Frequency response ($H(\omega)$)

The function $H(\\omega)$ that specifies a filter, multiplying an input's transform to produce the output's.

A filter is specified by a function $H(\omega)$ , its frequency response: given an input $x(t)$ with transform $\hat x(\omega)$ , the filter's output $y(t)$ has transform $\hat y(\omega) = H(\omega)\hat x(\omega)$ . By the Convolution Theorem read in reverse, this is exactly $y=h*x$ , where $h=\mathcal F^{-1}[H]$ is the filter's impulse response.

Examples

A low-pass filter has a frequency response that is $1$ for low $\omega$ and $0$ for high $\omega$ .