Signals And Systems Fundamentals

Learn Signals and Systems Fundamentals from Scratch and Master the theoretical foundations required to process signals

What you'll learn

Understand the fundamentals of the systems sub-area within the field of electrical engineering so as to get excited about the area

Understand and apply the continuous time Fourier transform, discrete time Fourier transform, Laplace transform, and z-Transform, to the analysis and description

Apply the concepts of Fourier series representations to analyze continuous and discrete time periodic signals.

To take advanced courses in the signals and systems area as well as applying the obtained knowledge into practical applications

Requirements

Desire to learn the subject of signals and systems

Knowledge of the Basics to electrical and computer engineering concepts

Description

Course Description of Signals and Systems FundamentalsThe course provides students with a comprehensive detailed introduction to the analysis of continuous and discrete-time signals and systems.Linear time-invariant systemsSignals Convolution and CorrelationFourier series representations of periodic signalsContinuous time and discrete time Fourier transformsLaplace transformZ-transform conceptFast Fourier transform (FFT) The COURSE GOALS are basically to provide an introduction to sophomores in the field of electrical engineering to the fundamental concepts in the sub-area of signals and systems. This course will be one of five fundamentals courses required of all electrical engineering majors. Another goal is to prepare students to take some more advanced courses in the area of signals and systems, namely in signal and image processing, and networks, communication and control.COURSE OBJECTIVES: When a student completes this course, s/he should be able to:• Understand the fundamentals of the systems sub-area within the field of electrical engineering so as to get excited about the area.• Understand linear time invariant systems.• Apply the concepts of Fourier series representations to analyze continuous and discrete time periodic signals.• Understand and apply the continuous time Fourier transform, discrete time Fourier transform, Laplace transform, and z-Transform, to the analysis and description of LTI continuous and discrete-time systems.• To take advanced courses in the systems area.DETAILED COURSE TOPICS:1. Signals and Systems: Continuous-time and discrete-time signals; commonly encountered signals; unit impulse and unit step functions; sampling and aliasing; continuous-time and discrete-time systems; basic properties.2. Linear Time-Invariant (LTI) Systems: The convolution sum; the convolution integral; properties; difference and differential equations.3. Fourier Series Representation of Periodic Signals: Continuous and discrete-time periodic signals; properties of continuous and discrete-time Fourier series; Fourier series and LTIsystems.4. Continuous-Time Fourier Transform: Properties; convolution and multiplication properties.5. Discrete-Time Fourier Transform: Properties; convolution and multiplication properties.6. Laplace Transform: Region of convergence; inverse Laplace transform; properties; analysis of LTI systems using the Laplace transform.7. z-Transform: Region of convergence; inverse z-transform; properties; analysis of LTI systems using the z-transform.COMPUTER USAGE: Programming assignments using MATLAB on PCs to reinforce concepts learned in class.HOMEWORK ASSIGNMENTS: Homeworks to reinforce the concepts learned in class .REQUIRED TEXT: A. V. Oppenheim and A. S. Willsky (with S. H. Nawab), Signals and Systems , Prentice Hall, 2 nd edition, 1997.PREREQUISITES BY TOPIC: Basic introduction to electrical engineering concepts

Overview

Section 1: Introduction and review of pre-requisite concepts in signal and systems

Lecture 1 Fourier transform of rectangular pulse

Lecture 2 Autocorrelation function and Power Spectral Density

Lecture 3 Frequency response and impulse response

Lecture 4 Impulse response and causality

Lecture 5 Relation between Laplace transform Fourier transform z-transform DTFT DFT & FFT

Lecture 6 Why cant an ideal filter be implemented in practice

Lecture 7 Time domain sampling - analytical representation

Section 2: Signals and Systems

Lecture 8 L1 Real sinusoidal and exponential signals

Lecture 9 L2 Complex exponential unit impulse and unit step signals

Lecture 10 L3 Complex exponential unit impulse and unit step functions

Lecture 11 L4 Periodic signals even and odd signals.mp4

Lecture 12 L5 Transformation of Independent variable - continuous time.mp4

Lecture 13 L6 Transformation of independent variable- Continuous time and discrete time exa

Lecture 14 L7 Transformation of independent variable - Discrete Time example.mp4

Lecture 15 L8 Relationship between Unit impulse and unit step functions Introduction to sys

Lecture 16 L9 System properties - memory invertibility and causality.mp4

Lecture 17 L10 System properties - Stability Time Invariance and Linearity.mp4

Lecture 18 L11 Linearity and linear systems with examples.mp4

Lecture 19 L12 LTI systems - impulse response and convolution.mp4

Lecture 20 L13 Convolution in Discrete Time.mp4

Lecture 21 L14 Convolution continuous time.mp4

Lecture 22 L15 Properties of LTI systemsconvolution.mp4

Lecture 23 L15 Properties of LTI systemsconvolution.mp4

Lecture 24 L17 Unit step response and introduction to Fourier series.mp4

Lecture 25 L18 Fourier series motivation and theory.mp4

Lecture 26 L19 Fourier series - Exponential form and sine-cosine form.mp4

Lecture 27 L20 Dirichlets conditions and properties of Fourier series.mp4

Lecture 28 L21 Fourier series of discrete time periodic signals.mp4

Lecture 29 Fourier series coefficient calculations

Lecture 30 Geometric representation of signals

Lecture 31 Gram Schmidt orthogonalization

Section 3: Digital Communication Fundamentals

Lecture 32 Introduction to Digital Communication

Lecture 33 Sampling reconstruction & Aliasing

Lecture 34 Quantization quantization noise signal to quantization noise power ratio

Lecture 35 Quantization SNR and PCM

Lecture 36 PCM word size and Baseband signaling - Line codes

Lecture 37 Processing gain in DPCM and Delta Modulation

Lecture 38 Slope overload in Delta Modulation

Lecture 39 Gaussian noise

Lecture 40 White Gaussian Noise

Lecture 41 Signal detection in the presence of AWGN - Binary Unipolar

Lecture 42 Error probability with binary polar signaling

Lecture 43 Error probability for M-ary signaling with M = 4

Lecture 44 Error probability with M-ary signaling over AWGN channel

Lecture 45 '

Lecture 46 Spectrum - Fourier analysis

Computer Engineering Students,Electrical Engineering Students,Telecommunication Engineering Students,Signal app developers and programmers