Practice+Exam+1_answers - Practice Exam#1 Challenge 07...

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Practice Exam #1 Practice Exam #1 Challenge 07 Practice Quiz #1 Short term calendar Wednesday – Exam #1 Friday – Project #1 due. Submission on the Summary Form .DOC (4 page limit). Submit Project #1 in class, no TA certification required. Monday – Project 1 interpretation.
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Practice Exam #1 Challenge 07 A signal having a z-transform: X(z)=(1+0.4 2 z -1 )/(1- 0.8 2 z -1 + 0.64 z -2 ) is to be inverted into the discrete-time domain, namely x[k]. x[k] = A( a cos( φ 1 )+ b sin( φ 2 )); (A= α k ). What is x[k]?
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Practice Exam #1 Challenge 07 Using the slacker friend, residuez : >> b=[1, 0.4*sqrt(2)]; a=[1, -0.8*sqrt(2), 0.64]; >> [R,p,C]= residuez (b,a) R = 0.5000 - 1.0000i 0.5000 + 1.0000i % Residues (Heaviside coefficients) p = 0.5657 + 0.5657i 0.5657 - 0.5657i % Pole locations C = [] >> Mp=abs(p') % pole magnitude Mp = 0.8000 0.8000 >> Ap=angle(p')/pi % phase angles x pi Ap = -0.2500 0.2500 ± π /4 0.8 90 ° 0.8 -90 ° or 90 ° , or f s /4
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Practice Exam #1 Challenge 07 Therefore: Refer to Table 1 of Lesson 7 (Inverse z-Transform) and Euler’s equation. 8 . 0 | | ; ) | 8 . 0 | 1 1 ) 1 5 . 0 ( ) | 8 . 0 | 1 1 ) 1 5 . 0 ( ) ( 1 4 / 1 4 / - - + - + = - - - z z e j z e j z X j j π π ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 { } 4 / sin 2 4 / cos | 8 . 0 | ] [ 2 1 | 8 . 0 | ] [ | 8 . 0 | 1 5 . 0 ] [ | 8 . 0 | 1 5 . 0 ] [ 4 / 4 / 4 / 4 / 4 / 4 / k k k u e e j e e k u e j k u e j k x k k j k j k j k j k k j k k j k π π π π π π π π + = - + + = - + + = - - -
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Practice Exam #1 Challenge 07 If you arre really lazy, you may have tried to perform a symbolic study as shown below. >> syms z >> f=(z^2 - (0.4*1.414)*z )/(z^2 -(0.8*1.414)*z + 0.64) f = (z^2-707/1250*z)/(z^2-707/625*z+16/25) >> iztrans(f) ans = sum(1/2*(1/_alpha)^n,_alpha = RootOf(625-707*_Z+400*_Z^2)) >> ?????????????? This answer is basically useless.
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Practice Exam #1 EEL 5525 Practice Exam #1 Fall 2011 Lectures 1-7 Name: ____________________________________ ID: _______________________________________ Instructions: Complete the exam on the space provided. When time is called, stop all work and follow the instructions provided. Any work that is not collected when called for will not be graded. The honor system will be strictly enforced. Allowed Open book Open notes Pocket calculators and laptops Figures and tables Internet access to Sakai (only) Disallowed Unauthorized Internet access Cell phones Exam Cover Sheet
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Practice Exam #1 Question 1 x(t) ADC DAC Interpolator Playback f s x[k] y(t) Memory Record ° Q1 : Sampling Theorem and Quantization You are to analyze the audio recording and playback system shown below. The input audio frequency range is f [0, 3.5] kHz. The listener’s hearing range is f [0, 8] kHz. The ADC operates at the programmable sample rate of f s = n8kHz, n an integer.
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Practice Exam #1 Question 1 a. What is the lowest sampling frequency f s that will insure that the original audio signal x ( t ) can be (theoretically) reconstructed from its time-series samples x [ k ], without aliasing?
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