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of linear and time-invariant components with -3(2, C-1/4F, and L-1 H. vs is the input, and...
The following circuit consists of linear time invariant components where R1 = 2, R2 = 3,...
The following circuit consists of linear time invariant
components where R1 = 2,
R2 = 3,
C = 0.25F, and L = 1H. Let vs be the input voltage.
(a) Solve the differential equation that describes
vc(t). Hint: First, find the current
going through the parallel branch of R1–C. Then, write
the Kirchoff's Voltage Law for the main loop.
(b) Find vc(t) given that vs(t) = 2.5 V at
t = 0. Assume that vc(0-) = 1V and
iL(0-) =...
6. (15) Consider the following causal linear time-invariant (LTT) discrete-time filter with input in and output...
6. (15) Consider the following causal linear time-invariant (LTT) discrete-time filter with input in and output yn described by y[n] = x[n] – rn - 2 for n 20 . Is this a finite impulse response (FIR) or infinite impulse response (IIR) filter? Why? • What are the initial conditions and their values for this causal and linear time-invariant system? Why? • Draw the block diagram of the filter relating input x[n) and output y[n] • Derive a formula for...
The impulse response h(t) of a linear time-invariant system is 2*pi[(t-2)/2]. Find and plot the output...
The impulse response h(t) of a linear time-invariant system is 2*pi[(t-2)/2]. Find and plot the output when the system is driven by an input signal that is identical to the impulse response.
Please dont use Laplace or Fourier A linear time-invariant continuous-time system has the impulse response h(t)...
Please dont use Laplace or Fourier
A linear time-invariant continuous-time system has the impulse response h(t) = (sin(t) + e-t) u(t) (a) Compute the step response s(t) for all 20. (b) Compute the output response y(t) for all t > 0 when the input is u(t)-(t-2) with no initial energy in the system.
For a continuous time linear time-invariant system, the input-output relation is the following (x(t) the input, y(t) the...
For a continuous time linear time-invariant system, the
input-output relation is the following (x(t) the input, y(t)
the
output):
, where h(t) is the impulse response function of the
system.
Please explain why a signal like e/“* is always an eigenvector
of
this linear map for any w. Also, if ¥(w),X(w),and H(w) are
the
Fourier transforms of y(t),x(t),and h(t), respectively.
Please
derive in detail the relation between Y(w),X(w),and H(w),
which means to reproduce the proof of the basic convolution
property...
Question 1: (2 marks) Find the zero-input response yz(t) for a linear time-invariant (LTI) system described...
Question 1: (2 marks) Find the zero-input response yz(t) for a linear time-invariant (LTI) system described by the following differential equation: j(t) + 5y(t) + 6y(t) = f(t) + 2x(t) with the initial conditions yz (0) = 0 and jz (0) = 10. Question 2: (4 marks) The impulse response of an LTI system is given by: h(t) = 3e?'u(t) Find the zero-state response yzs (t) of the system for each the following input signals using convolution with direct integration....
Q8) Consider the following causal linear time-invariant (LTI) discrete-time filter with input x[n...
Q8) Consider the following causal linear time-invariant (LTI) discrete-time filter with input x[n] and output y[n] described by bx[n-21- ax[n-3 for n 2 0, where a and b are real-valued positive coefficients. A) Is this a finite impulse response (FIR) or infinite impulse response (IIR) filter? Why? B) What are the initial conditions and their values? Why? C) Draw the block diagram of the filter relating input x[n] and output y[n] D) Derive a formula for the transfer function in...
Consider an linear time invariant system whose impulse response is shown in the
Consider an linear time invariant system whose impulse response is shown in the figure below. If the input x(t) = u(t) then what will be the output at t=1.5 seconds ?
4. Let S be a linear, time-invariant, and causal system whose input x(t) and corresponding output...
4. Let S be a linear, time-invariant, and causal system whose input x(t) and corresponding output y(t) are shown below: r(t) Page 1 of 2 Please go to next page... y(t) ? (a) Find the impulse response function h(t) of ? (b) Find the output of S when its input is e*, t<0, t2, t20
Te signal sn2mie' s-is . power signal. It is input to a linear time invariant j4n...
Te signal sn2mie' s-is . power signal. It is input to a linear time invariant j4n n +1 x(t) = is a power signal. It is input to a linear time invariant system whose impulse response is ht) 40sinc(t/20). The corresponding output is ) (a) Find the power of ) (b) Express a(t) by its trigonometric Fourier Series (c) Find ut). (d) Find the power of x)
The following circuit consists of linear time invariant
components where R1 = 2,
R2 = 3,
C = 0.25F, and L = 1H. Let vs be the input voltage.
(a) Solve the differential equation that describes
vc(t). Hint: First, find the current
going through the parallel branch of R1–C. Then, write
the Kirchoff's Voltage Law for the main loop.
(b) Find vc(t) given that vs(t) = 2.5 V at
t = 0. Assume that vc(0-) = 1V and
iL(0-) =...
6. (15) Consider the following causal linear time-invariant (LTT) discrete-time filter with input in and output yn described by y[n] = x[n] – rn - 2 for n 20 . Is this a finite impulse response (FIR) or infinite impulse response (IIR) filter? Why? • What are the initial conditions and their values for this causal and linear time-invariant system? Why? • Draw the block diagram of the filter relating input x[n) and output y[n] • Derive a formula for...
Please dont use Laplace or Fourier
A linear time-invariant continuous-time system has the impulse response h(t) = (sin(t) + e-t) u(t) (a) Compute the step response s(t) for all 20. (b) Compute the output response y(t) for all t > 0 when the input is u(t)-(t-2) with no initial energy in the system.
For a continuous time linear time-invariant system, the
input-output relation is the following (x(t) the input, y(t)
the
output):
, where h(t) is the impulse response function of the
system.
Please explain why a signal like e/“* is always an eigenvector
of
this linear map for any w. Also, if ¥(w),X(w),and H(w) are
the
Fourier transforms of y(t),x(t),and h(t), respectively.
Please
derive in detail the relation between Y(w),X(w),and H(w),
which means to reproduce the proof of the basic convolution
property...
Question 1: (2 marks) Find the zero-input response yz(t) for a linear time-invariant (LTI) system described by the following differential equation: j(t) + 5y(t) + 6y(t) = f(t) + 2x(t) with the initial conditions yz (0) = 0 and jz (0) = 10. Question 2: (4 marks) The impulse response of an LTI system is given by: h(t) = 3e?'u(t) Find the zero-state response yzs (t) of the system for each the following input signals using convolution with direct integration....
Q8) Consider the following causal linear time-invariant (LTI) discrete-time filter with input x[n] and output y[n] described by bx[n-21- ax[n-3 for n 2 0, where a and b are real-valued positive coefficients. A) Is this a finite impulse response (FIR) or infinite impulse response (IIR) filter? Why? B) What are the initial conditions and their values? Why? C) Draw the block diagram of the filter relating input x[n] and output y[n] D) Derive a formula for the transfer function in...
4. Let S be a linear, time-invariant, and causal system whose input x(t) and corresponding output y(t) are shown below: r(t) Page 1 of 2 Please go to next page... y(t) ? (a) Find the impulse response function h(t) of ? (b) Find the output of S when its input is e*, t<0, t2, t20
Te signal sn2mie' s-is . power signal. It is input to a linear time invariant j4n n +1 x(t) = is a power signal. It is input to a linear time invariant system whose impulse response is ht) 40sinc(t/20). The corresponding output is ) (a) Find the power of ) (b) Express a(t) by its trigonometric Fourier Series (c) Find ut). (d) Find the power of x)
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