Why is Fourier space not adecuate for (theoretical) filters?

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As far as I have seen, almost all theoretical filter design occurs in Laplace or Z-space. Also, there is a pervasive connection to real life analog filters in the design. If one is just thinking in a mathematical theoretical thing (or something that could be implemented digitally), why wouldn't one filter signals in Fourier Space?

Why is, say, multiplying the Fourier Transform of a certain function by a unit step up - step down function, and then making the Inverse Transform of the resulting signal a "band pass filter"? Why should one use Butterworth or similar things to make a digital filter?

wpkzz

Posted 2020-09-15T21:08:49.047

Reputation: 101

1dsp.stackexchange.com might be a better place for this question. – audionuma – 2020-09-16T05:06:09.323

Okey, I shall repost it there. Thanks. – wpkzz – 2020-10-08T17:00:03.160

No answers