# In designing a digital filter by impulse invariance method why is the scaling factor irrelevant?

I've come across a few examples that the scaling factor T in the eqn below can be arbitrarily chosen as unity. How is that possible? doesn't T have something to do with the Nyquist sampling rate?

$H(e^{jw})$ = $1/T$ * $\Sigma H_a(jw/T - j2k\pi/T)$

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In the abstracted world of digital filters, a scaling factor is a simple multiplication for a constant, so it doesn't affect the complexity of the filter:

While in certain cases the scaling coefficient can be used before a filter to avoid overflow during the signal manipulation, it doesn't affect the filtering operation since it multiplies equally each sample.

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