PPT-Fourier Analysis of Signals and

Systems Dr Babul Islam Dept of Applied Physics and Electronic Engineering University of Rajshahi 1 Outline Response of LTI system in time domain Properties of LTI systems Fourier analysis of signals. 5.1 Discrete-time Fourier Transform . Representation for discrete-time signals. Chapters 3, 4, 5. Chap. 3 . Periodic. Fourier Series. Chap. 4 . Aperiodic . Fourier Transform . Chap. 5 . Aperiodic . Periodic Signals. 3.1 Exponential/Sinusoidal Signals as . Building Blocks for Many Signals. Time/Frequency Domain Basis Sets. Time . Domain. Frequency Domain.  .  .  .  .  . .  . .  .  .  . Sparsity. Testing over the Boolean Hypercube. Grigory. . Yaroslavtsev. http://grigory.us. Joint with Andrew Arnold (Waterloo), . Arturs. . Backurs. (MIT), Eric . Blais. (Waterloo) and Krzysztof . from Fourier to Wavelets. Ming . Zhong. 2012.9. Overview (1). Harmonic analysis basics. Represent signals as the linear combination of basic overlapping, wave-like functions. Natural domain (space/time). 5.1 Discrete-time Fourier Transform . Representation for discrete-time signals. Chapters 3, 4, 5. Chap. 3 . Periodic. Fourier Series. Chap. 4 . Aperiodic . Fourier Transform . Chap. 5 . Aperiodic . Periodic Signals. 3.1 Exponential/Sinusoidal Signals as . Building Blocks for Many Signals. Time/Frequency Domain Basis Sets. Time . Domain. Frequency Domain.  .  .  .  .  . .  . .  .  .  . Why use complex exponentials? . Because they are useful building blocks which can be used to represent large and useful classes of signals. Response of LTI systems to these basic signals is particularly simple and useful.. Sparsity. Testing over the Boolean Hypercube. Grigory. . Yaroslavtsev. http://grigory.us. Joint with Andrew Arnold (Waterloo), . Arturs. . Backurs. (MIT), Eric . Blais. (Waterloo) and Krzysztof . Dept. of Electrical and Computer Engineering. The University of Texas at Austin. EE . 313 Linear Systems and Signals Fall 2017. Lecture 3 . http://. www.ece.utexas.edu. Junlin. . Hou. Huangyan. Pan. Yifan. Li. Jie. Liu. Mathematics and Music. The explanation of Fourier analysis in musicology. The application of the theory. Summary. contents. Mathermatics and Music. Fourier Transform Notation. For periodic signal. Fourier Transform can be used for BOTH time and frequency domains. For non-periodic signal. FFT for . infinite. period. Example: FFT for . infinite. 23 March 2011. Lowe. 1. Announcements. Lectures on both Monday, March 28. th. , and Wednesday, March 30. th. .. Fracture Testing. Aerodynamic Testing. Prepare for the Spectral Analysis sessions for next week: http://www.aoe.vt.edu/~aborgolt/aoe3054/manual/inst4/index.html. a 15-minute oral summary with 5-minutes additional to answer questions and. A 1-5 page written summary. Please confirm your topic selection with me by March 29. . Internet Directory. http://www.atmos.albany.edu/facstaff/roundy/ATM523. Carrier . is strong and stable sinusoidal signal . x(t) = A cos(. w. c . t + . q. ). Carrier transports . information. (audio, video, text, email) across the world. Why is the carrier required?. Audio and video signals cannot travel over large distances since they are weak.