Test: State Space System Analysis - Electronics and Communication Engineering (ECE) MCQ

Explanation: Although the state space or the internal description of the system still involves a relationship between the input and output signals, it also involves an additional set of variables, called State variables.

Explanation: The state variables provide information about all the internal signals in the system. As a result, the state-space description provides a more detailed description of the system than the input-output description.

Explanation: We define the state of a system at time n0 as the amount of information that must be provided at time n0, which, together with the input signal x(n) for n≥n0 determines output signal for n≥n0.

Explanation: According to the definition of state of a system, the system consists of two components called memory component and memory less component.

Explanation: The transpose of the matrix F is obtained by interchanging its rows and columns, and it is denoted by FT. The system thus obtained is known as Transposed system.

Explanation: If h(n) is the impulse response of the single input-single output system, and h1(n) is the impulse response of the transposed system, then we know that h(n)=h1(n). Thus, a single input-single output system and its transpose have identical impulse responses and hence the same input-output relationship.

Explanation: A closed form solution of the state space equations is easily obtained when the system matrix F is diagonal. Hence, by finding a matrix P so that F¹=PFP^-1 is diagonal, the solution of the state equations is simplified considerably.

Explanation: A number λ is an Eigen value of F and a nonzero vector U is the associated Eigen vector if
FU= λU
Thus, we obtain (F- λI)U=0.

Explanation: We know that (F- λI)U=0
The above equation has a nonzero solution U if the matrix F- λI is singular, which is the case if the determinant of (F- λI) is zero. That is, |F- λI|=0.
This determinant yields the characteristic polynomial of the matrix F.

Explanation: The parallel form realization is also known as normal form representation, because the matrix F is diagonal, and hence the state variables are uncoupled.