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

In an attempt to investigate the technical feasibility of a continuous-wave 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 second is essential. If the sampling frequency is set to 50 kHz, the number of samples obtained during the minimum measuring period of 1 second would amount to 50000. This is not practical in the light of the time required for the FFT operation. To overcome this problem, our new measuring method employs decimation 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 1/300 compared to the conventional technique by a combination of complex exponential functions, filtering and decimation, and thereby indicates the possibility of real-time continuous-wave Doppler data processing.