Signals and Systems — DU B. Sc. (Hons) Electronics Previous Year Question Papers

1.(a) Discuss the Eigen value and Eigen function in context with input and system . 1.(b) Determine whether a signal 5 is energy signal or power signal. 1.(c) Let x(t) be a signal with Nyquist rate . Determine the Nyquist rate for the signal , where x 1 . 1.(d) Write the Dirichlet conditions in context with Continuous time Fourier Series. 1.(e) Sketch the signal 2 1, where 3 1.(f) State Time Shifting property of continuous ‐time Fourier transform. 2.(a) Evaluate the output y(t) of the system whose impulse response is 3 and input 5 2.(b) Consider two LTI systems with unit impulse responses 2 2 and 1 3. Determine the unit impulse response equivalent of (i) Cascade configuration of and (ii) Parallel configuration and 3.(a) Consider continuous periodic signals whose Fourier series representation is as follows: ∑. Discuss whether, (i) is real or complex valued? (ii) is even or odd? 3.(b) A system is described by differential equation 2 2 . Find the transfer function of the system. Also sketch its magnitude response. 4.(a) Find the inverse transform of with ROC || 2, using contour integration method. 4.(b) Find the output of a causal system for unit step input . The transfer function of the system is given by . 5.(a) State Nyquist sampling theorem for low pass Band limited signals. Find the Nyquist rate for the signal 100 2 200. 5.(b) Write the transfer function of a Hilbert transformer. Also, determine the unit impulse response of Hilbert transformer. 6.(a) A Causal LTI system produce output for corresponding input . Then, determine the frequency response of the system. 6.(b) In a Signals and Systems class, Students of ECE‐A define the unit step signal as On the other hand, Student of ECE‐B define the unit step signal as (i) Comment on the applicability of both definitions of the unit step signal. (ii) Also, mention a relation between unit step signal , unit ramp signal , and Dirac delta function ,