Finding Signals Buried in Noise

The upper graph of the Waveform shows what appears to be a noise-only signal. However, it also includes a sine wave at 1 kHz, which is impossible to see in the Waveform graph since it is buried in the noise. However, in the Frequency Spectrum, it clearly becomes separated from the noise. This is because the energy of the noise is present at all frequencies, and hence is spread out across the entire spectrum at a much lower level than the sine wave which has all its energy concentrated in one frequency.

Experiment 1: Change the Frequency Resolution to 100 Hz and notice how the Sine wave also disappears from the Frequency Spectrum. Now change it to 1 Hz, and notice that the sine clearly stands out about the noise. When dealing with broadband noise, the noise reduced by 10 dB when increasing the Frequency Resolution by a factor of 10.

Experiment 2: Set Frequency Resolution to 10 Hz, Amplitude to 300m and Noise % to 1000. Make sure the Averaging Mode is RMS averaging and the Weghting Mode Linear. Note that after a few hundred averages that the "noise floor" of the Frequency Spectrum is nearly a straight line at about -19 dB. No matter how long we average, we will never get the noise any lower. However, if we are able to synchronize our averaging with the sine wave that we are searching for, things will get better. Select Vector Averaging mode. The noise floor rapidly drops, and you may need to hit the Autoscale button to see it again. With vector averaging, the noise floor will in principle keeps dropping forever, but you reach a point of diminishing returns (every doubling of time gives 3 dB more).

Requirements

Filename: find_sine_buried_in_noise.llb

Software Requirements

Application Software: LabVIEW Full Development System 6.0
Language(s): LabVIEW

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