# Why is there a T factor in the definition of Shah given in Matt Pharr's Physically Based Rendering?

Unlike what I read anywhere else, it defines Shah as: $$Ш_T(x)=T\sum\nolimits_i{\delta{(x-Ti)}}$$ And the T is still present in the reconstructed function: $$f\tilde(x)=T\sum\limits_{i=-\infty}^\infty{f(iT)r(x-iT)}$$ where r(x) is a reconstruction filter.
Everywhere else I can find gives: $$s_T{(x)}=\sum\nolimits_i{\delta{(x-Ti)}}$$ Can someone work out the maths for me? Why is the difference?
• Why is the difference? - they're just using a different definition with a scaling factor, it shouldn't really matter. Oct 26 '20 at 17:10
• It doesn't change anything if you have $T$ and then unscale it. It could be that they wanted a specific relationship to the Fourier transform. Similar to how one would choose different scaling factors for the DFT, e.g. to make it unitary. Oct 27 '20 at 7:17