Coherence Function
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Note that the averaging in the numerator occurs before the absolute value is taken.
The coherence is a real function between zero and one which gives ameasure of orrelationbetween and at each frequency . For example, imagine that is produced from via anTI filtering operation:
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Coherence Function
A function related tocross-correlationis thecoherence function, defined in terms of power spectral densities and the cross-spectral density by
In practice, these quantities can be estimated bytime-averaging , , and over successivesignalblocks. Let denote time averaging across frames as in Eq. (8.ห้องสมุดไป่ตู้)above. Then an estimate of the coherence, thesample coherence function , may be defined by
Then the magnitude-normalizedcross-spectrumin each frame is
so that the coherence function becomes
On the other hand, when and are uncorrelated (e.g., is anoiseprocess not derived from ), the sample coherence converges tozeroat all frequencies, as the number of blocks in the average goes to infinity.
A common use for the coherence function is in the validation of input/output data collected in an acoustics experiment for purposes ofsystem identification. For example, might be a known signal which is input to an unknown system, such as a reverberant room, say, and is the recorded response of the room. Ideally, the coherence should be at all frequencies. However, if the microphone is situated at anullin the room response for some frequency, it may record mostlynoiseat that frequency. This is indicated in the measured coherence by a significant dip below 1. An example is shown in Book III[69]for the case of a measuredquitar-bridge admittance.A more elementary example is given in the next section.
The coherence is a real function between zero and one which gives ameasure of orrelationbetween and at each frequency . For example, imagine that is produced from via anTI filtering operation:
批注本地保存成功开通会员云端永久保存去开通
Coherence Function
A function related tocross-correlationis thecoherence function, defined in terms of power spectral densities and the cross-spectral density by
In practice, these quantities can be estimated bytime-averaging , , and over successivesignalblocks. Let denote time averaging across frames as in Eq. (8.ห้องสมุดไป่ตู้)above. Then an estimate of the coherence, thesample coherence function , may be defined by
Then the magnitude-normalizedcross-spectrumin each frame is
so that the coherence function becomes
On the other hand, when and are uncorrelated (e.g., is anoiseprocess not derived from ), the sample coherence converges tozeroat all frequencies, as the number of blocks in the average goes to infinity.
A common use for the coherence function is in the validation of input/output data collected in an acoustics experiment for purposes ofsystem identification. For example, might be a known signal which is input to an unknown system, such as a reverberant room, say, and is the recorded response of the room. Ideally, the coherence should be at all frequencies. However, if the microphone is situated at anullin the room response for some frequency, it may record mostlynoiseat that frequency. This is indicated in the measured coherence by a significant dip below 1. An example is shown in Book III[69]for the case of a measuredquitar-bridge admittance.A more elementary example is given in the next section.