This lesson will introduce you to the most intuitive description for LTI systems used in signal processing. The frequency response of a system defined as the amplitude and phase of the system output in response to a unit complex sinusoid input signal. You will learn how the frequency response is related to the impulse response and the difference equation descriptions for LTI systems.
Frequency response provides powerful insight because it introduces the notion of filtering: separating or discriminating between signals based on their frequency content. An arbitrary input signal may be expressed as a weighted sum of complex sinusoids of different frequencies. The corresponding output is also a weighted sum of complex sinusoids, but the weights on the input sinusoids are multiplied by the frequency response of the system. The frequency response changes the amplitude and phase of each input sinusoid. Filtering is accomplished by reducing the amplitude of some input frequencies while leaving others unchanged.
A significant portion of your future study in signal processing will build on the concepts introduced in this lesson.