A set of orthonormal basis functions for a particular signal space are shown below.
(a) Given that x(t) = , calculate the signal space vector (a1, a2, a3) such that x(t) = .
(b) Given that y(t) can be represented by the vector (1,1,-2) in signal space using the orthonormal basis set above. Sketch y(t) below in time domain.
A set of orthonormal basis functions for a particular signal space are shown below. (a) Given tha...
Exercise 11. Given th=3(1 1 1-1)" and v2-(-1 1 3 5)T, verify that these vectors form an orthonormal set in R. Extend this set to an orthonormal basis for R4 by finding an orthonormal basis for the nullspace of 1 -1 113 5 Hint: First find a basis for the null space and then use the G-S process. Exercise 11. Given th=3(1 1 1-1)" and v2-(-1 1 3 5)T, verify that these vectors form an orthonormal set in R. Extend...
1. A 4-ary signal set is given as So(t)-0,0StsT SI(t)-A cos(oot), OStsT Si(t)A sin(oot) + A cos(oot), 0StsT Assume (oT = 2m for some integer n. The signals are transmitted over an AWGN with noise power spectral density = N-2. The receiver uses the ML decision rule (ie, he assumes all signals are equiprobable) Choose a suitable set of Orthonormal basis functions and find (and sketch) the geometric representation of this signal set (called signal constellation). Clearly identify the decisions...
t tao are real numbers) is a basis set for the analog complex signal space 1: Show that the set DiracDela(t-tao 2: Choose two discrete signals and calculate the inner product of these signals 3: Choose two analog signals and calculate the inner product of these signals
1. For the three following signal sets . Find the basis functions using Gram-Schmidt method. . Plot the corresponding signal space representation. . Find the distance between the two signals. (a) x(t) = Acos(2tht), y(t) = Asin(2T,fet), t E [0, e). [30 points] (b) (t) A cos(2m fct), y(t) A cos(2m fct+0), t E [0, Tb]. [30 points] (c) The signal set shown in Figure 1 [40 points xp V3A T/2 T To
An analog signal is given as below x(t) = 10sin 4rtt The signal is sampled by two different frequencies f, = 1Hz, f, = 10Hz respectively, and the output are yı, Yz. (i) Sketch signal x(t) in the time domain. (3 marks) (ii) Sketch frequency spectrum of x(t). (3 marks) (iii) After sampling, the continuous signal is converted to a discrete signal. Draw the two discrete signals Yı, Y2: (4 marks) (iv) Discuss whether f1, f, can successfully sample the...
here is the solution for the question but i need someone help to understand part b please. ф1(t) 2(t) 0. -1 Figure 7: Set of orthonormal basis functions in Problem 4 The signals si(t) and s2(t) are given by 201 (t) +dy(t) s2(t) h2(t) hi(t) (a) Design and draw the matched filter for the system using the above orthonormal basis functions to minimize the BER Result is in Fig. 8. (b) Design and draw the receiver for the system using...
Given the following set of three waveforms.s,(0),,(),s,(),,(0), and the set of functions )..), respectively, represented below , 1SIS 0, otherwise O otherwise 0 0, otherwise MITTED PAUL C e 12 - W)-0, otherwise Upints) Plot the signals (0,50), sf,M(,),and the functions甿 σ points) Calculate the energy of each signal s,(r),,,U), s,(n,(r). Ơ points) What is the dimensionality of the set ,(ns, (r), sto..(,) ?
5) The level curves of a function f(x,y) are given in the graph below. 2 X -1 -2 i Estimate f(3,3) ii Estimate Vf(-3, 1) Let u be a unit vector parallel to (1,4). Calculate Daf using your answer from i iv) Find the location of all critical points of the function f, on the set -5 <r< of these is a saddle point) iii) Let D be the domain bounded between the curves y = x and y= 2...
this is Q1 please solve Q2 2. Consider the same signal x(t) shown above in question 1 (a) write down the equation of the signal y(t) in terms x(t) in Fig. I and Fig.2 (b) Specify the operation(s) performed on X(t) to obtain each of signals of Fig.1 and Fig2 0.5 1 (Fig. 1) (Fig.2) 1 -2 -1 0 +1 +2 X(t) Questions Set # 3 CT signals combined time and amplitude Operations 1. Consider the signal x(1) (a) Sketch...
please give the correct answer with explanations, thank you Als a 3 x 4 matrix with column vectors a, a, a3, 24 50 A (a a2 a3 24 If you need to refer to these column vectors in any answer use a1 a2 etc for 1, 2 etc.) A has row reduced echelon form (RREF) 1042 0 1 2 0 0 0 0 1. State the values of rank(A) Number and nullity(A) Number 2. Find a basis for the column...