Fourier Series and Transforms Orthogonal functions Fourier Series Discrete Fourier Series.

Signal and System I The unit step response of an LTI system.

Signals and Systems Lecture #5 1. Complex Exponentials as Eigenfunctions of LTI Systems 2. Fourier Series representation of CT periodic signals 3. How.

FOURIER ANALYSIS TECHNIQUES Fourier series permit the extension of steady state analysis to general periodic signal. FOURIER SERIES.

Fourier Series Representations

Fourier Series Kamen and Heck.

By Ya Bao oct 1 Fourier Series Fourier series: how to get the spectrum of a periodic signal. Fourier transform: how.

Course Outline (Tentative) Fundamental Concepts of Signals and Systems Signals Systems Linear Time-Invariant (LTI) Systems Convolution integral and sum.

3.0 Fourier Series Representation of Periodic Signals 3.1 Exponential/Sinusoidal Signals as Building Blocks for Many Signals.

Signals & Systems Lecture 13: Chapter 3 Spectrum Representation.

CH#3 Fourier Series and Transform

Leo Lam © Signals and Systems EE235 Lecture 21.

5.0 Discrete-time Fourier Transform 5.1 Discrete-time Fourier Transform Representation for discrete-time signals Chapters 3, 4, 5 Chap 3 Periodic Fourier.

Leo Lam © Signals and Systems EE235 Lecture 25.

6.9 Dirichlet Problem for the Upper Half-Plane Consider the following problem: We solved this problem by Fourier Transform: We will solve this problem.

SIGNALS AND SIGNAL SPACE

ECE 8443 – Pattern Recognition EE 3512 – Signals: Continuous and Discrete Objectives: Eigenfunctions Fourier Series of CT Signals Trigonometric Fourier.

1 Convergence of Fourier Series Can we get Fourier Series representation for all periodic signals. I.e. are the coefficients from eqn 3.39 finite or in.

ECE 8443 – Pattern Recognition ECE 3163 – Signals and Systems Objectives: Eigenfunctions Fourier Series of CT Signals Trigonometric Fourier Series Dirichlet.

Frequency domain analysis and Fourier Transform

Professor Brendan Morris, SEB 3216, EE360: Signals and System I Fourier Series Motivation.

ENEE 322: Continuous-Time Fourier Transform (Chapter 4)

Fourier Series & Transforms

Fourier Series 1 Chapter 4:. TOPIC: 2 Fourier series definition Fourier coefficients The effect of symmetry on Fourier series coefficients Alternative.

Introduction and motivation Full range Fourier series Completeness and convergence theorems Fourier series of odd and even functions Arbitrary range Fourier.

CH#3 Fourier Series and Transform 1 st semester King Saud University College of Applied studies and Community Service 1301CT By: Nour Alhariqi.

Convergence of Fourier series It is known that a periodic signal x(t) has a Fourier series representation if it satisfies the following Dirichlet conditions:

الفريق الأكاديمي لجنة الهندسة الكهربائية 1 Discrete Fourier Series Given a periodic sequence with period N so that The Fourier series representation can.

Signal and System I The response of system to complex exponentials z - transform.

Introduction to Transforms

Advanced Digital Signal Processing

Neural data-analysis Workshop

EE360: Signals and System I

Lecture 8 Fourier Series & Spectrum

Fourier Series Prof. Woonchul Ham

MMSE Optimal Design: The Least Squares method

Fourier Integrals For non-periodic applications (or a specialized Fourier series when the period of the function is infinite: L) -L L -L- L

Digital Signal Processing

Notes Assignments Tutorial problems

Fourier Series September 18, 2000 EE 64, Section 1 ©Michael R. Gustafson II Pratt School of Engineering.

Signals & Systems (CNET - 221) Chapter-4 Fourier Series

3.Fourier Series Representation of Periodic Signal

Expansions Clicker questions.

Signals & Systems (CNET - 221) Chapter-4

Signals and Systems Lecture 11

Presentation transcript:

Continuous-time Fourier Series Prof. Siripong Potisuk

Orthogonal Expansion of CT Signals A linear combination of weighted orthogonal basis functions

Orthogonal Basis Functions

Periodic Complex Exponentials

Continuous-time Fourier Series A linear combination of harmonically related complex exponentials is an approximation or estimate to the given periodic signal

Continuous-time Fourier Series How good is in approximating ? Is it possible to obtain an exact representation of in the form of ?  # of basis functions (harmonics) needed  convergence of Fourier Series with an infinite # of harmonics How does one obtain the coefficients?

Minimum Mean Square Error (MMSE)

Fourier series coefficients

Dirichlet Conditions

Gibbs phenomenon

Example1 Find the complex Fourier series coefficients of the signal

Example 2 Find the complex Fourier series coefficients of the signal

Example 3 Find the complex Fourier series coefficients of the signal

Example 3: Line Spectrum