The sum of two signals e1 = 3 sin (4π × 103t) and e1=

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The sum of two signals e₁ = 3 sin (4π × 10³t) and e₁= 5 sin(4π × 256t) is sampled at 1024 Hz. The sampled signal is passed through a low pass filter with cut off at 2048 Hz. The output of the filter will contain components at—

1. 256 Hz and 10³ Hz
2. 256 Hz and 1024 Hz
3. 256 Hz Only
4. 1024 Hz Only

Correct Option: C

Given that
e₁= 3 sin(4π × 10³t), f_m1 = 2 × 10³ Hz
e₂ = 5 sin(4 π × 256t), f_m2 = 256 Hz
sampling frequency, f_s = 1024 Hz
cut-off frequency of LPF, ω_c = 2048 Hz
Since for proper reconstruction of signal f_s ≥ 2f_m
For f_m1, fs less than 2f_m1 so it will pass through the LPF,
while for f_m2, f_s > 2f_m2 [i.e. 1024 > (2 × 256)]
So the output of the filter will contain 256 Hz component only.