added 17 characters in body
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Eugene
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The specific chapter about this is here - Sampling Theory
Unlike what I read anywhere else, it defines Shah as: $$Ш_T(x)=T\sum\nolimits_i{\delta{(x-Ti)}}$$ Elsewhere it's always simply: $$s_T{(x)}=\sum\nolimits_i{\delta{(x-Ti)}}$$ 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 to understand? Why is the difference?

I haven't been doing maths for years, and even back in my school days, I don't think I was a good student, so please be gentle.

The specific chapter about this is here - Sampling Theory
Unlike what I read anywhere else, it defines Shah as: $$Ш_T(x)=T\sum\nolimits_i{\delta{(x-Ti)}}$$ Elsewhere it's always simply: $$s_T{(x)}=\sum\nolimits_i{\delta{(x-Ti)}}$$ 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.
Can someone work out the maths for me to understand?

I haven't been doing maths for years, and even back in my school days, I don't think I was a good student, so please be gentle.

The specific chapter about this is here - Sampling Theory
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?

I haven't been doing maths for years, and even back in my school days, I don't think I was a good student, so please be gentle.

Source Link
Eugene
  • 111
  • 2

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

The specific chapter about this is here - Sampling Theory
Unlike what I read anywhere else, it defines Shah as: $$Ш_T(x)=T\sum\nolimits_i{\delta{(x-Ti)}}$$ Elsewhere it's always simply: $$s_T{(x)}=\sum\nolimits_i{\delta{(x-Ti)}}$$ 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.
Can someone work out the maths for me to understand?

I haven't been doing maths for years, and even back in my school days, I don't think I was a good student, so please be gentle.