Convolution of two rectangular pulses

1. What is the convolution of 2 rectangular pulses?
2. What is the Fourier transform of a rectangular pulse?
3. Which type of figure is obtained on convoluting rectangular pulse of unequal width?

What is the convolution of 2 rectangular pulses?

The shaded areas are the overlap areas as a function of the shift, t, and the resulting convolution has a trapezoidal shape. If the rectangular pulses had had equal width, then the convolution would havec simplified to an isosceles triangular shape.

What is the Fourier transform of a rectangular pulse?

The Fourier transform of the rectangular pulse is real and its spectrum, a sinc function, is unbounded. This is equivalent to an upsampled pulse-train of upsampling factor L.

Which type of figure is obtained on convoluting rectangular pulse of unequal width?

Convolution of two unequal length rectangles results a trapezium. Convolution of two equal length rectangles results a triangle. A function convoluted itself is equal to integration of that function.