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Consider the system in Figure H(o) If Xi(w) 0 for |wl > 2W and X2(w) for w > W. For the following...
1- Let's consider an LTI system with an impulse response of where Wo a) Find H(s) and the associa...
1- Let's consider an LTI system with an impulse response of where Wo a) Find H(s) and the associated H(ja) b) For the cases of μ:0.2, 0.5, 1.0, and 2.0 sketch frequency spectra c) What type of filter can this system represent? d) How does the spectrum HI(jw) change as μ increases? Explain? 2- Consider the following waveform f(t) which is a one cycle of a sinusoid for 0 t π in seconds while zero elsewhere (Aperiodic Signal) fit) 10...
Question Systems: Consider the following system for the questions below (indicate relevant transition points and peak...
Question Systems: Consider the following system for the questions below (indicate relevant transition points and peak values when drawing frequency domain representations). Note that X (jw) is the frequency domain representation of the input and both filters use a scaled version of the filter, H(jw). y(t) x(t)- H(w) H(jw) cos(2w.t) H(w) W(0) -Wo Wo X(jw) -2wo-WOW O 2w, a) Draw the frequency response of the output of the first signal path, Y. (jw) b) Draw the frequency response of the...
2. Consider the system described by the ODE's 2x1-3x2 +4u Using the State Function of Pontryagin ...
2. Consider the system described by the ODE's 2x1-3x2 +4u Using the State Function of Pontryagin to find the input u that minimizes dt a. Determine the state function of Pontryagin H. b. Find the optimal input and H c. Find the matrix A that will yield the governing equations x1 ai If xi (0) : 0.x2(0) = O and xi (1) = İ. x 2(1) =0 determine the govem equations for λǐ(0) and λ2(0) in terms of the elements...
Question 4 Xi →ろ sin at it m2, PM Consider the system shown in figure where m is subjected to F Sin(w t). Calculat...
Question 4 Xi →ろ sin at it m2, PM Consider the system shown in figure where m is subjected to F Sin(w t). Calculate the system response when m1 m2 and Kt k2- k
Question 4 Xi →ろ sin at it m2, PM Consider the system shown in figure where m is subjected to F Sin(w t). Calculate the system response when m1 m2 and Kt k2- k
9.28 Consider the LSI system shown in Figure P9.28, whose input is the zero-mean random process...
9.28 Consider the LSI system shown in Figure P9.28, whose input is the zero-mean random process W(t) and whose output is the random process X(t). The frequency response of the system is H(w). Given Kww() = 8(T), find H(W) in terms of the cross-covariance K xw (T) or its Fourier transform. Wit) X(t) H (6) Figure P9.28 LSI system with white noise input.
Problem 3 Consider the following system: 2 213+w. where w denotes control input. Here we design a control system based on passivity. (a) Suppose that w =-r1 + x2 + 2.123 + u for a new control input u...
Problem 3 Consider the following system: 2 213+w. where w denotes control input. Here we design a control system based on passivity. (a) Suppose that w =-r1 + x2 + 2.123 + u for a new control input u. Show that the state equation can be written as the following cascade form: i fa(2) +F(z)y, 22u yT2, where z = [ri, r3]T e R2. Find the expression for fa (z) and F(z). (b) Show that when y0, the origin 0...
1. Consider the system shown in the figure below. The system is an integrator, in which...
1. Consider the system shown in the figure below. The system is an integrator, in which the output is the integral: y(t)x()dr -00 Integrator x(t) y(t) (a) We may determine the impulse response h(t) by applying an impulse signal to the integrator, i.e. x(t) -5(t). What is the impulse response? Answer: (10 points) (b) The output of the integrator may be found by apply convolution method to determine the output. The convolution of the two signals is expressed a)ht -...
Consider the subspace W CR4 given by 22 W= - {O ER4 21 + x2 +...
Consider the subspace W CR4 given by 22 W= - {O ER4 21 + x2 + 34 = 0 and 32 +33 +24 = 0 23 24, Find an orthonormal basis H = {h1, h2, h3, h4} for R$ with the property that h¡ and he are elements of an orthonormal basis for W, where orthonormality is defined with respect to the dot product on R4 x R4
Consider a real LTI system with the following properties. 1 - Its frequency response H(w) is...
Consider a real LTI system with the following properties. 1 - Its frequency response H(w) is real and linear on [0, 1] (and therefore on ( - 11,0] by symmetry) as illustrated below (warning: the true values and signs of Q and b may not be those shown in the graph which is only for illustration). 2. It preserves the input ( - 1)". 3- It transforms the periodic sequence X[n]shown below into a constant sequence. What must be the...
