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i got a system with transfer function given by:

$$H(\omega)=1-e^{-j\omega}$$ I already plot it, and that seems to be a periodic function with $$H(0)=0$$ $$H(\pi)=2$$ $$H(\infty)=1$$ is that enough to show that this is a FIR bandpass filter. thank you very much

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You can rewrite the transfer function as $$ H(\omega) = 2je^{-j\omega/2}\sin(\omega/2) $$ which gives $$|H(\omega)| = 2|\sin(\omega/2)| $$ I assume we're talking about a discrete-time system, so there is no frequency \$\omega=\infty\$. We're just considering the range \$\omega\in [0,\pi]\$. This means that the system is a highpass filter. It's magnitude response increases from $$|H(0)|=0$$ to $$|H(\pi)|=2.$$ Also note that \$H(0)\$ and \$H(\pi)\$ can be easily computed directly from the filter coefficients: $$H(0) = \sum_{k=0}^{n-1}h_k = 1 - 1 = 0$$ $$H(\pi) = \sum_{k=0}^{n-1}(-1)^kh_k = 1 - (-1) = 2$$

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