Ece4330 Lecture 14 The Fourier Series Prof. Mohamad Hassoun

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Adding the first 1,000,000 terms of the harmonic series, the partial sum is only 14.357; and for the first trillion terms, it is approximately 28. It has been pointed out that to reach a sum of 100, we would have to add up 1043terms of the harmonic series.

ECE4330 Lecture 19: The Fourier Transform (cont.) Prof. Mohamad Hassoun Some Applications of the Fourier Transform: • Highlights of last lecture • Fourier Transform in Communication Theory: Application • Low-Pass Filters: Ideal vs. Practical (Butterworth Filters) Highlights of last lecture: Fourier analysis of LTIC systems mohamad hassoun

solved examples in fourier series. | PDF

Lecture 24 Discrete-Time Fourier Transform (DTFT): Application to System Analysis and Filter Design (example files) Pole-Zero placement and filter response. Watch Video Background Mohamad H. Hassoun received the BS, MS, and Ph.D. degrees in electrical engineering from Wayne State University (WSU), Detroit, Michigan, in 1981, 1982, and 1986, respectively. He is a Professor in the Department of Electrical and Computer Engineering at Wayne State University, and served as Interim Chair in 94/95. He founded the Computation

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Handy Board Robotics ECE 3300: Intro to Electrical Circuits ECE 3620: Intro to Microcomputers ECE3040: Numerical Methods for Engineers ECE 4330: Linear System and Signals ECE 4331: Systems and Signals Lab ECE 5995: Deep Learning: Fundamentals and Applications ECE 7030: Mathematical Methods in Engineering I Instructor Report Academic Misconduct

ECE4330 Lecture 7 Time Domain Analysis of LTI Systems Prof. Mohamad Hassoun Linear Time-Invariant (LTI) Systems Consider the linear system: System analysis: (1) Generate a mathematical model which is typically a linear algebraic equation(s) or, more generally, a linear differential equation; (2) Solve the equation(s). This lecture covers the following topics: The significance of phase information: Signal transmission example Applications of the Fourier transform o Fourier transform in a basic communication system o Low-pass filters: ideal vs practical (Butterworth filters) o Filter Design: low-pass, high-pass, band-pass, band-reject, notch, and all-pass Analog filter design as a numerical

Lecture 9: Time Domain Analysis of LTI Systems (Cont.) Prof. Mohamad Hassoun ECE4330 Lecture 4: Signals Prof. Mohamad Hassoun In this course, we deal with signals that are functions of time, f(t). • Highlights of last lecture • Fourier Transform in Communication Theory: Application • Low-Pass Filters: Ideal vs. Practical (Butterworth Filters)

ECE4330 Lecture 4: Signals Prof. Mohamad Hassoun
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ECE4330 Lecture 18: The Fourier Transform Prof. Mohamad Hassoun
ECE4330 Lecture 17: The Fourier Transform Prof. Mohamad Hassoun

Transcendental real numbers are a subset of irrational numbers. Examples: , , 3. The formal definition of transcendental numbers is provided later in this lecture.

8 9 10 11 12 13 14 15 16 17 19 21 22 e atu(t) eat u ( —t) jwot cos sin sgn t Cos u(t) A Short Table of Fourier Transforms (a (a jw)n+ ‚2n6(w) — • Highlights of last lecture • Fourier Transform in Communication Theory: Application • Low-Pass Filters: Ideal vs. Practical (Butterworth Filters)

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Proof of property (iii): { ? ( )}=∫ ? ( ) − =∫ ( ) −( −?) = ( −?) Exponential Fourier Series Spectra The exponential Fourier series spectra of a periodic signal () are the plots of the magnitude and angle of the complex Fourier series coefficients. ECE4330 Lecture 7 Time Domain Analysis of LTI Systems Prof. Mohamad Hassoun Linear Time-Invariant (LTI) Systems Consider the linear system: more ge Example. Determine the output voltage ( ) in the following resistive circuit that is driven by the voltage source ( ).

The above result shows that the heating effect due to an ac source is equivalent to that of a dc source that has the rms-value of the ac source. For example, the power outlet (in the USA) supplies a 170 voltage that has amplitude 0 = 170, then = ≅ 120 Volts. √2 In other words, a battery that has a voltage of 120 Volt will generate the same amount of heat as the ac outlet voltage. Adding the first 1,000,000 terms of the harmonic series, the partial sum is only 14.357; and for the first trillion terms, it is approximately 28. It has been pointed out that to reach a sum of 100, we would have to add up 1043 terms of the harmonic series. A computer adding up 1 million terms per second would take about 1037 seconds to complete the job which is on the order of about Lecture 15: The Fourier Series (continued) Prof. Mohamad Hassoun The Exponential Form Fourier Series: Exponential Fourier Series spectra of a signal are the plots of the magnitude and angle of the complex Fourier coefficients vs ω.

