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The magnitude function |H(ω)| can be zero at some frequencies, but it cannot be zero over any finite band of frequencies.

The magnitude function |H(ω)| can be zero at some frequencies, but it cannot be zero over any finite band of frequencies. Correct Answer True

One important conclusion that we made from the Paley-Wiener theorem is that the magnitude function |H(ω)| can be zero at some frequencies, but it cannot be zero over any finite band of frequencies, since the integral then becomes infinite. Consequently, any ideal filter is non-causal.

Related Questions

Which of the following statements are correct? 1. A lowpass filter passes low frequencies and stops high frequencies. 2. A highpass filter passes high frequencies and rejects low frequencies 3. A bandpass filter passes frequencies within a frequency band and attenuates frequencies outside the band. 4. A bandstop filter passes frequencies within the band and blocks/attenuates frequencies outside a frequency band.
The magnitude |H(ω)| cannot be constant in any finite range of frequencies and the transition from pass-band to stop-band cannot be infinitely sharp.
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