# Accession Number:

## AD0627645

# Title:

## DETECTION OF SONAR SINUSOIDS OF UNKNOWN FREQUENCY AND KNOWN OR UNKNOWN PHASE

# Descriptive Note:

# Corporate Author:

## RAND CORP SANTA MONICA CA

# Personal Author(s):

# Report Date:

## 1965-12-01

# Pagination or Media Count:

## 80.0

# Abstract:

The problem of detecting a constant sine wave of unknown frequency and amplitude in gaussian noise is discussed. It is assumed that the sinusoid may appear at any one of a finite number of known frequencies, and the probability of its occurrence at each of these frequencies is assumed to be equal. Two cases are treated. The first assumes that the frequency is not known and the phase of the signal is known, allowing coherent detection. The second acknowledges that the initial phase indeed could not be known, and an analysis of the incoherent detector is made. For large output signal-to-noise ratios the problem in both cases becomes that of detecting one of m approximately orthogonal signals in a noise background. The magnitude of the error in the orthogonality approximation is considered. A physical realization of an approximately optimum detector structure is studied in some detail, and the effect of finite observation time is considered. The results indicate that the difference between the two cases is small and quite predictable. It can be assumed that the initial phase is known, the gaussian character of the quantities that arise may be retained, and finally, the answers can be adjusted to account for the actual lack of knowledge concerning the phase.

# Descriptors:

# Subject Categories:

- Cybernetics
- Acoustic Detection and Detectors