Effect of Spectrum on the Measurement of Noise

A substantial discrepancy was found to exist between the sigma (standard deviation) of the noise present in radar data as determined by subtraction of data smoothed by a low-pass filter from the raw data and use of successive differences to isolate the noise. An investigation revealed that implicit in the equation based on the successive differences approach was the assumption that the noise was white, bandlimited, and with a cutoff frequency equal to the Shannon frequency. Hence, analyses were performed to take into account other situations, namely: band-limited white noise having a cutoff frequency less than the Shannon frequency; white noise modified by an RC filter; and spurious sinusoidal signal present. By taking into account these various types of noise spectra, it was possible to obtain excellent agreement between the two methods for measuring the noise sigmas.