A vector x = [1, 1, -j, 1] is projected onto y = [-j, 1, -j,...

Transcribed Image Text:

A vector x = [1, 1, -j, 1] is projected onto y = [-j, 1, -j, -j] to give vector z. a) (2) Find the inner product < x,y >. b) (2) Find the self-inner product of y. c) (2) Find the projection coefficient. d) (2) Write down the vector z. The impulse responses of two LTI systems are given below. These two LTI systems are connected in parallel and added together to form an overall LTI system ho(t). h₁ (t) = 2 e 2t u(t) h₂ (t) = 8(t-1) e) (2) Find the system functions H₁ (s) and H₂ (s). f) (2) Find the frequency response of the overall system H, (jw). If an input x(t) cos(2t) is applied to the LTI system h₁ (t), g) (2) Find the corresponding magnitude response and phase response (in terms of π). = If an input x (t) = cos(2t) is applied to the LTI system h₂ (t), h) (2) Find the corresponding magnitude response and phase response (in terms of π). If an input x(t) = cos(2t) is applied to the overall LTI system ho(t) to give the output y(t), i) (2) Write down the output y(t). Another LTI system has impulse response h[n] = u[n 1] – u[n – 5]. j) (2) Find the system function H(z) and the frequency response H(ejw). A vector x = [1, 1, -j, 1] is projected onto y = [-j, 1, -j, -j] to give vector z. a) (2) Find the inner product < x,y >. b) (2) Find the self-inner product of y. c) (2) Find the projection coefficient. d) (2) Write down the vector z. The impulse responses of two LTI systems are given below. These two LTI systems are connected in parallel and added together to form an overall LTI system ho(t). h₁ (t) = 2 e 2t u(t) h₂ (t) = 8(t-1) e) (2) Find the system functions H₁ (s) and H₂ (s). f) (2) Find the frequency response of the overall system H, (jw). If an input x(t) cos(2t) is applied to the LTI system h₁ (t), g) (2) Find the corresponding magnitude response and phase response (in terms of π). = If an input x (t) = cos(2t) is applied to the LTI system h₂ (t), h) (2) Find the corresponding magnitude response and phase response (in terms of π). If an input x(t) = cos(2t) is applied to the overall LTI system ho(t) to give the output y(t), i) (2) Write down the output y(t). Another LTI system has impulse response h[n] = u[n 1] – u[n – 5]. j) (2) Find the system function H(z) and the frequency response H(ejw).

Answer rating: 100% (QA)

a The inner product is calculated by taking the dot product of the two vectors 1 j 1 1 j j j 1 1 j b The selfinner product of vec y is calculated by taking the dot product of vec y with itself j j 1 1 ... View the full answer