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So let's say i have this frequency response of a digital filter:

My question is how can i classify this type of filter ( low pass, high pass,...)?

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It's a bandpass filter whose frequency response suppresses the low and high frequencies (with its zeros at $\omega = 0$ and $\omega = \pi$) and amplifies the band in between.

The bandwidth of the filter can be defined by reference to $-3_{dB}$ points, which would give you approximately $W_{-3dB} \approx 0.2\pi$, with a center frequency of $\omega_c = 0.5\pi$.

I would however not consider this bandwidth to be a descriptive one.

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  • $\begingroup$ So basically the high frequencies are $\omega =\pi$ and the low frequencies are $\omega=0$ or $\omega=2\pi$ ? $\endgroup$ – J. Barbosa May 31 '16 at 19:02
  • $\begingroup$ in the discrete time domain, low frequencies are around $\omega = 2\pi k$ and high frequencies are around $\omega = \pi + 2\pi k$ for $k \in Z$ $\endgroup$ – Fat32 May 31 '16 at 19:06

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