A fast algorithm for high-accuracy frequency measurement. Application to ultrasonic Doppler sonar

Abstract

In an attempt to investigate the technical feasibility of a CW Doppler sonar, we have examined a method of measuring low velocities with a high-velocity resolution, or frequency resolution, by use of a simple circuit configuration employing digital signal processing technique. The following discussion presents the results of the investigation. In the measuring method described below, the fast Fourier transform (FFT) of undersampled data is calculated and the Doppler shift is obtained by searching for a peak frequency of the power spectrum. To achieve the intended frequency resolution of 1 Hz by FFT operation, measurement of data for a minimum measuring period of 1 s is essential. If the sampling frequency is set to 50 kHz, the number of samples obtained during the minimum measuring period of 1 s would amount to 50 000. This is not practical in light of the time required for the FFT operation. To overcome this problem, our new measuring method employs a decima-tion technique for reducing the number of samples down to 1024 while maintaining a frequency resolution of about 1 Hz. This paper describes how the processing time can be drastically reduced to about 1/300th compared to the conventional technique by a combination of complex exponential functions, filtering and decimation, and thereby indicates the possibility of real-time CW Doppler data processing.

Application of the multiple signal classification (MUSIC) method for one-pulse burst-echo Doppler sonar data

“…In the pulse wave method, on the other hand, a burst-pulse signal is transmitted and the Doppler frequency shift of the reflected burst-echo signal over the transmitted one is measured. The burst pulse can be regarded as periodic truncation of the 3 Author to whom correspondence should be addressed. continuous wave; the typical pulse duration is 2-10 ms and the repetition frequency is 10-30 Hz.…”

“…This means that the pulse Doppler sonar is difficult to use for low-velocity measurements. Although some methods have been proposed to counter this problem [3], most of them use multiple burst-echo signals and result in a low time resolution, which means that the time interval between individual velocity measurements becomes long.…”