## Convolution Theorem: DFT of convolution is product of DFTs $y = h * x \quad \Rightarrow \quad Y[m] = H[m] \cdot X[m]$ ↓ apply inverse DFT to recover time-domain output signal. - can be used for filter analysis to understand how a given impulse response might effect a signal. (h) $H(m)$ is complex number in the frequency domain. $H[m] = Ae^{j\phi} \quad \text{ ("gain")}$ $X[m] = Be^{j\theta} \text{ encodes magnitude and phase of a given sinusoid in the signal}$ $Y[m]$ has magnitude $AB$, phase $\phi+\theta$ $H[m]$ determines how much each sinusoidal component gets scaled by $A$ and delayed by $\phi$