Signals and Systems A Practical Approach 2nd. Edition by D. Sundararajan | 9783031193767 | 3031193768 | Holooly

Analog and Digital Signals and Systems

Signals and Systems A Practical Approach

85 SOLVED PROBLEMS

Question: 12.9

Determine the observability of the system, described by A=[0 -1 2 3], C=[1 -1] ...

Verified Answer:

(sI − A) = s\left [ \begin{matrix} 1 & ...

Question: 12.8

Determine the controllability of the system, described by A=[0 -1 2 3], B=[0 1] ...

Verified Answer:

(sI − A) = s \left [ \begin{matrix} 1 &...

Question: 12.7

Find a closed-form expression for the state output q(t) of the system, described by A=[2 1 3 4], B=[1 0] using the frequency-domain method, with zero initial conditions and the input u(t), the unit-step function. ...

Verified Answer:

(sI − A) = s\left [ \begin{matrix} 1 & ...

Question: 11.6

Find a closed-form expression for the output y(n) of the system,described by the state-space model given in Example 11.1, using the frequencydomain method, with the initial conditions y(−1) = 2 and y(−2) = 3 and the input u(n), the unit-step function. ...

Verified Answer:

The initial state vector

q(0)= \left [ \beg...

Question: 11.9

Derive the state-space model of the system in Example 11.1 with the new state vector that is related to old state vector as q1(n) = 2q1(n) + q2(n) q2(n) = q1(n) – q2(n) Verify that the transfer function remains the same using either state-space model. ...

Verified Answer:

P={\left[\begin{array}{cc}{2}&{1}\\ {1}...

Question: 11.7

Find a closed-form expression for the impulse response of the system, described by the state-space model given in Example 11.1, using the frequency-domain method. ...

Verified Answer:

The transfer function of a system is given by [lat...

Question: 11.8

Find the zero-input, zero-state, transient, steady-state, and complete responses of the system governed by the difference equation y(n) = 2x(n) – x(n – 1) + 3x(n – 2) + 9/20y(n – 1) – 1/20y(n – 2) with the initial conditions y(-1) = 3 and y(-2) = 2 and the input x(n) = u(n), the unit-step function. ...

Verified Answer:

The corresponding state-space model is

A=\l...

Question: 12.4

Solve the problem of Example 12.2 using the frequency-domain method. ...

Verified Answer:

The initial state vector is

q(0^{-})=\left[...

Question: 12.6

Derive the state-space model of the system in Example 12.1 with the new state vector that is related to old state vector as q1(t) = q1(t) + 2q2(t) q2(t) = -3q1(t) + 4q2(t) Verify that the transfer function remains the same using either state-space model. ...

Verified Answer:

P=\left[{\begin{array}{r r}{1\,2}\\ {-3\,4}...

Question: 11.4

Find a closed-form expression for the output y(n) of the system, described by the state-space model given in Example 11.1, using the time-domain method, with the initial conditions y(-1) = 2 and y(-2) = 3 and the input u(n), the unit-step function. ...

Verified Answer:

The initial state vector was determined, from the ...

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