Title: FREQUENCY COMPONENTS OF A STEP FUNCTION AND A SINUSOID

Significant efforts have been devoted, spanning many years, to the problem of sinusoid detection in noise. Many of these efforts have produced superb, yet complex, algorithms which may be difficult to use for a wide segment of the Digital Signal Processing (DSP) community. This paper presents a simple, easily implemented and high effective method which solves this problem. This method severely degrades non-sinusoidal noise while leaving the embedded sinusoid(s) relatively undisturbed. The algorithm, simply put, exploits the difference between the net effect of integration and differentiation of sinusoids versus the effect of these operations on random noise and other signalmore » sequences. The cross-correlation of sine wave with its differentiated (and/or integrated) self is quite high. Conversely, the cross-reduction of a noise sequence with its differentiated (and/or integrated) self is much lower. Therefore, it is reasonable to assume that for sequences consisting of a sinusoid in noise, significant signal-to-noise-ratios (SNRs) in the correlation results are achievable using a combination of differentiation (and/or integration) and cross-correlation operations on such sequences. This technique has been applied to actual Doppler radar data, as well as to synthesized data, with excellent improvement in signal detection capability. 4 refs.« less

Significant efforts have been devoted, spanning many years, to the problem of sinusoid detection in noise. Many of these efforts have produced superb, yet complex, algorithms which may be difficult to use for a wide segment of the Digital Signal Processing (DSP) community. This paper presents a simple, easily implemented and high effective method which solves this problem. This method severely degrades non-sinusoidal noise while leaving the embedded sinusoid(s) relatively undisturbed. The algorithm, simply put, exploits the difference between the net effect of integration and differentiation of sinusoids versus the effect of these operations on random noise and other signalmore » sequences. The cross-correlation of sine wave with its differentiated (and/or integrated) self is quite high. Conversely, the cross-reduction of a noise sequence with its differentiated (and/or integrated) self is much lower. Therefore, it is reasonable to assume that for sequences consisting of a sinusoid in noise, significant signal-to-noise-ratios (SNRs) in the correlation results are achievable using a combination of differentiation (and/or integration) and cross-correlation operations on such sequences. This technique has been applied to actual Doppler radar data, as well as to synthesized data, with excellent improvement in signal detection capability. 4 refs.« less

The role of each microstructural component (i.e., ultrafine-grain, stable retained austenite, and tempered martensite matrix) in a three-step heat cycled, low carbon Fe-6Ni cryogenic alloy, which had shown excellent cryogenic properties, were studied independently through investigations of the mechanical properties and transformational behaviors of two simulated alloys. As a result, it was found that each component contributed to overall properties of the cryogenic alloy uniquely as follows: the ductile-brittle transition temperature is suppressed effectively by grain refinement; stable retained austenite in ferritic steel increases the cryogenic toughness by grain refinement; and the martensite matrix of ferritic steel affects the Charpymore » upper shelf energy alone. It also was found that an excellent cryogenic toughness was obtainable by the combined effects of each microstructural component of the alloy.« less