MATLAB: Am I unable to find the Fourier transform of a SINC function in Symbolic Math Toolbox 5.3 (R2009b)

cosSymbolic Math Toolbox

When I execute
syms t
fourier(sin(t)/t)
Symbolic Math Toolbox returns
 ans =
 transform::fourier(sin(t)/t, t, -w)
This Fourier transform should have a closed-form expression.

Best Answer

This enhancement has been incorporated in Release 2011a (R2011a). For previous product releases, read below for any possible workarounds:
This is a limitation in Symbolic Math Toolbox.
As a workaround, express the SIN function as the sum of complex exponentials in order to obtain the closed-form expression:
syms t
fourier((exp(j*t) - exp(-j*t))/(2*j*t))
 ans =
 (pi*(2*heaviside(1 - w) - 1))/2 - (pi*(2*heaviside(- w - 1) - 1))/2
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