Frequency Response Descriptions for LTI Systems

An introduction to the description of the input output characteristics of linear time-invariant systems based on frequency response. The frequency response is the Fourier transform of the impulse response, and is also related to the difference equation description. Frequency response converts the convolution represented by the impulse response into multiplication and leads to the idea of filtering. Frequency response indicates how a system responds to sinusoids - since most signals can be represented as a weighted combination of sinusoids, the response of a linear system to sinusoids thus indicates how the system responds to arbitrary inputs.