Filter corner frequency

Cut off / corner frequency.

Thinking of a DAC, spiting, say 2000 values/sec and the associated LPF at the output:

According to what I've read up to now, the filter should have a (-3dB) cut off frequency of 2KHz.

My question: why from the beginning I accept to design with an atenuated output since my interest is to have the signal restored with the right level, that is with 0dB attenuation.

In other words, shouldn't I design for a corner frequency where my highest signal of interest is not attenuated at all?

I do not discard misunderstand things or plainly ignoring many.

It is a complicated subject. Math is here. Requirements for anti-alias filtering is here. Look particularly at Oversampling

A filter is usually needed with an ADC to prevent aliasing of out-of-band noise. It's no so critical with a DAC since aliasing is not a consideration and their noise level is usually just the quantizing noise of 1 LSB.

For 2000 values/sec output from a DAC the highest sine-wave frequency you can reproduce is 1kHz. A 2KHz roll-off filter will have only a slight effect on this 1KHz signal amplitude. But, depending upon your application, you many not need a filter.

If the DAC uses zero-order hold (a staircase-type output) you need the filter to include 1/sinc() function (analog or in software) to cancel the effects of the zero-order hold. The 1/sinc will amplify higher frequencies.

Here is the practical theory: Digital-to-Analog Conversion

One easy option is to use oversampling.. then you can pretty much ignore the effect of zero-order hold.