Unit Impulse, Unit Step
- Ryan Hirst
Unit Impulse and Unit Step functions. Switch On the lower panel to multiply f(x-τ) by u or δ. Click to select/activate gray text.
I give δ(t) a height of 1 at the peak. Say I vary the position δ with the parameter t. According to Newton, to represent the figure f(x-τ) by the (convolution) integral f(t)*δ(t), I must maintain a ratio of equality between the areas of the two figures, in the limit as Δt→ 0. I am making up δ, so I will satisfy this condition by definition:<br>
- δ(t) has an area of 1
- Part I 1. Sine or cosine from two points: http://www.geogebratube.org/material/show/id/49208 →2. Unit Step, Unit Impulse 3. Triangle function λ: http://www.geogebratube.org/material/show/id/50926 4. Sum λ1+ λ2 is a scalene triangle: http://www.geogebratube.org/material/show/id/50004