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The output $y(t)$ of a linear time invariant system is related to its input $x(t)$ by the following equation:

$y(t)=0.5 x\left(t-t_{d}+\mathrm{T}\right)+x\left(t-t_{d}\right)+0.5 x\left(t-t_{d}-\mathrm{T}\right)$.

The filter transfer function $\mathrm{H}(\omega)$ of such a system is given by

1. $(1+\cos \omega \mathrm{T}) e^{-j \omega t_d}$
2. $(1+0.5 \cos \omega \mathrm{T}) e^{-j \omega t_d}$
3. $(1+\cos \omega \mathrm{T}) e^{-j \omega t_d}$
4. $(1-0.5 \cos \omega \mathrm{T}) e^{-j \omega t_d}$