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I want to put a low pass filter infront of my ADC. The ADC's sampling rate is 10MHz. I want to sample a signal with a maximum frequency of 50 kHz. So my cutoff frequency for this low pass should be slightly higher than 50 kHz, right?

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Correct and the closer to 50 kHz (but above) the easier it is to make an effective anti-alias filter. But no need to go crazy about it. A 2nd order low-pass filter set at 100 kHz will provide 40 dB attenuation at 1 MHz and 80 dB attenuation at 10 MHz and, those aliased artefacts that might sneak through could easily become lower in amplitude than the resolution of your ADC.

You need to concern yourself with the parts of the spectrum that pose a threat and if there's nothing expected above 5 MHz (half the sample rate) then why bother? But if there are things happening above 5 MHz, what amplitude do they have? If they are already 40 dB down in amplitude then the filter has an easier life reducing them to an amplitude below where they might cause problems.

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  • \$\begingroup\$ Ok thanks let say I have a square wave of 50 kHz. I thought about using a low pass filter with a cut off frequency of 5MHz (100*50kHz). Or should I go lower like 1MHz or even 500 kHz? \$\endgroup\$ Nov 22, 2020 at 15:48
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    \$\begingroup\$ Then it isn't a square wave any more. A square wave is composed of a fundamental and odd harmonics so, if the fundamental is 50 kHz then there are significant "wanted" harmonics at 150 kHz, 250 kHz, 350 kHz etc.. Of course, if you don't care about preserving those harmonics then you can have the low-pass filter set just above 50 kHz but, what you then get in the digital domain is neither a sinewave nor a square wave but something halfway between. \$\endgroup\$
    – Andy aka
    Nov 22, 2020 at 15:50

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