GATE ECE 2019 Paper 1 — page 18

Questions 52–54 of 65. Imported answers require review unless explicitly marked reviewed.

Consider a unity feedback system, as in the figure shown, with an integral compensator

and open-loop transfer function

, where

. The positive value of

for which there are exactly two poles of the unity feedback system on the

axis is equal to ______ (rounded off to two decimal places).

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Consider the homogeneous ordinary differential equation

, with

as a general solution. Given that

and

, the value of

, rounded off to two decimal places, is ______.

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Let

be a length-7 discrete-time finite impulse response filter, given by

, and

is zero for

. A length-3 finite impulse response approximation

has to be obtained such that

is minimized, where

and

are the discrete-time Fourier transforms of

and

, respectively. For the filter that minimizes

, the value of

, rounded off to 2 decimal places, is ______.

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2019 · Paper 1