# Frequency response

Frequency response

Frequency response is the measure of any system's spectrum response at the output to a signal of varying frequency (but constant amplitude) at its input. In the audible range it is usually referred to in connection with electronic amplifiers, microphones and loudspeakers. Radio spectrum frequency response can refer to measurements of coaxial cables, category cables, video switchers and wireless communications devices. Subsonic frequency response measurements can include earthquakes and electroencephalography (brain waves).

The frequency response is typically characterized by the "magnitude" of the system's response, measured in dB, and the "phase", measured in radians, versus frequency. The frequency response of a system can be measured by applying a "test signal", for example:
*applying an impulse to the system and measuring its response (see impulse response)
*sweeping a constant-amplitude pure tone through the bandwidth of interest and measuring the output level and phase shift relative to the input
*applying a signal with a wide frequency spectrum (for example digitally-generated maximum length sequence noise, or analog filtered white noise equivalent, like pink noise), and calculating the impulse response by deconvolution of this input signal and the output signal of the system.

These typical response measurements can be plotted in two ways: by plotting the magnitude and phase measurements to obtain a Bode plot or by plotting the imaginary part of the frequency response against the real part of the frequency response to obtain a Nyquist plot.

Once a frequency response has been measured (e.g., as an impulse response), providing the system is linear and time-invariant, its characteristic can be approximated with arbitrary accuracy by a digital filter. Similarly, if a system is demonstrated to have a poor frequency response, a digital or analog filter can be applied to the signals prior to their reproduction to compensate for these deficiencies.

Frequency response measurements can be used directly to quantify system performance and design control systems. However, frequency response analysis is not suggested if the system has slow dynamics.

Frequency response curves are often used to indicate the accuracy of amplifiers and speakers for reproducing audio. As an example, a high fidelity amplifier may be said to have a frequency response of 20 Hz - 20,000 Hz ±1 dB. This means that the system amplifies all frequencies within that range within the limits quoted. 'Good frequency response' therefore does not guarantee a specific fidelity, but only indicates that a piece of equipment meets the basic frequency response requirements.

"By measuring gain and phase over a range of frequencies, the full frequency response of the system can be plotted." [Laubwald, Elke and Mark Readman, control-systems-principles.co.uk. "Frequency Response Analysis." [http://www.control-systems-principles.co.uk/whitepapers/frequency-response-analysis1.pdf] ]

ee also

* Transfer function
* Bode plot
* Bandwidth (signal processing)
* Audio system measurements
* Transient response & steady-state response

References

* University of Michigan: [http://www.engin.umich.edu/group/ctm/freq/freq.html Frequency Response Analysis and Design Tutorial]
* Smith, Julius O. III: [http://ccrma.stanford.edu/~jos/filters/ Introduction to Digital Filters with Audio Applications] has a nice chapter on [http://ccrma.stanford.edu/~jos/filters/Frequency_Response_I.html Frequency Response]

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