1
GATE ECE 1997
Subjective
+5
-0
In Fig. 1, a linear time invariant discrete system is shown. Blocks labeled D represent unit delay elements. For $$n\, < 0,$$ you may assume that $$x\left( n \right),$$ $${y_1}\left( n \right),\,\,{y_2}\left( n \right)$$ are all zero.

(a) Find the expression for $${y_1}\left( n \right)$$ and $${y_2}\left( n \right)$$ in terms of $$x\left( n \right).$$
(b) Find the transfer function $${y_2}\left( z \right)/X\left( z \right)$$ in the $$z$$-domain.
(c) If $$x\left( n \right) = 1$$ at $$n = 0$$ or $$x\left( n \right) = 0$$ otherwise
Find $${y_2}\left( n \right).$$
2
GATE ECE 1996
Subjective
+5
-0
In the linear time-invariant system shown in Fig. 1, blocks labeled D represent unit delay elements. Find the expression for $$y\left( n \right),$$ and also the transfer function $${{Y\left( z \right)} \over {X\left( z \right)}}$$ in the $$z$$-domain.
3
GATE ECE 1996
Subjective
+5
-0
A system having a unit impulse response $$h\left( n \right)$$ = $$u\left( n \right)$$ is excited by a signal $$x\left( n \right)$$ $$ = \,{\alpha ^n}\,\,u\left( n \right).\,$$ Determine the output $$y\left( n \right)$$
Questions Asked from Discrete Time Linear Time Invariant Systems (Marks 5)
Number in Brackets after Paper Indicates No. of Questions
GATE ECE Subjects
Network Theory
Control Systems
Electronic Devices and VLSI
Analog Circuits
Digital Circuits
Microprocessors
Signals and Systems
Representation of Continuous Time Signal Fourier Series
Fourier Transform
Continuous Time Signal Laplace Transform
Discrete Time Signal Fourier Series Fourier Transform
Discrete Fourier Transform and Fast Fourier Transform
Discrete Time Signal Z Transform
Continuous Time Linear Invariant System
Discrete Time Linear Time Invariant Systems
Transmission of Signal Through Continuous Time LTI Systems
Sampling
Transmission of Signal Through Discrete Time Lti Systems
Miscellaneous
Communications
Electromagnetics
General Aptitude