Question

Formula for Fourier sine transform of f(t) is given by
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Answer 1

Step-by-step explanation:

the fourier transform of a translation by real number a is given by f (f (t-a) ) (x) = e- i ʎaf(f)(ʎ).

Answer 2

Answer:$f(t)=\sqrt{\frac{2}{\pi } }\int\limits^\infty_0 {fs}(w) sin wt\, dw$

Step-by-step explanation:

Any periodic function () having period T satisfying the Dirichlet condition can be expressed by the following series

f(t)=$\frac{a_{0} }{2} +\int\limits^\infty_n(a_{n}cosnwt+b_{n} sinnwt)$

As the Fourier sine transform

As if f(t) is odd function f(-t)=-f(t)

As then, Fourier sine transform is given by

$F_{s} (w)=\sqrt{\frac{2}{\pi}} \int\limits^ \infty_b {f(t)sin wt} \, dt$

As the inverse fourier sine transform is given by

$f(t)=\sqrt{\frac{2}{\pi } }\int\limits^\infty_0 {fs}(w) sin wt\, dw$

#SPJ3