Question

Consider two real valued signals, x(t) band-limited to [- 500 Hz, 500 Hz] and y(t) band-limited to [-1 kHz, 1kHz]. For z(t) = x(t) y(t), the Nyquist sampling frequency (in kHz) is

• A. 3

Answer 1

The correct option is A 3
Multiplication in time domain = convolution in frequency domain
$x_1\left(t\right).x_2\left(t\right)\leftrightarrow X_1\left(\omega {)}^{\ast }{X}_2\right(\omega )$

So, highest frequency component contained by the convolved signal z(t)= 1500 Hz

$\therefore \text{Nyquist rate= 2 x 1500=3000 Hz= 3 kHz}$