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Definition of Frequency Response
Frequency response is used to understand how to control a system. Part of this is identifying how the system reacts to various inputs, called dynamic response. For testing purposes, the least complex input signal you can apply to a system is called a sine wave. The objective is to build a dynamic response through the input of different frequencies and to measure the resulting amplitude and phase. The version of the dynamic response that emerges is called the frequency response.
Why Frequency Response Is Important
Frequency response measurements are important because they allow you to gauge a system's performance and use that information to design control systems. For example, with an electric guitar amplifier, the frequency response will tell you what range of frequency outputs will remain constant or won't produce distortion. You can then design system controls like an equalizer to offset distortion according to the frequency level. The musician won't then have to try to figure this out by turning dials that tune into distorting frequencies. Instead he can simply plug in the guitar, set the sound level, adjust the equalizer and then play.
However, keep in mind that in some academic and engineering circles, frequency response is considered outdated as a testing method. Some universities do not even teach frequency response in system dynamics courses. However, this does not negate the fact that it is a practical tool that has stood the test of time for control and signal processing engineers.
Impulse Response
Impulse response can get much more complex than frequency response for the simple reason that impulse response has much wider applications. Impulse response refers to the reaction of a dynamic system to any type of external input or change and is usually expressed as a function of time. This means a dynamic system may actually refer to a physical object such as a planet. For example, the earth revolves around the sun. Now imagine an asteroid the size of Jupiter hurls right past Earth and changes Earth's orbit around the sun. Earth is the dynamic system and the change of Earth's orbit is the impulse response to the passing asteroid.
Why Impulse Response Is Important
Impulse response is important because it tells you about the nature of a system or its tendencies. Understanding the nature of a system can tell you how that system might react under various circumstances and stresses. As such, fields such as astronomy, engineering and economics have applied the principles of impulse response to a diverse range of applications. In astronomy, impulse response dates back to Sir Issac Newton and his conclusions regarding planetary motions. When economists talk about "shock" to the economy, they are referring to an impulse response. By studying impulse responses, economists attempt to better understand the nature of the economic system when subjected to a specific set of inputs.