Convolution

Author: John J Weber III, PhD Corresponding Textbook Sections:

• Section 7.7 – Convolution

Prerequisite Knowledge

de Moivre's Formula Revisited

Suppose we do not recall the formulas for $\cos{(\alpha +\beta)}$ and $\sin{(\alpha +\beta)}$, then use de Movire's formula:

$e^{i(\alpha +\beta)}=\cos{(\alpha +\beta)}+i\sin{(\alpha +\beta)}$ and $e^{i(\alpha +\beta)}=e^{i\alpha}e^{i\beta}=\left[\cos{(\alpha)}+i\sin{(\alpha)}\right]\left[\cos{(\beta)}+i\sin{(\beta)}\right]$

Practice

Find an equivalent expression for the following:

1. $\cos{(\alpha +\beta)}$
2. $\cos{(\alpha -\beta)}$
3. $\sin{(2\alpha)}$

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Last Modified: Sunday, 8 November 2020 18:50 EDT