3. (5 pts) CT FS properties. Observe that x1[n] is odd, what are the properties of the spectrum coefficients (mag and phase)? Observe that x3[n] is even, what are the properties of the spectrum coefficients (mag and phase)?
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3. (5 pts) CT FS properties. Observe that x1[n] is odd, what are the properties of...
2. (10 pts) CT FS properties. If x4[n] is the same as x3[n], but shifted to the right by 1, then what are the spectral coefficients of x4[n]? Hint: text, page 221.
1. (45 pts) DT FS. Find the fundamental period and the Fourier Series (FS) spectral coefficients for these periodic signals. Sketch the spectrum in magnitude and phase. Express each x[n] as the sum of the spectral coefficients for k = [0, N-1]. a. ?1[?] = ???( ? 3 ?) b. ?2 [?] = cos ( ? 3 ?) + sin( ? 4 ?) c. ?3[?]
3. (25 pts.) Let X1, X2, X3 be independent random variables such that Xi~ Poisson (A), i 1,2,3. Let N = X1 + X2+X3. (a) What is the distribution of N? (b) Find the conditional distribution of (X1, X2, X3) | N. (c) Now let N, X1, X2, X3, be random variables such that N~ Poisson(A), (X1, X2, X3) | N Trinomial(N; pi,p2.ps) where pi+p2+p3 = 1. Find the unconditional distribution of (X1, X2, X3). 3. (25 pts.) Let X1,...
5. (4 points) Let x1 [n] be a discrete-time signal defined as 21 [n] = 2e-n/4u[n], n e Z, and u[n] is the unit step sequence. Mark all of the true statements. (xv) x1[-n] = 2er/4uſ-n]. (xvi) O x1[n] is real valued. (xvii) O x1[n] is neither purely odd nor purely even, but it is periodic. (xviii) O x1[-n] = -2er/4u[-n]. 6. (4 points) Similarly, 22[n] = 2e-4nu[n], n e Z. Mark all of the true statements. (xix) O Pæ{rz[n]...
Solve this problem using the two-phase method. What special case do you observe? Max Zz4X1-2X2+X3 X1+2X2+X3 3 2X1-3X2+6X3 100 X1,X2,X3>0
Question 7 6 pts What are the (n, M,d) parameters of the following code: {(x1, 22, 23, 24, 25) € (Z13)5 : x1 + x2 + x3 + x4 + X5 = 0} n = M= d = Enter only positive integers without any decimal points, symbols, punctuation or spaces.
a) b) DTF magnitude for N-8 use the properties of DFT to fill the missing DFT valves. fs-16KHz, provide proper analog (f) and digital (omega) frequency values corresponding to each k in the horizontal axis of the DFT plot For the given DFT magnitude plot use the properties of DFT/DFS and find IX(8)l, IX(12)I, IX(-11)l c) 7 5 3 2 0 55453525150 Kad 2 a) b) DTF magnitude for N-8 use the properties of DFT to fill the missing DFT...
signal & system cours Signals and Systeme Q2 b) Given two signals x1(n)=[-1 2 0 -2 l) and x3[n] = [5 -4 0 4 -51 (5 Marks) Prove that sum of two signals is an odd signal. Prove that the product of two signals is an even signal. 1) 1 Signals and Systems Q5 b) How can you derive the Discrete-Time Fourier transform from the z-transform? (5 marks)
(Fs ) -2 3-2 out prito Qu.5 Write a java program that will accept any mumber from the use and will returs whether the eatered number is even or odd. For user input you can use JOptionlPane or Scanner (Pts 3) OR Qu.6 Write a java program which will allow user to enter the marks. If entered marks are mone tha 60 then program should print pass otherwise fail. For user input you can use JOptionPane O Scanner Pts 3)...
efficients Wi for the signal w(t) sin(16rt) 14. (8 pts) Determine the FS coefficients W, for the signal w(t) 3 cos(12rt)-5 sin(16rt). (c) (9 pts) Suppose a MATLAB anonymous function X already exists that correctly defines X() Write MATLAB code that uses X to reconstruct and then plot a 10-periodic replication of e(t) over-10sts10. efficients Wi for the signal w(t) sin(16rt) 14. (8 pts) Determine the FS coefficients W, for the signal w(t) 3 cos(12rt)-5 sin(16rt). (c) (9 pts) Suppose...