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I have the following integration:

[tex]\int_{-\infty}^{\infty}e^{-j2\pi f_ct[a_p-a_q]}g(t[1+a_p]-kT_s-\tau_p)g(t[1+a_q]-mT_s-\tau_q)\,dt[/tex]

where g(t) is 1 in the interval [0,Ts]. This means that the integration has value when both function g(t[1+a_p]-kT_s-\tau_p) and g(t[1+a_q]-mT_s-\tau_q) are 1. Both are 1 when:

[tex]0\leq t[1+a_p]-kT_s-\tau_p\leq T_s[/tex]

and

[tex]0\leq t[1+a_q]-mT_s-\tau_q\leq T_s[/tex]

Which implies that both are 1 when:

[tex]t=\frac{(\tau_p-\tau_q)+(k-m)T_s}{a_p-a_q}[/tex]

But the integration over a point is zero, which can be the answer of the physical problem I have in hand. Where did I go wrong in the process?

Thanks.

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# What is mathematically wrong with this integration?

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