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

This preview shows pages 1–9. Sign up to view the full content.

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.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
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]?
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

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
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 + = - + + = - + + = - - -
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.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
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
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.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
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?
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### What students are saying

• As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

Kiran Temple University Fox School of Business ‘17, Course Hero Intern

• I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

Dana University of Pennsylvania ‘17, Course Hero Intern

• The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

Jill Tulane University ‘16, Course Hero Intern