1. Assume the following LTI system where the input signal is an impulse train (i. e., $x(t) = \sum_{n=-\infty}^{\infty} \delta(t - nT_0)$). $x(t)$ $y(t)$ $h(t)$ $X(\omega)$ $Y(\omega)$ $H(\omega)$ d) Sketch the magnitude and phase spectra of the output if the system is a filter with $H(\omega) = \frac{1}{1 + j\omega}$.
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The Fourier Transform of an impulse train is another impulse train, so we have X(w) = Σn=-∞ δ(w - nWo), where Wo is the fundamental frequency of the impulse train. Show more…
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