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Frequency response
 
 
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Frequency response is the measure of any system's spectrum
Frequency spectrum

Familiar concepts associated with a frequency are colors, musical notes, radio/TV channels, and even the regular rotation of the earth. A source of light can have many colors mixed together and in different amounts ....
 response at the output to a signal of varying frequency
Frequency

Frequency is the number of occurrences of a repeating event per unit time. It is also referred to as temporal frequency.The period is the duration of one cycle in a repeating event, so the period is the reciprocal of the frequency....
 (but constant amplitude) at its input. In the audible range it is usually referred to in connection with electronic amplifier
Electronic amplifier

An electronic amplifier is a device for increasing the Power and/or amplitude of a Signal . It does this by taking energy from a power supply and controlling the output to match the input signal shape but with a larger amplitude....
s, microphone
Microphone

A microphone, sometimes referred to as a mike or?more recently?mic, is an acoustic-to-electric transducer or sensor that converts sound into an electrical signal....
s and loudspeakers. Radio spectrum frequency response can refer to measurements of coaxial cable
Coaxial cable

Coaxial cable is a cable consisting of an inner conductor, surrounded by a tubular insulating layer typically made from a flexible material with a high dielectric constant, all of which is then surrounded by another conductive layer , and then finally covered again with a thin insulating layer on the outside....
s, category cables
Category 6 cable

Category 6 cable, commonly referred to as Cat-6, is a cable standard for Gigabit Ethernet and other network protocols that is backward compatible with the Category 5 cable and Category 3 cable standards....
, video switchers and wireless
Wireless

Wireless communication is the transfer of information over a distance without the use of electrical conductors or "wires". The distances involved may be short or long ....
 communications devices. Subsonic frequency response measurements can include earthquakes and electroencephalography
Electroencephalography

Electroencephalography is the recording of electrical activity along the scalp produced by the firing of neurons within the brain. In clinical contexts, EEG refers to the recording of the brain's spontaneous electrical activity over a short period of time, usually 20-40 minutes, as recorded from multiple electrodes placed on the scalp....
 (brain waves).

The frequency response is typically characterized by the magnitude
Amplitude

Amplitude is the magnitude of change in the oscillating variable, with each oscillation, within an oscillating system. For instance, sound waves are oscillations in atmospheric pressure and their amplitudes are proportional to the change in pressure during one oscillation....
 of the system's response, measured in dB
Decibel

The decibel is a logarithmic units of measurement that expresses the magnitude of a physical quantity relative to a specified or implied reference level....
, and the phase
Phase (waves)

The phase of an oscillation or wave is the fraction of a complete cycle corresponding to an offset in the displacement from a specified reference point at time t = 0....
, measured in radians, versus frequency.






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Frequency response is the measure of any system's spectrum
Frequency spectrum

Familiar concepts associated with a frequency are colors, musical notes, radio/TV channels, and even the regular rotation of the earth. A source of light can have many colors mixed together and in different amounts ....
 response at the output to a signal of varying frequency
Frequency

Frequency is the number of occurrences of a repeating event per unit time. It is also referred to as temporal frequency.The period is the duration of one cycle in a repeating event, so the period is the reciprocal of the frequency....
 (but constant amplitude) at its input. In the audible range it is usually referred to in connection with electronic amplifier
Electronic amplifier

An electronic amplifier is a device for increasing the Power and/or amplitude of a Signal . It does this by taking energy from a power supply and controlling the output to match the input signal shape but with a larger amplitude....
s, microphone
Microphone

A microphone, sometimes referred to as a mike or?more recently?mic, is an acoustic-to-electric transducer or sensor that converts sound into an electrical signal....
s and loudspeakers. Radio spectrum frequency response can refer to measurements of coaxial cable
Coaxial cable

Coaxial cable is a cable consisting of an inner conductor, surrounded by a tubular insulating layer typically made from a flexible material with a high dielectric constant, all of which is then surrounded by another conductive layer , and then finally covered again with a thin insulating layer on the outside....
s, category cables
Category 6 cable

Category 6 cable, commonly referred to as Cat-6, is a cable standard for Gigabit Ethernet and other network protocols that is backward compatible with the Category 5 cable and Category 3 cable standards....
, video switchers and wireless
Wireless

Wireless communication is the transfer of information over a distance without the use of electrical conductors or "wires". The distances involved may be short or long ....
 communications devices. Subsonic frequency response measurements can include earthquakes and electroencephalography
Electroencephalography

Electroencephalography is the recording of electrical activity along the scalp produced by the firing of neurons within the brain. In clinical contexts, EEG refers to the recording of the brain's spontaneous electrical activity over a short period of time, usually 20-40 minutes, as recorded from multiple electrodes placed on the scalp....
 (brain waves).

