Many applications require the detection of a few discrete sinusoids. The Goertzel filter is an IIR filter that uses the feedback to generate a very high Q bandpass filter where the coefficients are easily generated from the required centre frequency, according to the following equations. The most common configuration for using this technique is to measure the signal energy before and after the filter and to compare the two. If the energies are similar then the input signal is centred in the pass-band, if the output energy is significantly lower than the input energy then the signal is outside the pass band. The Goertzel algorithm is most commonly implemented as a second order recursive IIR filter, as shown below.
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