A new method of optical frequency beat counting based on fast Fourier transform (FFT) analysis is described. Signals with a worse signal-to-noise ratio can be counted correctly comparing to the conventional counting method of detecting each period separately. The systematic error of FFT counting below 10 Hz is demonstrated and can be decreased. Additionally the modulation width of a frequency-stabilized laser with high frequency modulation index can be simultaneously measured during a carrier frequency measurement against an optical frequency synthesizer or other laser.
The secretiveness of sonar operation can be achieved by using continuous frequency-modulated sounding signals with reduced power and significantly prolonged repeat time. The application of matched filtration in the sonar receiver provides optimal conditions for detection against the background of white noise and reverberation, and a very good resolution of distance measurements of motionless targets. The article shows that target movement causes large range measurement errors when linear and hyperbolic frequency modulations are used. The formulas for the calculation of these errors are given. It is shown that for signals with linear frequency modulation the range resolution and detection conditions deteriorate. The use of hyperbolic frequency modulation largely eliminates these adverse effects.