1. Famous convolution signals

2. * From X1 (rectangle) convolution with itself -2 2
The result will be a triangle (X3) X1 -1 1 2
From
The ending point of the X1(first) signal + the
ending point of the X1 (second) signal * X1 -1 1 2
The starting point of the X1(first) signal + the starting point of the X1 (second) signal
1 + 1 X3 -2 2

3. * h = 8 X1 (rectangle) convolution with itself
OR convolution with another rectangle of the same width X1 -1 1 2
Then we get the height from
Area of X1 multiplied by Area of X1 equals Area of X3
A1 x A2 = A3 * X1 -1 1 2
2 x 2=4
2 x 2=4
0.5 x 4 x h
multiply h X3
h = 8 -2 2

4. * From h = 16 X1 (rectangle) convolution with X2 (rectangle) -3 3
The result will be a trapezoid (X3) X1 -1 1 2
From
The ending of the X1(first) signal + the
ending of the X2 (second) signal * X2 -2 2 3
The starting of the X1(first) signal + the
starting of the X2 (second) signal X3
1 + 2 -3 3
h = 16

5. * Then h = 16 X1 (rectangle) convolution with X2 (rectangle) -3 -1 1 3
We want to get the region of the constant
part in the signal
The starting of the X1(first) signal + the
ending of the X2 (second) signal * X2 -2 2 3
1- 2
The ending of the X1(first) signal + the
starting of the X2 (second) signal X3 -3 -1 1 3
h = 16

6. * h = 12 h = 16 X1 (rectangle) convolution with X2 (rectangle) h -3 -1
Then we get the height from
Area of X1 multiplied by Area of X2 equals Area of X3
A1 x A2 = A3 * X2 -2 2 3
2 x 2=4
4 x 3=12
0.5 x h x (6+2)
multiply h X3
h = 12 -3 -1 1 3
h = 16

7. * From h = 16 Another example
X1 (rectangle) convolution with X2 (rectangle)
The result will be a trapezoid (X3) X1 -3 3
2^1/2
From
The ending of the X1(first) signal + the
ending of the X2 (second) signal *
2^1/2 X2 -2 2
The starting of the X1(first) signal + the
starting of the X2 (second) signal X3
3 + 2 -5 5
h = 16

8. * Then h = 16 Another example
X1 (rectangle) convolution with X2 (rectangle) X1 -3 3
2^1/2
Then
We want to get the region of the constant
part in the signal
The starting of the X1(first) signal + the
ending of the X2 (second) signal * X2
2^1/2
3 - 2 -2 2
The ending of the X1(first) signal + the
starting of the X2 (second) signal X3 -5 -1 1 5
h = 16

9. Another example
X1 (rectangle) convolution with X2 (rectangle) X1 -3 3
2^1/2
Then we get the height from
Area of X1 multiplied by Area of X2 equals Area of X3
A1 x A2 = A3 * X2
2^1/2
6x(2^0.5)
4x(2^0.5)
0.5 x h x (10+2)
multiply -2 2 h X3
h = 8 -5 -1 1 5
h = 16

10. h = 16 Area of trapezoid: A = 0.5 x h x (a + b) Or
A = 2 x (0.5 x c x h + d x h) h -5 -1 5 1 c d a b
h = 16

11. * Note that it could be in the opposite way,
the trapezoid is given and you need to simplify it to two rectangles. -1 1 -7 7 8
1.5^1/2
1.5^1/2 -4 4 -3 3 *