Signals and systems electrical engineering miscellaneous Difficult Questions and Answers

Signals and systems electrical engineering miscellaneous

Given a sequence x[n], to generate the sequence y[n] = x[3 – 4n].Which one of the following procedures would be correct?

1. First delay x[n] by 3 sample to generate z₁[n], then pick every 4th smmple of z₁[n] to generate z₂[n], and then finally time reverse z₂[n] to obtain y[n]
1. First advancex[n] by 3 samples to generate z₁[n], then pick every 4th sample of z₁[n] to generate z₂[n], and then finally time reverse z₂[n] to obtain y[n]
1. First pick every fourth sample of x[n] to generate v₁[n], time-reverse v₁[n] to obtain v₂[n], and finally advance v₂[n] by 3 sample to obtain y[n]
1. First pick every fourth sample of x[n] to generate v₁[n], time-reverse v₁[n] to obtain v₂[n], and finally delay v₂[n] by 3 samples to obtain y[n]

The impulse response of a causal linear timeinvariant system is given as h(t).
Now consider the following two statements:
Statement I: Principle of superposition holds
Statement II: h(t) = 0 for t < 0 Which one of the following statements is correct?

1. Statement (I) is correct and Statement (II) is wrong
1. Statement (II) is correct and Statement (I) is wrong
1. Both Statement (I) and Statement (II) are wrong
1. Both Statement (I) and Statement (II) are correct

A signal e^-αt sin(ωt) is the input to a Linear Time Invariant system. Given K and φ are constants, the output of the system will be of the form Ke^-βt sin(vt + φ), where

1. β need not be equal to α but v equal to ω
1. v need not be equal to ω but β equal to α
1. β equal to α and v equal to ω
1. β need not be equal to α and v need not be equal to ω

The Fourier Series coefficients, of a periodic signal x(t),expressed as

are given by
a_–2 = – j1; a_–2 = 0.5 + j0.2; a_o = j2; a₁ = 0.5 – j0.2; a₂= 2+ j1; and a_k = 0; for |k| > 2.
Which of the following is true?

1. x(t) has finite energy because only finitely many coefficients are non-zero
1. x(t) has zero average value because it is periodic
1. The imaginary part of x(t) is constant
1. The real part of x(t) x(t) is even

A cascade of 3 Liner Time Invariant systems is causal and unstable. From this, we conclude that

1. each system in the cascade is individually causal and unstable
1. at least one system is unstable and at least one system is causal
1. at least one system is causal and all systems are unstable
1. the majority are unstable and the majority are causal