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Magnitude response of a low pass filter with 6 dB per octave or 20 dB per decade roll-off. Measuring the frequency response typically involves exciting the system with an input signal and measuring the resulting output signal, calculating the frequency spectra of the two signals (for example, using the fast Fourier transform for discrete signals), and comparing the spectra to isolate the ...
It is usually a combination of a Bode magnitude plot, expressing the magnitude (usually in decibels) of the frequency response, and a Bode phase plot, expressing the phase shift. As originally conceived by Hendrik Wade Bode in the 1930s, the plot is an asymptotic approximation of the frequency response, using straight line segments .
A phase response curve (PRC) illustrates the transient change (phase response) in the cycle period of an oscillation induced by a perturbation as a function of the phase at which it is received. PRCs are used in various fields; examples of biological oscillations are the heartbeat, circadian rhythms , and the regular, repetitive firing observed ...
An example is for high-resolution audio in which the frequency response (magnitude and phase) for steady state signals (sum of sinusoids) is the primary filter requirement, while an unconstrained impulse response may cause unexpected degradation due to time spreading of transient signals. [2] [3]
The magnitude plot indicates that the moving-average filter passes low frequencies with a gain near 1 and attenuates high frequencies, and is thus a crude low-pass filter. The phase plot is linear except for discontinuities at the two frequencies where the magnitude goes to zero. The size of the discontinuities is π, representing a sign reversal.
Using phase retrieval algorithms, it is possible to characterize complex optical systems and their aberrations. [6] For example, phase retrieval was used to diagnose and repair the flawed optics of the Hubble Space Telescope. [7] [8] Other applications of phase retrieval include X-ray crystallography [9] and transmission electron microscopy.
The frequency response plot from Butterworth's 1930 paper. [1] The Butterworth filter is a type of signal processing filter designed to have a frequency response that is as flat as possible in the passband. It is also referred to as a maximally flat magnitude filter.
Such a system is called a maximum-phase system because it has the maximum group delay of the set of systems that have the same magnitude response. In this set of equal-magnitude-response systems, the maximum phase system will have maximum energy delay. For example, the two continuous-time LTI systems described by the transfer functions + + +