List of practice Questions

If x(t) $\leftrightarrow$ X($\omega$), then FT of tx(t) is:

The Fourier transform of a real valued time signal has _ _ _ _ .

In FFT computation, reducing complexity from $O(N^2)$ to $O(N \log_2 N)$ relies fundamentally on _______.

What is the Fourier Transform of a Gaussian function $e^{-t^2}$ ?

What is the primary difference between CTFT and DTFT?

Let \( X(\omega) \) be the Fourier transform of the signal
\( x(t) = e^{-4t}\cos(t), \; -\infty < t < \infty \).

The value of the derivative of \( X(\omega) \) at \( \omega = 0 \) is _____________
(rounded off to 1 decimal place).