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h[n]=(-1)[itex]^{n}[/itex][itex]\frac{sin(\frac{\pi}{2}n}{sin(\pi n}[/itex]

useful properties:

x[n]y[n] --> X[Ω]*Y[Ω]

[itex]\frac{sin(\frac{\pi}{2}n}{sin(\pi n}[/itex] --> rect[[itex]\frac{2Ω}{\pi}[/itex]

I have no clue how to deal with the (-1)[itex]^{n}[\itex] the DTFT of that doesn't converge. . .

any help would be appreciated