Consider a continuous time LTI system, whose frequency response is
$H (j ω) = {\begin{matrix} 1, & | ω | \leq 200 0, & o t h e r w i s e \end{matrix}$

When the input to this system is a signal x(t) with fundamental period $T = \frac{π}{6} a n d a_{K}$ is fourier series coefficient of output. For $K \geq P$ it is guaranteed that $a_{K} = 0$ then the value of P is _________
17

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Solution

The correct option is A 17
$ω_{0} = \frac{2 π}{π / 6} \Rightarrow 12 r a d / s e c$

Highest frequency allowed by the filter
$= \frac{200}{12} = 16.667 = 16$

$∴ a_{K} = 0; K \geq 17$

$∴ P = 17$

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Consider a continuous time LTI system, whose frequency response is H(jω)={1,|ω|≤2000,otherwise When the input to this system is a signal x(t) with fundamental period T=π6 and aK is fourier series coefficient of output. For K≥P it is guaranteed that aK=0 then the value of P is _________17

The correct option is A 17ω0=2ππ/6⇒12 rad/sec Highest frequency allowed by the filter =20012=16.667=16 ∴ aK=0;K≥17 ∴ P=17

The correct option is A 17
$ω_{0} = \frac{2 π}{π / 6} \Rightarrow 12 r a d / s e c$

Highest frequency allowed by the filter
$= \frac{200}{12} = 16.667 = 16$

$∴ a_{K} = 0; K \geq 17$

$∴ P = 17$