A cascade of 3 linear time invariant system is causal and unstable. From this, we conclude that

1.  Each system in the cascade is individual of causal and unstable

2.  At least one system is unstable and at least one system is causal

3.  at least one system is causal and all the systems are unstable

4.  The majorities are unstable and the majorities are causal.

4

At least one system is unstable and at least one system is causal

Explanation :
No Explanation available for this question

The Fourier series coefficients, of a period signal x(t), expressed as are given by =-j1;0.5+j0.2; a0=j2; a2=0.5-j0.2; a2=2+j1; and ak =0; for |k|>2. Which of the following is true

1.  x(t) has finite energy because only finial many coefficients are non-zero

2.  x(t) has average value because it is periodic

3.  The imaginary part of x(t) is constant

4.  The real part of x (t) is even.

4

x(t) has finite energy because only finial many coefficients are non-zero

Explanation :
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The z-transform of a signal x[n] is given by 4z-3+3z-1+2-6z2+2z3 It is applied to a system with a transfer function H (z) =3z-1-2. Let the output be y (n). Which of the following is true

1.  y(n) is non-causal with finite support

2.  y(n) is causal with infinite support

3.  y(n)=0;|n|>3

4.  Re[Y(z)]z=ejθ=-Re[Y(z)]z=ejθ

4

Explanation :
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The period of the signal is

1.  0.4 Πs

2.  0.8 Πs

3.  1.25 Πs

4.  2.5 Πs.

4

2.5 Πs.

Explanation :
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The system represented by the input-output relationship t>0 is

1.  Linear and causal

2.  Linear but not causal

3.  Causal but not linear

4.  Neither linear nor causal.

4

Linear but not causal

Explanation :
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The second harmonic component of the periodic wave form given in the figure has an amplitude of

1.  0

2.  1

3.

4.

4

0

Explanation :
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At t=0, the function has

1.  A minimum

2.  A discontinuity

3.  A point of inflection

4.  A maximum.

4

A maximum.

Explanation :
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X(t) is a positive rectangular pulse from t=-1 to t=+1 with unit height as shown in the figure. The value of {where X() is the Fourier transform of x(t) } is

1.  2.

2.  2Π

3.  4

4.  4Π.

4

4Π.

Explanation :
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Given the finite length input x[n] and the corresponding finite length output y[n] of an LTI system as shown below. The impulse response h[n] of the system is

1.  h[n]={1, 0, 0, 1}

2.  h[n]={1, 0, 1}

3.  h[n]={1, 1, 1, 1}

4.  h[n]={1, 1, 1}

4

Explanation :
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1.  g(t)=f(2t-3)

2.

3.

4.

4