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Full width at half maximum. In a distribution, full width at half maximum (FWHM) is the difference between the two values of the independent variable at which the dependent variable is equal to half of its maximum value. In other words, it is the width of a spectrum curve measured between those points on the y-axis which are half the maximum ...
There are two of these half-power frequencies, one above, and one below the resonance frequency Δ ω = ω 2 − ω 1 , {\displaystyle \Delta \omega =\omega _{2}-\omega _{1}\,,} where Δ ω is the bandwidth, ω 1 is the lower half-power frequency and ω 2 is the upper half-power frequency.
The half-power point is the point at which the output power has dropped to half of its peak value; that is, at a level of approximately −3 dB. [1] [a]In filters, optical filters, and electronic amplifiers, [2] the half-power point is also known as half-power bandwidth and is a commonly used definition for the cutoff frequency.
If the maximum gain is 0 dB, the 3 dB bandwidth is the frequency range where attenuation is less than 3 dB. 3 dB attenuation is also where power is half its maximum. This same half-power gain convention is also used in spectral width, and more generally for the extent of functions as full width at half maximum (FWHM).
An example of an analogue electronic band-pass filter is an RLC circuit (a resistor–inductor–capacitor circuit). These filters can also be created by combining a low-pass filter with a high-pass filter. [1] A bandpass signal is a signal containing a band of frequencies not adjacent to zero frequency, such as a signal that comes out of a ...
It is sometimes taken to be the point in the filter response where a transition band and passband meet, for example, as defined by a half-power point (a frequency for which the output of the circuit is approximately −3.01 dB of the nominal passband value). Alternatively, a stopband corner frequency may be specified as a point where a ...
Its cutoff frequency (the half-power point of approximately −3 dB or a voltage gain of 1/ √ 2 ≈ 0.7071) is normalized to 𝜔 = 1 radian per second. Butterworth only dealt with filters with an even number of poles in his paper, though odd-order filters can be created with the addition of a single-pole filter applied to the output of the ...
The frequency response of a filter is generally represented using a Bode plot, and the filter is characterized by its cutoff frequency and rate of frequency rolloff. In all cases, at the cutoff frequency, the filter attenuates the input power by half or 3 dB.