ECE 8443 – Pattern Recognition EE 3512 – Signals: Continuous and Discrete Objectives: Review Resources: Wiki: Superheterodyne Receivers RE: Superheterodyne Receivers MIT 6.003: Lecture 15 NASA: Electromagnetic Spectrum Wiki: Superheterodyne Receivers RE: Superheterodyne Receivers MIT 6.003: Lecture 15 NASA: Electromagnetic Spectrum LECTURE 13: REVIEW FOR EXAM NO. 1 URL:

EE 3512: Lecture 13, Slide 1 1)Basic Properties of Signals  Continuous Signals  Discrete-Time Signals  Digital Signals  Real/Complex Signals  Properties: Periodic, Even/Odd 2)More Properties of Signals  Types: Impulse, Unit Step, Ramp, Sinewaves  Time-Shift  Continuous, Piecewise-Continuous  Derivatives of a CT Signal  Sampling 3)Basic System Properties  Causality  Linearity  Time-Invariance 4)Basic Statistical Models  Digital Signals  Mean, Standard Deviation, Variance  Covariance, Correlation  Noise, Gaussian Noise, White Noise Exam No. 1 Review – Major Concepts 5)Discrete-Time Convolution  Representation of DT Signals  Response of an LTI System (Convolution)  Impulse Response  Graphical Convolution  Analytic Convolution  Properties of Convolution: o Commutative o Distributive o Associative  Properties of DT LTI Systems 6)Difference and Differential Eqs.  Linear Constant-Coefficient  Response of 1 st -Order Systems  Differential Equations  Numerical Solutions  Representation of CT Signals Using Pulses 7)Continuous-Time Convolution  Response of a CT LTI System  Graphical Convolution  Analytic Convolution  Properties of Convolution o Sifting o Commutative, Distributive, Associative  Useful Properties of CT LTI Systems

EE 3512: Lecture 13, Slide 2 8)Fourier Series  Complex Fourier Series  Trigonometric Fourier Series  Convergence  Gibbs Phenomena 9)Trigonometric Fourier Series  Analysis Equations  Even/Odd Symmetry  Line Spectra  Power Spectra  Properties 10)The Fourier Transform  Analysis/Synthesis Equations  Frequency Response of an LTI System  Existence  Fourier Transforms of Periodic Signals 11)Fourier Transform Properties  Linearity  Time Shift and Time Reversal  Multiplication, Integration  Convolution  Parseval’s Theorem  Duality Exam No. 1 Review – Major Concepts (Cont.) 12)Modulation and Demodulation  Generalized Fourier Transform  Amplitude Modulation  Frequency and Phase Modulation  Synchronous Demodulation of an AM Signal  Asynchronous Demodulation  DSB and SSB Modulation  Frequency Domain Multiplexing 13)Review 14)Exam No. 1

EE 3512: Lecture 13, Slide 3 How to model the input and output behavior of a linear time-invariant system: Time Domain vs. Frequency Domain Discrete-Time vs. Continuous Time for a wide range of signals including: Impulse Unit Step Ramp Sinewaves and Other Periodic Signals Time-limited Signals (e.g., Unit Pulse) Infinite Duration Signals (e.g., exponential) … and this is just the first 1/3 of the course Exam No. 1 Review – But What Did We Really Learn?

EE 3512: Lecture 13, Slide 4 Summary Introduced a two-stage process for demodulating broadcast signals known as the Superheterodyne receiver. Reviewed the material covered on the first exam: Sects. 1.0 – 3.9.