TELECOMMUNICATION 1 2012-2013 Fall Project SINC FUNCTION‚ SSB-AM‚ FM Name: Onur Mustafa Erdoğan ID Number: 10014044 Submission Date: 24.12.2012 Abstract: In these project‚ I will analyze Fourier Transform of sinc function and it’s modulation.(SSB-AM‚FM) I will explain SSB-AM and FM theoretically and solve their math model in steps. After all‚ I’ll use simulations and graphics to prove my solutions and In the and‚ I will write my conclusions down. Introduction SSB-AM [1]In
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this examination and that I have reported all such incidents observed by me in which unpermitted aid is given.” Signature Name Student ID Question 1: [4 points] Consider a linear time-invariant (LTI) system with impulse response h(t) whose Fourier transform is H(f ) = ∧(f ). Recall that ∧(f ) is non-zero only from f = −1 to f = +1. Find the output of the system if the input is: (a) x(t) = sin 0.5πt Solution: ∧(0.25) sin 0.5πt = 0.75 sin 0.5πt (b) x(t) = cos 10πt Solution: ∧(5) cos 10πt = 0 Question
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Mathematical Functions. U. S. Department of Commerce‚ Washington‚ DC‚ 1972. S. Benedetto and E. Biglieri. Principles of Digital Transmission. Kluwer‚ New York‚ 1999. [ZTF89] R.E. Ziemer‚ W.H. Trantor‚ and D.R. Fannin. Signals and Systems: Continuous and Discrete. MacMillan‚ New York‚ 1989.
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Lecture 13: Edge Detection c Bryan S. Morse‚ Brigham Young University‚ 1998–2000 Last modified on February 12‚ 2000 at 10:00 AM Contents 13.1 Introduction . . . . . . . . . . . . . . 13.2 First-Derivative Methods . . . . . . . 13.2.1 Roberts Kernels . . . . . . . . . 13.2.2 Kirsch Compass Kernels . . . . 13.2.3 Prewitt Kernels . . . . . . . . . 13.2.4 Sobel Kernels . . . . . . . . . . 13.2.5 Edge Extraction . . . . . . . . . 13.3 Second-Derivative Methods . . . . . . 13.3.1 Laplacian Operators
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generation. Pre-lab Assignment : Given signal x(t) = sinc(t)‚ x(t). 1. Find out the Fourier transform of x(t)‚ X(f )‚ sketch them; 2. Find out the Nyquist sampling frequency of 3. Given sampling rate terms of fs ‚ write down the expression of the Fourier transform of xs (t) → Xs (f ) in fs = 1 Hz‚ sketch the sampled signal X(f ). xs (t) = x(kTs ) and the Fourier 4. Let sampling frequency transform of xs (t). fs = 2Hz ‚ repeat 4. fs = 0.5Hz ‚ repeat 4. fs = 1.5Hz ‚ repeat 4. fs
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being multiplication. • Real Time Systems demand instantaneous response to environmental variables and quick execution of taken decision. • Multiplication algorithms find applications in Digital Signal Processing (DSP) for discrete Fourier transforms‚ Fast Fourier transforms‚ convolution‚ digital filters‚ etc. Therefore any new multiplication algorithm opens up a new approach for improving existing schemes. This calls for a ‘time efficient’ algorithm for ‘multiplication’ to improve processor throughput
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ANSWERS BRIEF AND TO THE POINT. DON’T WASTE TIME WRITING LONG DISCUSSIONS. SOME Useful Facts • xn = f0 G(nf0 )‚ where xn are the Fourier Series coefficients of periodic signal x(t)‚ and G(f ) is the Fourier Transform of a single period of x(t). • “Convolution of a signal of width w1 with a signal of width w2 results in a signal of width w1 + w2 .” • From the Fourier Transform table: k=∞ n=∞ w(t) = k=−∞ δ(t − kT ) ⇐⇒ W (f ) = 1/T n=−∞ δ(f − n/T ) 2 1. 10% dB problem: The output signal
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scalloping in the two-ray result‚ with an envelope that decays twice as fast (on log-log scale) as the free-space result. 2. (10) Given an RF pulse s(t) = 10−3 rect( t ) cos(2π870 · 106 t + π/6) volts .001 (2) • find S(f )‚ the Fourier transform‚ and sketch the energy density spectrum in the frequency domain • Find the complex envelope s(t) with respect to the reference cos(2π870 · 106 t). ˜ • find the energy delivered to a 50 Ω load 3. (Additional assignment for ECE 6784 group
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AFFILIATED INSTITUTIONS ANNA UNIVERSITY‚ CHENNAI R-2008 B.E. MECHATRONICS ENGINEERING II - VIII SEMESTERS CURRICULA AND SYLLABI SEMESTER II SL. COURSE No. CODE THEORY 1. HS2161 2. MA2161 3. PH2161 4. CY2161 5. a ME2151 5. b 5. c 6. a 6. b EE2151 EC2151 GE2151 GE2152 COURSE TITLE L T P C Technical English – II* Mathematics – II* Engineering Physics – II* Engineering Chemistry – II* Engineering Mechanics (For non-circuit branches) Circuit Theory (For branches under Electrical Faculty) Electric
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fendpaper.qxd 11/4/10 12:05 PM Page 2 Systems of Units. Some Important Conversion Factors The most important systems of units are shown in the table below. The mks system is also known as the International System of Units (abbreviated SI )‚ and the abbreviations sec (instead of s)‚ gm (instead of g)‚ and nt (instead of N) are also used. System of units Length Mass Time Force cgs system centimeter (cm) gram (g) second (s) dyne mks system meter (m) kilogram (kg) second (s) newton
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