- 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 wirelesscommunications devices. Subsonic frequency response measurements can include earthquakesand 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
*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 sequencenoise, or analog filtered white noiseequivalent, like pink noise), and calculating the impulse response by deconvolutionof 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 plotor 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 filtercan 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 fidelityamplifier 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 responseof 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] ]
Bandwidth (signal processing)
Audio system measurements
Transient response& steady-state response
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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