Fourier transform of a rectangular pulse

Question

I'm interested in knowing: 1. Why the frequency content has a larger magnitude at low frequencies 2. Why the magnitude is zero at frequencies which are composed of multiples of the rectangular pulse's period

\$x(t)\$:

\$X(j\omega)\$:

Answer 1

Take a look at these two periodic-signal transformations: -

The first example has a duty cycle of 0.27 and as can be seen (if you did a fourier transformation), the spectral content at closest to 3f is quite small. Should the rectangular wave have a duty-cycle of exactly one-third, the spectral content at 3f would be zero.

Similar story for a 50:50 AC square wave; the duty cycle is 0.5 therefore the spectral content at 2f (and 4f and 6f etc..) is always zero.

Picture stolen from here and please note that the article continues to show how the fourier spectrum is evaluated (for further reading).

The non-periodic example in your question produces a continuous spectrum but the nulls and the peaks still align with the examples above.

As for the low frequency being so high in the OP's example, it's because the pulse has significant DC content