Convolution

Convolution of two rectangular pulses example

Convolution of two rectangular pulses example
  1. What is the convolution of 2 rectangular pulses?
  2. When a rectangular pulse is convolved with itself the result is?

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.

When a rectangular pulse is convolved with itself the result is?

Convolution of a Rectangle with Itself Twice

The convolution outputs are smoother (fewer discontinuities) than the convolution inputs. So sometimes convolution with a pulse-like function (e.g., a rectangle) is referred to as a smoothing operation. Figure 10.

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