Given the following set of three waveforms.s,(0),,(),s,(),,(0), and the set of functions )..), respectively, represented below...
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
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.
4,0< t<2 0, otherwise alwl(t) +a2w2(t) + a33(t) i(t) 0.5 wg(,) 10.5 2 2 -0.5 0.5 0.5
4,0
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...
can you please solve this problem step by step, thank
you!!
1. Consider a DSB-SC signal with noise passes through a demodulator shown below. ViC0) 2(0) но но 0) The input signal plus noise is v,(t)-5,() + n'(t) where 5,0): Am(1)cos2r/rt, m(1) cos 2π/J is the message signal with f-</м , carrier frequency is f> fe , and noise n' (r) has power spectral density function G,じ)= η . The local carrier is v,(1)s 2 cosZrw. The carrier filter is...
Instructions: If you require uniformly distributed random
numbers
in [0, 1], use Matlab’s built in uniform random number generator
rand. Also,
you may NOT use any Matlab built-in functions that explicitly
perform the task
asked for in the problem.
Problem 6. Let α > 0 and set f(x)- ae-ale, for x e(-oo, oo). (a) Make a plot of f (b) Show that f is a probability density function (Hint: -, when z S 0, and x-r, when 0.) (c) If...
1. Consider a feedback system given below: T(s) Disturbance Controller Dynamics R(S) + Gc(s) G.(s) U(s) Sensor H(s) IMs) Sensor noise where the input and transfer functions are given as follows: R(s) = –,7,(s) = 0, N(s) = 0, G, - 15,6, -_- , and H(s) = 1. s's + 3) a. Derive the system transfer function Y(s)/R(s) = G,, poles, $, On, and, from the response function y(t), the performance measures: rise time Tr, peak time Tp, percent overshoot...
2. You are given the following multivariate PDF 0 else where S = {(z, y, z) |エ2 + y2 + 22-1). (a) (5 points) Let T be the set of all points that lie inside the largest cylinder by volume that can be inseribed in the region of S. Similarly let U be the set of all points that lie inside the largest cube that can be inscribed in the region of S. What would the probabilities P[(X, Y, Z)...
Matlab help
1) Given the functions x1()= tu()-tuft-1) and X2(t)=10e-5,11(), do the following: 1. Plotx,(t) and x2(0) using MATLAB 2. Use MATLAB to find and plot x(0=x:@*.x2(t), where * denotes convolution. 3. Find x(t)=x;()*X2(1) by hand using Laplace transforms. 4. Plot the result of part 3 in MATLAB and compare it to that found in part 2. 2) Given the transfer function shown below, do the following: 1. Find the system's impulse response and plot it using MATLAB 2. Repeat...
imaginary axis crossing points, respectively (l any).] 9.3 The figure below shows a feedback control system with internal rate compensation r(s) y(s) S(s +2) Bs (a) Set K1-2 and K2-5 and sketch the root locus with β the varied parameter where β> 0 (b) Can system be a marginally stable? if it is not marginally stable please explain why (c) Determine the value of B such that the closed loop system is critically damped.
imaginary axis crossing points, respectively (l...
The state space model of an interconnected three tank water storage system is given by the following equation: -3 1 0 1rh dt os lo 0 3] 10 1-3 The heights of water in the tanks are, respectively, h,h2,h3. Each tank has an independent input flow; the volume flow rates of input water into the three tanks are, respectively, qǐ1,W2,4a. Each tank also has a water discharge outlet and the volume flow rates of water coming out of the tanks...