I read that foam windscreens are effective against breathing. However, what it does is just filtering. Shouldn't it be possible to do the same thing with a digital filter? It should be as easy as recording the frequency response of the foam.
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The job of a foam screen is to attenuate the velocity of wind before it hits the microphone. If you don't reduce the wind, then the mic will be overdriven, and you will get a badly distorted signal. You can't just filter that out after the fact.
This is also why an analog compressor or a digital compressor with a lot of headroom is a good idea between your mic and recording device. The compressor can attenuate hot signals while mostly preserving their shape.
It may help to think of the flow of information in stages:
[Sound in Free Air] -> [Microphone] -> [Cable] -> [Audio Interface] -> [Computer]
At the Sound in Free Air stage you have effectively infinite variability in sound pressure. A butterfly can flap its wings, a jackhammer can drill into the pavement, and a hurricane-force wind can blow.
The Microphone is really any transducer that takes sound pressure and turns it into an electrical signal. Theoretically, a perfect transducer could be built that can handle everything from the butterfly to the hurricane. Practically, it is too hard and we are familiar with equipment that is tuned for specific sound pressure levels and frequency ranges. Different microphones are preferred for vocals, various kinds of instruments and even individual drums in a drum kit. Our microphones are imperfect, but that's where part of their charm comes from. If we overload the microphone, then we lose signal detail. That lost detail can never be perfectly recovered. A nice sine wave distorts into something like a square wave. But if you look at a square wave, there is no way to know if it was once a perfect sine wave or had additional harmonics.
The same problem is repeated at the audio interface. If the signal is too hot coming off your microphone, then you have another opportunity to distort it and lose information. Maybe you want the distortion effect, so you turn up your preamp or use some distortion effects. You still can't get the original signal back because the distortion process destroys information that was originally encoded in the signal.
Compression and the additional headroom that a 24-bit or 32-bit ADC give you will help deal with a hot signal coming off your mic (or your synthesizer, or guitar, or ...), but it can't help you if the sound you are trying to record is already overloading your microphone.
So you put a wind screen on the mic to keep the wind from overloading your mic and ruining your recording. Good windscreens are expensive - the foam ones aren't all that effective. But no wind screen is perfect. Be careful in high wind!