View lecture_17_ece4330t.pdf from ECE 4330 at Wayne State University. ECE4330 Lecture 17 The Fourier Transform Prof. Mohamad Hassoun The Fourier Transform is a complex valued function, (), that

ECE4330 Lecture 17 The Fourier Transform Prof. Mohamad Hassoun The Fourier Transform is a complex valued function, (?), that provides a very useful analytical representation of the frequency content of a (periodic and non-periodic) signal ( ). It works for causal [e.g., −2 ( )]as well as ever-lasting [e.g.,3cos(5 )]signals. ECE4330 Lecture 4: Signals Prof. Mohamad Hassoun In this course, we deal with signals that are functions of time, f(t).

Courses Taught by Professor Hassoun

Lecture 15: The Fourier Series (continued) Prof. Mohamad Hassoun The Exponential Form Fourier Series: Exponential Fourier Series spectra of a signal are the plots of the magnitude and angle of the complex Fourier coefficients vs ω. Driving innovation in intralogistics and mobile robotics. · Berufserfahrung: ifm · Ausbildung: Hochschule Furtwangen University · Standort: Freiburg im Breisgau · 500+ Kontakte auf LinkedIn. Sehen Sie sich das Profil von Mohamed Hassoun auf LinkedIn, einer professionellen Community mit mehr als 1 Milliarde Mitgliedern, an. ECE4330 Lecture 18: The Fourier Transform (cont.) Prof. Mohamad Hassoun Some Applications of the Fourier Transform: • The Sinusoidal Steady-State Phasor Analysis Method: Derivation • Distortion-less signal Transmission • Essential Signal Bandwidth

ECE4330 Lecture 6 Signals (Cont.) Prof. Mohamad Hassoun Piece-Wise Function Representation in Mathcad from the Programming Menu to insert the vertical line. Also, “if” and ECE4330 Lecture 18 The Fourier Transform (cont.) Prof. Mohamad Hassoun Relationship between (?)(and ) As was shown earlier, the zero-state response of a linear system can be obtained from the system’s impulse response through convolution, Prereq: ECE 3330; Prereq. or coreq: ECE 3040. Open only to students enrolled in professional engineering programs. Continuous-time and discrete-time linear systems and signals. Properties of linear systems. Classical analysis methods and convolution. System analysis method for zero-state and zero-input response. Laplace transform and its application to linear

ECE4330 Lecture 18 The Fourier Transform (cont.) Prof. Mohamad Hassoun Relationship between (?)(and ) As was shown earlier, the zero-state response of a linear system can be obtained from the system’s impulse response through convolution, Lecture 9: Time Domain Analysis of LTI Systems (Cont.) Prof. Mohamad Hassoun

This lecture covers the following topics: The significance of phase information: Signal transmission example Applications of the Fourier transform o Fourier transform in a basic communication system o Low-pass filters: ideal vs practical (Butterworth filters) o Filter Design: low-pass, high-pass, band-pass, band-reject, notch, and all-pass Analog filter design as a numerical

Showing 1 to 8 of 8 lecture_17_ece4330t.pdf ECE4330 Lecture 17 The Fourier Transform Prof. Mohamad Hassoun The Fourier Transform is a complex valued function, (), that provides a very useful analytical representation of the frequency content of a (periodic and non-periodic) signal (). It works for Solutions available ECE 4330 Wayne State University Sum of sinusoidal signals re 0) is at 2 0, 0, 4 0, etc. Think Fourier series !!!

Topical Outline 1. Introduction ( 1week) Definitions of power, rms, average quantities, Fourier Series; Review of time domain and frequency domain analysis of LRC circuits; Review of linear regulators; Types of power converters; Typical applications of power converters 2. Principles of power conversion (2 weeks) Ideal switch converters and state variables; Volt-sec and charge

ECE4330 Lecture 8: Time Domain Analysis of LTI Systems (Cont.) Prof. Mohamad Hassoun Consider a dynamic linear time-invariant (LTI) system with switching at =0. We are interested in solving for the system response ?( ) to an input signal ( ), ≥0.

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