x(t,f)=int(δ(t_1-t_0)*(a/π)^(1/4)*exp(-(a/2)(t_1-t)^2)*exp(-i2πft_1) dt_1) (from -∞ to +∞) I am asked to solve this integral, which is the short-time Fourier transform. I would appreciate your help. Thank you!
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$\int_{-\infty}^{\infty} \delta(t- t_1)f(t)dt= f(t_1)$ for any function, f.