Frequency response

It has been suggested that Full frequency response be merged into this article or section. (Discuss)

Frequency response is the measure of any system's output spectrum in response to an input signal.^[1] 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).

Frequency response requirements differ depending on the application.^[2] In high fidelity audio, an amplifier requires a frequency response of at least 20–20,000 Hz, with a tolerance as tight as ±0.1 dB in the mid-range frequencies around 1000 Hz, however, in telephony, a frequency response of 400–4000 Hz, with a tolerance of ±1 dB is sufficient for intelligibility of speech.^[2]

Frequency response curves are often used to indicate the accuracy of electronic components or systems.^[1] When a system or component reproduces all desired input signals with no emphasis or attenuation of a particular frequency band, the system or component is said to be "flat", or to have a flat frequency response curve.^[1]

Frequency response of a low pass filter with 6 dB per octave or 20 dB per decade

The frequency response is typically characterized by the magnitude of the system's response, measured in decibels (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.^{[citation needed]}

See also

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

References

Notes

1. ^ ^{a b c} Stark, 2002, p. 51.
2. ^ ^{a b} Luther, 1999, p. 141.

Bibliography

• Luther, Arch C.; Inglis, Andrew F. Video engineering, McGraw-Hill, 1999. ISBN 0-07-135017-9
• Stark, Scott Hunter. Live Sound Reinforcement, Vallejo, California, Artistpro.com, 1996–2002. ISBN 0-918371-07-4

External links

• University of Michigan: Frequency Response Analysis and Design Tutorial
• Smith, Julius O. III: Introduction to Digital Filters with Audio Applications has a nice chapter on Frequency Response