That's easy to know with a transversal filter. For a typical IIR, the transient decays exponentially and the time for it to fade out depends on (among other conditions) the number of bits used. (You know that, but whitehat09 might not.)
A Fixed-Point Introduction by Example
Handling Spectral Inversion in Baseband Processing
Understanding the Phasing Method of Single Sideband Modulation
An Interesting Fourier Transform 1/f Noise
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