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

Question

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)\$

Answer 1

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.