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Famous convolution signals

Famous convolution signals. 2. X1. 2. -1. -1. 1. 1. X1. X3. 0. X1 (rectangle) convolution with itself. The result will be a triangle (X3). From. The ending point of the X1(first) signal + the ending point of the X1 (second) signal. *. - 1 - 1.

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Famous convolution signals

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  1. Famous convolution signals

  2. 2 X1 2 -1 -1 1 1 X1 X3 0 X1 (rectangle) convolution with itself The result will be a triangle (X3) From The ending point of the X1(first) signal + the ending point of the X1 (second) signal * - 1 - 1 The starting point of the X1(first) signal + the starting point of the X1 (second) signal 1 + 1 -2 2

  3. 2 X1 2 -1 -1 1 1 X1 X3 0 X1 (rectangle) convolution with itself OR convolution with another rectangle of the same width Then we get the height from Area of X1 multiplied by Area of X1 equals Area of X3 A1 x A2 = A3 * 2 x 2=4 2 x 2=4 0.5 x 4 x h multiply h h = 8 -2 2

  4. 2 X1 3 -1 1 X2 -2 2 X3 0 X1 (rectangle) convolution with X2 (rectangle) The result will be a trapezoid (X3) From The ending of the X1(first) signal + the ending of the X2 (second) signal * - 1 - 2 The starting of the X1(first) signal + the starting of the X2 (second) signal 1 + 2 -3 3 h = 16

  5. 2 X1 3 -1 1 X2 -2 2 X3 0 X1 (rectangle) convolution with X2 (rectangle) 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 * 1- 2 The ending of the X1(first) signal + the starting of the X2 (second) signal - 1 + 2 -3 -1 1 3 h = 16

  6. 2 X1 3 -1 1 X2 -2 2 X3 0 X1 (rectangle) convolution with X2 (rectangle) Then we get the height from Area of X1 multiplied by Area of X2 equals Area of X3 A1 x A2 = A3 * 2 x 2=4 4 x 3=12 0.5 x h x (6+2) multiply h h = 12 -3 1 -1 3 h = 16

  7. X1 2^1/2 -3 3 X2 2^1/2 -2 2 X3 0 Another example X1 (rectangle) convolution with X2 (rectangle) The result will be a trapezoid (X3) From The ending of the X1(first) signal + the ending of the X2 (second) signal * - 3 - 2 The starting of the X1(first) signal + the starting of the X2 (second) signal 3 + 2 -5 5 h = 16

  8. X1 2^1/2 -3 3 X3 0 Another example X1 (rectangle) convolution with X2 (rectangle) 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 - 3 + 2 -5 -1 1 5 h = 16

  9. X1 2^1/2 -3 3 X3 0 Another example X1 (rectangle) convolution with X2 (rectangle) 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 h = 8 -5 1 -1 5 h = 16

  10. 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 0 1 c d a b h = 16

  11. 8 -7 -1 1 7 -3 3 -4 4 0 • Note that it could be in the opposite way, the trapezoid is given and you need to simplify it to two rectangles. 1.5^1/2 1.5^1/2 *

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