Signal processing

[amp_mcq option1=”$${1 \over 3} < \left| z \right| < {1 \over 2}$$" option2="$$\left| z \right| > {1 \over 2}$$” option3=”$$\left| z \right| < {1 \over 3}$$" option4="$$2 < \left| z \right| < 3$$" correct="option3"]

Detailed SolutionThe ROC of z-transform of the discrete time sequence $$x\left( n \right) = {\left( {{1 \over 3}} \right)^n}u\left( n \right) – {\left( {{1 \over 2}} \right)^n}u\left( { – n – 1} \right)$$ is

Detailed SolutionThe Fourier series of a real periodic function has only P. Cosine terms if it is even Q. Sine terms if it is even R. Cosine terms if it is odd S. Sine terms if it is odd Which of the above statements are correct?

[amp_mcq option1=”$$\left| z \right| < {5 \over 6}$$" option2="$$\left| z \right| > {5 \over 6}$$” option3=”$${5 \over 6} < \left| z \right| < {6 \over 5}$$" option4="$${6 \over 5} < \left| z \right| < \infty $$" correct="option3"]

Detailed SolutionThe region of convergence of z-transform of the sequence $${\left( {{5 \over 6}} \right)^n}u\left( n \right) – {\left( {{6 \over 5}} \right)^n}u\left( { – n – 1} \right)$$ must be

Detailed SolutionThe impulse response of an LTI system can be obtained by

Detailed SolutionIf $$F\left( s \right) = L\left[ {f\left( t \right)} \right] = {{2\left( {s + 1} \right)} \over {{s^2} + 4s + 7}}$$ then the initial and final values of f(t) are respectively

Detailed SolutionThe inverse Laplace transform of the function $${{s + 5} \over {\left( {s + 1} \right)\left( {s + 3} \right)}}$$ is

Detailed SolutionThe impulse response and the excitation function of a linear time invariant causal system are shown in figure (a) and (b) respectively. The output of the system at t = 2 sec is equal to

Detailed SolutionThe z-transform of a signal is given by $$C\left( z \right) = {1 \over 4}{{{z^{ – 1}}\left( {1 – {z^{ – 4}}} \right)} \over {{{\left( {1 – {z^{ – 1}}} \right)}^2}}}.$$ Its final value is

[amp_mcq option1=”|z| > 1″ option2=”|z| < 1" option3="(Real part of z) > 0″ option4=”(Real part of z) < 0" correct="option2"]

Detailed SolutionThe region of convergence of the z-transform of a unit step function is

Detailed SolutionIncreased pulse-width in the flat-top sampling, leads to