Time domain threshold crossing for signals in noise
This work investigates the discrimination of times between threshold crossings for deterministic periodic signals with added band-limited noise. The methods include very low signal to noise ratio (one or less). Investigation has concentrated on the theory of double threshold crossings, with especial care taken in the effects of correlations in the noise, and their effects on the probability of detection of double crossings. A computer program has been written to evaluate these probabilities for a wide range of signal to noise ratiOS, a wide range of signal to bandwidth ratios, and a range of times between crossings of up to two signal periods. Correlations due to the extreme cases of a Brickwall filter and a second order Butterworth filter have been included; other filters can easily be included in the program. The method is simulated and demonstrated by implementing on a digital signal processor (DSP) using a TMS32020. Results from the DSP technique are in agreement with the theoretical evaluations. Probability results could be used to determine optimum time thresholds and windows for signal detection and frequency discrimination, to determine the signal length for adequate discrimination, and to evaluate channel capacities. The ability to treat high noise, including exact effects of time correlations, promises new applications in electronic signal detection, communications, and pulse discrimination neural networks.