The frequency response is typically characterized by the magnitude
Amplitude

Amplitude is the magnitude of change in the oscillating variable, with each oscillation, within an oscillating system. For instance, sound waves are oscillations in atmospheric pressure and their amplitudes are proportional to the change in pressure during one oscillation....
 of the system's response, measured in dB
Decibel

The decibel is a logarithmic units of measurement that expresses the magnitude of a physical quantity relative to a specified or implied reference level....
, and the phase
Phase (waves)

The phase of an oscillation or wave is the fraction of a complete cycle corresponding to an offset in the displacement from a specified reference point at time t = 0....
, 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
    Impulse response

    The impulse response of a system is its output when presented with a very brief input signal, an impulse. Mathematically, an impulse can be modeled as a Dirac delta function for continuous-time systems, or as the Kronecker delta for discrete-time systems....
    )
  • 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
    Maximum length sequence

    A maximum length sequence is a type of pseudorandom binary sequence.They are polynomial rings generated using maximal linear feedback shift registers and are so called because they are periodic function and reproduce every binary sequence that can be reproduced by the shift registers ....
     noise, or analog filtered white noise
    White noise

    White noise is a random signal with a flat power spectral density. In other words, the signal contains equal power within a fixed bandwidth at any center frequency....
     equivalent, like pink noise
    Pink noise

    Pink noise or 1/? noise is a signal or process with a frequency spectrum such that the spectral density is proportional to the reciprocal of the frequency....
    ), and calculating the impulse response by deconvolution
    Deconvolution

    In mathematics, deconvolution is an Algorithm process used to reverse the effects of convolution on recorded data. The concept of deconvolution is widely used in the techniques of signal processing and ....
     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
Bode plot

A Bode magnitude plot is a plot of logarithm magnitude versus frequency, plotted with a log-frequency axis, to show the transfer function or frequency response of a LTI system theory system....
 or by plotting the imaginary part of the frequency response against the real part of the frequency response to obtain a Nyquist plot
Nyquist plot

A Nyquist plot is used in control system and signal processing for assessing the stability of a system with feedback. It is represented by a graph in polar coordinates in which the gain and phase of a frequency response are plotted....
.

Once a frequency response has been measured (e.g., as an impulse response), providing the system is linear and time-invariant
LTI system theory

Linear time-invariant system theory, most commonly known as LTI system theory, comes from applied mathematics and has direct applications in NMR spectroscopy, seismology, electrical networks, signal processing, control theory, and other technical areas....
, its characteristic can be approximated with arbitrary accuracy by a digital filter
Digital filter

In electronics, computer science and mathematics, a digital filter is a system that performs mathematical operations on a Sampling , discrete-time Signal to reduce or enhance certain aspects of that signal....
. 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
High fidelity

High fidelity or hi-fi reproduction is a term used by home stereo listeners and home audio enthusiasts to refer to high-quality sound reproduction or video that are very faithful to the original performance....
 amplifier may be said to have a frequency response of 20 Hz
Hertz

The hertz is a measure of frequency per unit of time, or the number of list of cycles per second. It is the SI base unit of frequency in the International System of Units , and is used worldwide in both general-purpose and scientific contexts....
 - 20,000 Hz ±1 dB
Decibel

The decibel is a logarithmic units of measurement that expresses the magnitude of a physical quantity relative to a specified or implied reference level....
. 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
Full frequency response

If a sound is said to have Full Frequency Response, then the sound is composed of frequencies from across the entire audible spectrum. Human hearing is limited to sounds between approximately 20 Hz and 20 kHz, depending on age....
 of the system can be plotted."

See also

  • Transfer function
    Transfer function

    A transfer function is a mathematical representation, in terms of spatial or temporal frequency, of the relation between the input and output of a system analysis....
  • Bode plot
    Bode plot

    A Bode magnitude plot is a plot of logarithm magnitude versus frequency, plotted with a log-frequency axis, to show the transfer function or frequency response of a LTI system theory system....
  • Bandwidth (signal processing)
  • Audio system measurements
    Audio system measurements

    Audio system measurements are made for several purposes. Designers take measurements so that they can specify the performance of a piece of equipment....
  • Transient response
    Transient response

    In electrical engineering and Mechanical Engineering, a transient response or natural response is the response of a system to a change from equilibrium....
     & steady-state response


External links

  • University of Michigan
    University of Michigan

    The University of Michigan, Ann Arbor, Michigan is a public university research university located in the state of Michigan. It is the state's oldest university and the flagship campus of the University of Michigan, which also includes two regional campuses in University of Michigan-Flint and University of Michigan-Dearborn....
    :
  • Smith, Julius O. III: has a nice chapter on