The GATE Grind

GATE 2020 EE – Question 16

Signals and Systems · Representation of continuous and discrete time signals, shifting and scaling properties · 1 mark · Multiple choice

$x_R$ and $x_A$ are, respectively, the rms and average values of $x(t)=x(t-T)$, and similarly, $y_R$ and $y_A$ are, respectively, the rms and average values of $y(t)=kx(t)$. $k,T$ are independent of $t$. Which of the following is true?

  1. $y_A=kx_A;\ y_R=kx_R$
  2. $y_A=kx_A;\ y_R\ne kx_R$
  3. $y_A\ne kx_A;\ y_R=kx_R$
  4. $y_A\ne kx_A;\ y_R\ne kx_R$

Practise this question in The GATE Grind →

Show answer and explanation

Correct answer: (A) $y_A=kx_A;\ y_R=kx_R$

Explanation

Averaging and squaring are applied to the scaled signal, so $y_A=\frac1T\int kx\,dt=kx_A$ and $y_R=\sqrt{\frac1T\int k^2x^2dt}=kx_R$ (taking $k>0$).