# Minimum sample frequency that allows reconstruction of information signal but VIOLATES Nyquist?

Say in the frequency spectrum, you have an information signal between (-100, 100) Hz, and a noise signal between (-700, -500) and between (500, 700) Hz. What is the minimum possible sample frequency that allows reconstruction of the information signal without distortion? Any ideal filter can be used.

At first I thought Fs = 400 Hz. But when plotting this out in the frequency domain, I believe aliasing will occur if the noise signal has non-zero components at say -700 or -500 Hz. When Fs = 800 Hz, the same phenomen occurs. But When Fs = 800 + 0.00000001 (some really small number), the potential for aliasing is zero if an ideal low-pass filter is used. Am I right in my reasoning?

• Re-read the problem statement! "Any ideal filter can be used" <--- there is no noise, because it can completely be filtered away. – Marcus Müller Feb 20 '19 at 16:02
• Note that in this case you won't be able to sample at less than 200 Hz, so there's no violation of Nyquist's theorem, which only states sufficient conditions anyway. – MBaz Feb 20 '19 at 16:51