Relative signal levels of a sinusoid with and without background noise

In the process of looking at some order data, a question about the accuracy of the measurement of the signal level of discrete frequency signals which were close to the general noise level.  To answer this question, a small DATS worksheet was created which generated 2 signals.  The first signal was a 35 Hz sinusoid which, by itself the spectrum level was measured to be approximately -9 dB (ref 1 V) as seen in Figure 1.

Spectrum level of 35Hz sinusoid
Fig 1: Spectrum level of 35Hz sinusoid

A second signal which consisted of Gaussian noise signal was created.  The average spectrum level of the Gaussian random noise was calculated to be approximately -11.8 dB (ref 1 Volt) or within 3 dB of the measured sinusoid level (Figure 2).

Average spectrum level of Gaussian random signal
Figure 2: Average spectrum level of Gaussian random signal

The Gaussian random noise signal was added to the 35 Hz discrete frequency signal.  The spectral results of these combined signals was used to measure the level of the 35 Hz sinusoid signal. The measured level of the sinusoid signal when embedded in the Gaussian random noise signal was measured to be approximately -6 dB (ref 1 Volt). or approximately 3 dB higher due to the influence of the Gaussian random noise signal (Figure 3).

Spectrum level of combined signal compared to simple sinusoid
Figure 3: Spectrum level of combined signal compared to simple sinusoid

The cursor readouts are seen below in Figure 4 showing the influence of the Gaussian random noise on the actual level measured of the sinusoid.

Cursor readout of spectrum level of simple sinusoid and combined signal
Figure 4: Cursor readout of spectrum level of simple sinusoid and combined signal

The important fact to take away from this is if the noise level is relatively close to the level of discrete frequency signals, the measured level of the discrete frequency signal is influenced.  Experimenting with parameters in the Gaussian random noise generation DPU demonstrated if the Average spectrum level of the Gaussian random noise signal is within approximately 9 dB of the level of the sinusoid, the level of the sinusoid embedded in the Gaussian random noise is influenced by approximately 1 dB (≈12%).

Conclusion

Be aware, if you are measuring signal levels which are close to the generalized noise floor of the signal, the amplitudes of the signals can be significantly influenced.  As a rule of thumb, an accurate reading of the level of the sinusoid will only be read from the cursor readout if the level of the Gaussian random noise is at least 10 dB lower than the level of the discrete frequency signal.

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John Mathey

Senior Technical Specialist at Prosig
John Mathey graduated with a MS degree from the University of Toledo in 1972. John has over 35 years of experience with instrumentation, measurement, and analysis. Twenty-five of those years were spent at Ford Motor Company solving and providing training for vehicle noise, vibration, and harshness (NVH) issues. He is now a technical specialist at Prosig USA, Inc. where he provides technical support to Prosig customers in the U.S.A.

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