For the R-L circuit shown in Fig, the input voltage. v_i(t) = u (t) The current i(t) is

The equivalent inductance measured between the terminals 1 and 2 for the circuit shown in figure, is

Let x(t) and y(t) (with Fourier transforms X(f) and Y(f) respectively) be related as shown in Fig.(1) & (2).

Then Y(f) is

A 1 kHz sinusoidal signal is ideally sampled at 1500 samples /sec and the sampled signal is passed through an ideal low-pass filter with cut-off frequency 800 Hz. The output signal has the frequency