Inelectrical engineering andtelecommunications, thecenter frequency of a filter or channel is a measure of a central frequency between the upper and lowercutoff frequencies. It is usually defined as either thearithmetic mean or thegeometric mean of the lower cutoff frequency and the upper cutoff frequency of aband-pass system or aband-stop system.
Typically, the geometric mean is used in systems based on certain transformations oflowpass filter designs, where thefrequency response is constructed to be symmetric on alogarithmic frequency scale.[1] The geometric center frequency corresponds to a mapping of the DC response of the prototype lowpass filter, which is aresonant frequency sometimes equal to the peak frequency of such systems, for example as in aButterworth filter.
The arithmetic definition is used in more general situations, such as in describingpassbandtelecommunication systems, where filters are not necessarily symmetric but are treated on a linear frequency scale for applications such asfrequency-division multiplexing.[2]