$A s i g n a l x_{t} i s g i v e n a s, a n d a n o t h e r s i g n a l x_{2} i s g i v e n a s, B o t h t h e s i g n a l a r e s a m p l e d a t 1000 s a m p l e s / s e c, t h e n t h e r a t i o o f t i m e p e r i o d o f x_{2} (t) t o x_{1} (t) a f t e r s a m p l i n g i s . . . . . x_{1} (t) = 4 s i n (10 π t) x_{2} = 16 c o s (\frac{π}{2} t + 60^{\circ})$
20

Open in App

Solution

The correct option is A 20
$G i v e n, x_{1} (t) = 4 s i n (10 π t) s a m p l i n g f r e q u e n c y, x_{1} (t) = x_{1} (n T_{s}) = 4 s i n (10 π (n T)) = 4 s i n (10 π \frac{n}{1000}) x_{1} (n T_{s}) = 4 s i n (\frac{π}{100} n) a f t e r s a m p l i n g, x_{2} (t) = x_{2} (n T_{s}) = 16 c o s (\frac{π}{2} (n T_{s} + 60^{\circ}) = 16 c o s (\frac{π}{2} \frac{n}{1000} + 60^{\circ}) x_{2} [n T_{3}] = 16 c o s (\frac{π}{2000} n + 60^{\circ}) t i m e p e r i o d o f x_{1} (n T_{s}) i s N_{1} \frac{ω}{2 π} = \frac{m}{N_{1}} \frac{π / 100}{2 π} = \frac{m}{N_{1}} \Rightarrow N_{1} = 200 T i m e p e r i o d o f x_{2} [n T_{s}] i s N_{2}, \frac{ω}{2 π} = \frac{m}{N_{1}} \Rightarrow N_{1} = 200 t i m e p e r i o d o f x_{2} [n T_{s}] i s N_{2}, \frac{ω}{2 π} = \frac{m}{N_{2}} \frac{π / 2000}{2 π} = \frac{m}{N_{2}} = N_{2} = 4000 \frac{N_{2}}{N_{1}} = \frac{4000}{200} = 20$

Suggest Corrections

Similar questions

x_{1} (t) a n d x_{2} (t)

x_{1} (t) = 6 s i n c (100 t) c o s (200 t) a n d x_{2} (t) = 10 s i n c^{2} (100 t)

N_{1}

N_{2}

\frac{N_{1}}{N_{2}}

x (t) = s i n c (200 t) s i n c^{2} (1000 t)

s a m p l e / s e c .

(50 π t)

t_{s} = 0.025

x_{1} (t)

x_{2} (t) = - x_{1} (t) r e c t (\frac{- t + 1}{2}) ?

Join BYJU'S Learning Program