# Accession Number:

## AD0751576

# Title:

## Coherence Estimation as Affected by Weighting Functions and Fast Fourier Transform Size.

# Descriptive Note:

## Research rept.,

# Corporate Author:

## NAVAL UNDERWATER SYSTEMS CENTER NEWPORT R I

# Personal Author(s):

# Report Date:

## 1972-10-12

# Pagination or Media Count:

## 23.0

# Abstract:

Given two wide-sense stationary random processes, the complex coherence function is the complex cross power spectral density function divided by the square root of the product of the two real auto power spectral density functions. Estimation of the magnitude square of the complex coherence MSC with fast Fourier transform FFT processing is investigated for synthetic data. The procedure used to partition the given finite time histories into n segments. Each segment, consisting of P data points, is multiplied by a smooth weighting function before computing the FFT. Cross and auto spectra are then averaged over a large number of segments before forming the coherence ratio. It is demonstrated that, when the magnitude of the first derivative of either the auto spectrum or the phase of the complex coherence is large, 1 multiplication by a weighting function is absolutely necessary and 2 P must be large enough to ensure sufficient spectral resolution. Author

# Descriptors:

# Subject Categories:

- Statistics and Probability
- Cybernetics