1. For each of the following questions, you must show a detailed solution process or proof...
need solution and code for this signal and system problem 1) Linearity: In order for a system to be linear it must satisfy the following equation: In other words, the response of a linear system to an input that is a linear combination of two signals is the linear combination of the responses of the system to each one of these signals. Let xi)- u(t) -u(t-1) and x2t) u- u(t-2) be input signals to the systems described by the i/o...
For a continuous time linear time-invariant system, the input-output relation is the following (x(t) the input, y(t) the output): , where h(t) is the impulse response function of the system. Please explain why a signal like e/“* is always an eigenvector of this linear map for any w. Also, if ¥(w),X(w),and H(w) are the Fourier transforms of y(t),x(t),and h(t), respectively. Please derive in detail the relation between Y(w),X(w),and H(w), which means to reproduce the proof of the basic convolution property...
i need all questions quickly. - Answer the following questions in details. 1) Determine whether the following signals are periodic or non-periodic. If they are periodic, find the fundamental period. a) b) te=cos(+1) 2) Find the even and odd parts of the following signals: x(t) = (1 + r) cos (104) X(t) = ejt 3) A discrete-time signal [n] is shown below. Sketch and label each of the following signals. (a) xn-21 (b) x[21] (c)--) (d) x[-n21 a) 4) Determine...
NOTE: L Answer all questions and sub-questions. Bl. A neat detailed step-by-step answer to earn full credit. i. Partial credit given only if you show intermediate steps. iv. Even if the "final answer" is correct, I will check the steps 1. This question has 5 sub-questions. Answer all of them (35 POINTS) a. Is the following differential equation: i. Linear or non-linear? Why? ii. Time variant or time invariant? Why? b. In the following OP-AMP circuit: Find: HINT: Vacts as...
Do each of the following eight (8) problems. The problems have equal weight. For each problem, in order to receive maximum possible credit, show the steps of the solution clearly,and provide appropriate explanation. Return this exam with your answer sheets . Chapter continunous-time system, with time t in seconds () input fO, and output yo. is specified by the equation y(t) = 1.5cos(2x500 + 0.8ft). a. Is this system instantaneous (memoryless) or dynamic (with memory)? Justify your answer Show that...
(1) Give a careful, detailed proof of the following Proposition. The sequence {2jnEN s unbounded Your proof should use the Archimedean Property and Russell's Paradox (2) Working directly from the basic definition of convergence to a ->0o Vn y together limit, show that limn-+ n- r and lim, imply that limn→х (2xn-3y.) 2x-3y (3) Give a proof, by induction, of the following Proposition. For 0 〈 n E N. suppose that the functions fı, . . . , f,: R...
determine whether 20 total pts] For each of the following systems described by their input-output behavior, or not the system is (1) linear,(2) time-invariant, (3) causal. For each case, make sure that you explain why. a. (5 pts] y[n] Axn] +B where A and B are nonzero constants d. 5 pts] y[n] x[n cos(0.25n)
Question 1.. Detemine if the following systems are linear or not (a) (5 points) y(t) = tx(t (b) (5 points) y(t) = 2(t (c) (5 points) y(t) = 2.r(t) +3 15 points Question 2 Determine if the following systems are time-invariant or not 10 points (a) (5 points) y(t) = x(2t) (b) (5 points) y(t) =r(t)u(t) 5 points Question 3 Determine if the following systems are causal or not (a) (5 points) y(t) = r(-t) 20 points Question 4 Consider...
can someone please explain why they only considered 0,2 and 5 as their frequencies and didn't include -2 and -5? Also, how did they get the angles for the changes column? please explain with steps. thank you 1. (i) (8 pts) The input signal z(t) to a continuous time (CT) linear time-invariant (LTI) system is given by x(t) 12 cos 2t +sin 5t The output y(t) is found to be given by y(t) 3-4 sin 2t 0.5 sin 5t At...
use 18 rules of inference to solve the following problem. Do not use conditional proof, indirect proof, or assumed premises.for each proof you must write the premises in that proof. 1. X v Y prove /S v Y 2. z 3.( x•z)---> s