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3. Find at least two different sets of orthonormal basis signals for a 4-dimensional signal space 3. Find at least...
A set of orthonormal basis functions for a particular signal space are shown below. (a) Given tha...
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
3. Use the Gram-Schmidt method to find an orthonormal basis of the vector space Span <...
3. Use the Gram-Schmidt method to find an orthonormal basis of the vector space Span < 2
(15 pts) Given the 5-point signal space diagram shown below, can you find an alter- native 2-dimensional signal set with the same number of signals, lower average energy and a lower probability of sy...
(15 pts) Given the 5-point signal space diagram shown below, can you find an alter- native 2-dimensional signal set with the same number of signals, lower average energy and a lower probability of symbol error at high SNR? Assume signals are equally likely. Draw and label your signals very neatly. Justify your answer 3 3 -21 -1 -2 -3
(15 pts) Given the 5-point signal space diagram shown below, can you find an alter- native 2-dimensional signal set with the...
1. For the three following signal sets . Find the basis functions using Gram-Schmidt method. ....
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
Find an orthonormal basis for the column space of the matrix: 2 1 3 1 -1...
Find an orthonormal basis for the column space of the matrix: 2 1 3 1 -1 0
Exercise 25. Let , be an orthonormal basis of a two-dimensional subspace S of R" and...
Exercise 25. Let , be an orthonormal basis of a two-dimensional subspace S of R" and A xyT + (i) Show that x+y and x -y are eigenvectors of A. What are their corresponding eigenvalues? (ii) Show that 0 is an eigenvalue of R" with n - 2 linearly independent eigenvectors. (iii) Explain why A is diagonalizable.
Exercise 25. Let , be an orthonormal basis of a two-dimensional subspace S of R" and A xyT + (i) Show that x+y...
Exercise 20 Let fr,y} be an orthonormal basis of a two-dimensional subspace S of R" and...
Exercise 20 Let fr,y} be an orthonormal basis of a two-dimensional subspace S of R" and T A= xx SL (i) Show that N(A (ii) Show that the rank of A is 2 (iii Show that x and y are eigenvectors of A for an eigenvalue X of A. What is A?
Exercise 20 Let fr,y} be an orthonormal basis of a two-dimensional subspace S of R" and T A= xx SL (i) Show that N(A (ii) Show that 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) a...
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...
A = 1487 -1 2 -2 13 - 4 Find an orthonormal basis of the column...
A = 1487 -1 2 -2 13 - 4 Find an orthonormal basis of the column space of
t tao are real numbers) is a basis set for the analog complex signal space 1:...
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
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
3. Use the Gram-Schmidt method to find an orthonormal basis of the vector space Span < 2
(15 pts) Given the 5-point signal space diagram shown below, can you find an alter- native 2-dimensional signal set with the same number of signals, lower average energy and a lower probability of symbol error at high SNR? Assume signals are equally likely. Draw and label your signals very neatly. Justify your answer 3 3 -21 -1 -2 -3
(15 pts) Given the 5-point signal space diagram shown below, can you find an alter- native 2-dimensional signal set with the...
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
Find an orthonormal basis for the column space of the matrix: 2 1 3 1 -1 0
Exercise 25. Let , be an orthonormal basis of a two-dimensional subspace S of R" and A xyT + (i) Show that x+y and x -y are eigenvectors of A. What are their corresponding eigenvalues? (ii) Show that 0 is an eigenvalue of R" with n - 2 linearly independent eigenvectors. (iii) Explain why A is diagonalizable.
Exercise 25. Let , be an orthonormal basis of a two-dimensional subspace S of R" and A xyT + (i) Show that x+y...
Exercise 20 Let fr,y} be an orthonormal basis of a two-dimensional subspace S of R" and T A= xx SL (i) Show that N(A (ii) Show that the rank of A is 2 (iii Show that x and y are eigenvectors of A for an eigenvalue X of A. What is A?
Exercise 20 Let fr,y} be an orthonormal basis of a two-dimensional subspace S of R" and T A= xx SL (i) Show that N(A (ii) Show that 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...
A = 1487 -1 2 -2 13 - 4 Find an orthonormal basis of the column space of
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
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