Hi,
"The output filter smoothens (sic) the output signal and removes the high-frequency PWM carrier signal"
I don't understand this. What is the carrier signal that's being removed? I thought the carrier was simply the period between two successive duty cycles. How would that get removed?
It's the PWM sample frequency that's being removed (like in any form of digital audio).
Proper digital audio use a PWM frequency of at least 300kHz, to represent 0..20kHz faithfully.
I have to disagree a bit with the datasheet though, as a steep cut off of anything above 3kHz (which a 6kHz sample frequency will do) is a bit low and while there are language differences, it won't work well for Danish (and will probably be a challenge in most languages).
I have done a wee bit of research in how low pass filtering of voice elements will change them into sounding like other sounds and the only reason that a 3kHz wall might work is because we use context and other clues to guess the words.
For a more understandable speech, you need to keep at least up to 6kHz (and for precision, count on 8..16kHz).