5. Consider a CT system with transfer function This system is called an integrutor because t by h...
the subject is in digital signal processing
5. Consider a CT system with transfer function This system is called an integrutor because t by he d to the ingent t y)-x(r)dr. Discretize the above system using the bilinear transform. (a) What is the transfer function H'(:) of the resulting DT system b) If xin] is the input and yin] is the output of the resulting DT system, write the (c) Obtain an expression for the frequency response H'(o) of the...
1- Let's consider an LTI system with an impulse response of where Wo a) Find H(s) and the associated H(ja) b) For the cases of μ:0.2, 0.5, 1.0, and 2.0 sketch frequency spectra c) What type of filter can this system represent? d) How does the spectrum HI(jw) change as μ increases? Explain? 2- Consider the following waveform f(t) which is a one cycle of a sinusoid for 0 t π in seconds while zero elsewhere (Aperiodic Signal) fit) 10...
Question Systems: Consider the following system for the questions below (indicate relevant transition points and peak values when drawing frequency domain representations). Note that X (jw) is the frequency domain representation of the input and both filters use a scaled version of the filter, H(jw). y(t) x(t)- H(w) H(jw) cos(2w.t) H(w) W(0) -Wo Wo X(jw) -2wo-WOW O 2w, a) Draw the frequency response of the output of the first signal path, Y. (jw) b) Draw the frequency response of the...
2. Consider the system described by the ODE's 2x1-3x2 +4u Using the State Function of Pontryagin to find the input u that minimizes dt a. Determine the state function of Pontryagin H. b. Find the optimal input and H c. Find the matrix A that will yield the governing equations x1 ai If xi (0) : 0.x2(0) = O and xi (1) = İ. x 2(1) =0 determine the govem equations for λǐ(0) and λ2(0) in terms of the elements...
Question 4 Xi →ろ sin at it m2, PM Consider the system shown in figure where m is subjected to F Sin(w t). Calculate the system response when m1 m2 and Kt k2- k
Question 4 Xi →ろ sin at it m2, PM Consider the system shown in figure where m is subjected to F Sin(w t). Calculate the system response when m1 m2 and Kt k2- k
9.28 Consider the LSI system shown in Figure P9.28, whose input is the zero-mean random process W(t) and whose output is the random process X(t). The frequency response of the system is H(w). Given Kww() = 8(T), find H(W) in terms of the cross-covariance K xw (T) or its Fourier transform. Wit) X(t) H (6) Figure P9.28 LSI system with white noise input.
Problem 3 Consider the following system: 2 213+w. where w denotes control input. Here we design a control system based on passivity. (a) Suppose that w =-r1 + x2 + 2.123 + u for a new control input u. Show that the state equation can be written as the following cascade form: i fa(2) +F(z)y, 22u yT2, where z = [ri, r3]T e R2. Find the expression for fa (z) and F(z). (b) Show that when y0, the origin 0...
1. Consider the system shown in the figure below. The system is an integrator, in which the output is the integral: y(t)x()dr -00 Integrator x(t) y(t) (a) We may determine the impulse response h(t) by applying an impulse signal to the integrator, i.e. x(t) -5(t). What is the impulse response? Answer: (10 points) (b) The output of the integrator may be found by apply convolution method to determine the output. The convolution of the two signals is expressed a)ht -...
Consider the subspace W CR4 given by 22 W= - {O ER4 21 + x2 + 34 = 0 and 32 +33 +24 = 0 23 24, Find an orthonormal basis H = {h1, h2, h3, h4} for R$ with the property that h¡ and he are elements of an orthonormal basis for W, where orthonormality is defined with respect to the dot product on R4 x R4
Consider a real LTI system with the following properties. 1 - Its frequency response H(w) is real and linear on [0, 1] (and therefore on ( - 11,0] by symmetry) as illustrated below (warning: the true values and signs of Q and b may not be those shown in the graph which is only for illustration). 2. It preserves the input ( - 1)". 3- It transforms the periodic sequence X[n]shown below into a constant sequence. What must be the...
the subject is in digital signal processing
5. Consider a CT system with transfer function This system is called an integrutor because t by he d to the ingent t y)-x(r)dr. Discretize the above system using the bilinear transform. (a) What is the transfer function H'(:) of the resulting DT system b) If xin] is the input and yin] is the output of the resulting DT system, write the (c) Obtain an expression for the frequency response H'(o) of the...
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