# GATE Papers >> EEE >> 2019 >> Question No 16

Question No. 16

A system transfer function is $H(s)=\frac{a_1s^2+b_1s+c_1}{a_2s^2+b_2s+c_2}$ . If $a_1=b_1=0$, and all other coefficients are positive, the transfer function represents a

##### Answer : (A) low pass filter

Solution of Question No 16 of GATE 2019 EEE Paper

It is given that

$\mathrm H(\mathrm s)=\frac{{\mathrm a}_1\mathrm s^2+{\mathrm b}_1\mathrm s+{\mathrm c}_1}{{\mathrm a}_2\mathrm s^2+{\mathrm b}_2\mathrm s+{\mathrm c}_2}$

If a1 = b1 = 0, then H(s) becomes

$\begin{array}{l}\mathrm H(\mathrm s)=\frac{{\mathrm c}_1}{{\mathrm a}_2\mathrm s^2+{\mathrm b}_2\mathrm s+{\mathrm c}_2}\\\mathrm H(0)=\frac{{\mathrm c}_1}{{\mathrm c}_2}\left(\mathrm i.\mathrm e.,\;\mathrm{as}\;\mathrm{low}\;\mathrm{frequency}\;\mathrm s\rightarrow0\Rightarrow\mathrm\omega\rightarrow0\right)\\\mathrm H(\infty)=0\left(\mathrm i.\mathrm e.,\;\mathrm{as}\;\mathrm{high}\;\mathrm{frequency}\;\mathrm s\rightarrow\infty\Rightarrow\mathrm\omega\rightarrow\infty\right)\end{array}$

So the system passes low frequency and blocks high frequency. So it represents a low pass filter.

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