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# SIGNALS & SYSTEMS ECSE 2410

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This 4 page Class Notes was uploaded by Immanuel Brakus PhD on Monday October 19, 2015. The Class Notes belongs to ECSE 2410 at Rensselaer Polytechnic Institute taught by Richard Radke in Fall. Since its upload, it has received 65 views. For similar materials see /class/224766/ecse-2410-rensselaer-polytechnic-institute in ELECTRICAL AND COMPUTER ENGINEERING at Rensselaer Polytechnic Institute.

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Date Created: 10/19/15

Signals and Systems exam 2 Poles and zeros will not be on exam 2 Exam 1 will be inclass on Friday April 13 Two onesided pages of handwritten notes are permitted ie the page you made for Exam 1 and a new page for Exam 2 No electronic devices of any type including calculators and cell phones are permitted The exam will start promptly at 830 AM Section 1 and 1000 AM Section 2 Section 1 should expect to stay in the classroom through 950 AM bring a book to read or some other work no laptops please Section 1 should depart the classroom and leave the area promptly at 950 so that Section 2 can enter The exam cover page and the Fourier Transform property tables that will be provided closer to the exam but you will be given Tables 4142 on pp 328329 of the book If you have a Dean39s Excuse for any special accommodations eg timeandahalf or any other issues please let both me and Dr Vastola know immediately by email so we can plan the timing of the exam Even if you told us already for Exam 1 please remind us for Exam 2 There are several back exams on LMS to study from Some AM Bode and Laplace problems may appear in Exam 3 in some years A partial list is Blank exams Spring 2002 exam 3 Fall 2002 exam 3 Spring 2003 see both exams 2 and 3 Fall 2004 see both exams 2 and 3 Solved exams Fall 2009 Fall 2010 Fall 2011 HW9l7 Fourier Transform 40 4 l Fourier Transform properties and examples 4244 DiscreteTime Fourier Transform 50 51 DTFT examples 52 53 Sampling Theorem leClConverterInputhwpw7bgjh6txt4122012 103107 PM 70 71 Aliasing and upsamplingdownsampling 72 73 Amplitude Modulation 80 8 2 FrequencyDivision Multiplexing Bode plots 65 Laplace transform 90 9 1 HW 9 Due Friday 32 at the beginning of class 421a 421g 421i 422c In 421a make the signal look like one you already know the FT of instead of integrating directly In the remaining problems use direct integration to obtain the result You39ll need an integral table for a couple of the problems HW 10 Due Tuesday 3612 5 points for each part of each problem 50 points total 423 Change quotshould be ablequot to quotmustquot 424a HW11 4J9 426aa 436ab HW12 leClConverterInputhwpw7bgjh6txt4122012 103107 PM 81 83 84 Be sure to show your work For problem 84 change the cutoff frequency of the lowpass filter to 300 instead of 400 Clearly justify your answer in each problem HW13 73 74 a and d 721 abcd 722 In all of these problems be sure to give a clear explanation for your answer using sketches in the frequency domain and Fourier Transform properties Just giving a Nyquist rate or a yesno without justifying your answer will not receive full credit You will need to refer to Tables 41 and 42 on pp 328329 which give FTs for common signals and properties of FTs In 74d note that the frequency of the cosine is the same as the Nyquist frequency of the original signal In 72lcd be sure to read the conditions carefully these are not as straightforward as a and b In 722 note that you re being asked for a range on the sampling period T in the time domain instead of the sampling rate w in the frequency domain As a general note the Nyquist rate is an actual number not a range That is we say quotThe Nyquist rate is 10000quot but not quotThe Nyquist rate is gt 10000quot HW 14 76 77 79 Clearly justify your answer for each part HW15 622ab 627acd Bode magnitude only When sketching Bode plots be sure to indicate important values on the y aXis and the slopes of any diagonal lines in units of dbdecade Don39t forget to include the in uence of constants if any Also remember that in each of these problems you re to determine the straightline Bode approximation not create the leClConverterInputhwpw7bgjh6txt4l22012 103107 PM actual magnitude response with a tool like Matlab HW16 628 i iii Vi deferred from HW 15 Vii Xi new 632 Please note that you should do both magnitude and phase plots for all 5 parts of 628a HW17 921 abcgi 929 ac In 921 remember to specify the ROC as well as the algebraic Laplace transform Compute all the Laplace transforms from the defining integral no tables or properties except for the basic one eXpatut we did in class In 929 don t forget to include the ROC in parts a and b HW 18 922a b c d f g You must use Tables 91 and 92 on pp 691692 Note that the Partial Fraction Expansion approach only works properly when the order of the numerator polynomial is less than that of the denominator polynomial So for parts f and g you must first simplify Xs to a constant plus a fraction that satisfies this property For part f you then need to find a way to apply lines 13 and 14 of Table 92 In doing this the value of alpha from the ROC is important For part g you should use the properties to solve for the IFT leClConverterInputhwpw7bgjh6txt4122012 103107 PM

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