Fall 2014 EE 445S Real-Time Digital Signal Processing Laboratory Prof. EvansHomework #4Random Signals and CorrelationAssigned on Saturday, October 25th, 2014Due on Friday, October 31, 2014, by 11:00am sharpHomework submitted after 11:00am will be subject to a penalty of 2 points per minute late.Reading: Johnson, Sethares & Klein, chapters 4, 5, 6, and 8, and Appendix B; Course readerappendix L & S; and Haykin, Communication Systems, excerpts to be given in a handout.Office hours for the teaching assistants and Prof. Evans; bold indicates a 30-minute timeslot.Time Slot Monday Tuesday Wednesday Thursday Friday9:30 am Evans(UTC 1.130)Rao(UTC 1.130)10:00 am Evans(UTC 1.130)Evans(UTC 1.130)10:30 am11:00 am Evans(UTC 1.130)Evans(UTC 1.130)Evans(UTC 1.130)12:00 pm Evans(UTC 1.130)Evans(UTC 1.130)Evans(cafe)12:30 pm Evans(cafe)1:00 pm Evans(cafe)2:00 pm3:00 pm3:30 pm Kundu(ACA 111)4:00 pm Kundu(ACA 111)4:30 pm Kundu(ACA 111)5:00 pm Rao(ACA 111)Kundu(ACA 111)5:30 pm Rao(ACA 111)Kundu(ACA 111)6:00 pm Rao(ACA 111)Kundu(ACA 111)6:30 pm Rao(ACA 111)7:00 pm Rao(ACA 111)You may use any computer program to help you solve these problems, check answers, etc. Pleasesubmit any MATLAB code that you have written for the homework solution. The MATLAB code inthe Johnson, Sethares and Klein book also runs in LabVIEW Mathscript and GNU Octave. Please seethe note on page vii of the SRD book for more informationAs stated on the course descriptor, “Discussion of homework questions is encouraged. Please besure to submit your own independent homework solution.”4.1. Spectral Analysis of a Random Signal. 40 points.a) Johnson, Sethares & Klein, exercise B.2 on page 414. 12 points.b) Johnson, Sethares & Klein, exercise 3.4, on page 43. Please submit the plots with yourhomework solution. 12 points.c) Plot spectrum of a pseudo-noise (PN) sequence of length 31 of +1 and -1 amplitudes; i.e., a bitof value ‘1’ maps to +1 and a bit of value ‘0’ maps to -1. You can find a length 31 PN sequencein Appendix L of the course reader, or you could use seqgen.pn to generate one in Matlab. Arethere any frequencies at which the magnitude spectrum is exactly zero? 16 points.4.2 Finding a Known Marker in a Noisy Received Signal. 30 points.Johnson, Sethares & Klein, exercise 8.8, page 160. In the code for correx.m, define header to be(a) A sequence of length 31 of all +1 entries. The Matlab command ones might be helpful.(b) A maximal length pseudo-noise sequence of length 31 with entries +1 and -1.Explain why there is a difference in detection performance between the two different headers.4.3 Finding a Known Marker in a Distorted Received Signal. 30 points.Johnson, Sethares & Klein, exercise 8.18, page 164. Please use the following values:(a) a = 0.2 and b = 0.3, and(b) a = -0.1 and b =