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 signal …
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Los Alamos National Lab., NM (United States)
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New Mexico
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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 signal 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.
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