Noise Estimation

The data of individual measurements fluctuate irregularly around an effective value (random errors). These deviations are caused by the noise of the signal source. The absolute value of the noise, which depends on different experimental conditions, can be estimated from the deviations of the base line. In spectroscopy it is also possible to use the spectra of optical attenuators, e.g., of a sieve or a grey filter. Then the noise must be minimized by optimizing the on-line low-pass output filter of the apparatus or the gate filter of the derivative device. The dimension of the noise is given in [mm]. 

---

Figure 17. FTIR absorbance (lower), VCD (middle) and VCD noise estimate (upper) for the 1800-1500-cm" region of poly-7-benzyl-L-glutamate, 2 mg/ml in CHCI3, path length 0.5 mm, resolution 4 cm". (Reproduced by permission of Wiley, from ref. 99.)...

Tests. Air is scanned in the absorbance mode for 10 min. peak-to-peak noise is recorded at 500 nm. The root mean square (RMS) noise is then calculated. The RMS noise measurement is a measure of the standard deviation of the background signals. Modem spectrophotometers are usually equipped with the noise estimation function. For older spectrophotometers, the RMS noise can be estimated by multiplying the highest peak-to-peak noise level by a factor of 0.7 (Figure 10.8). 

The spectrum of (-)-a-pinene as a 50 pm film of neat liquid using a Bomem spectrometer with a polarizing interferometer attachment is a composite of 60 000 VCD scans and 12 000 transmission scans and took 19.5 hours to be measured. A spectrum with comparable signal to noise ratio is shown in Fig. 6.3-9. This was measured in our laboratory with a PEM-based VCD spectrometer and is a composite of only 5000 scans (five blocks of 1024 scans each). The noise estimate shown as the upper trace is the difference between two 5000 scan VCD spectra. 

Figure 6.11. The actual test signal, the test signal with noise and its de-noised estimates using three different filter constants.

Burgess, G. L., Dippnall, W. M., Ravandi, M. R., and Cherry, N. M. (2004). Retrospective noise estimates for British nuclear workers using an alternative approach. Amt Occup Hyg 48, 117-127. 

Fig. 3.14 Impedance modulus for Aluzinc in 0.1 M Na2S04 after 14 days of immersion measured with two total amplitudes (a) 8 mV and (b) 48 mV continuous line - IZI, - noise estimated from...

The purpose of the error microphone is to measure the unwanted noise field after destructive interference. The adaptive filter takes this measurement and produces an estimate of the noise process, which is then used to adjust the filter parameters so as to improve the cancellation effect. In general, there may be a multiple error microphones producing an improved noise estimate however, Oppenheim et al. (1994) presents a scheme using only a single input sensor. The approach is evaluated using both computer generated noise and with recordings of aircraft noise. 

Seismometer Self-Noise and Measuring Methods, Fig.1 Self-noise estimates of the vertical component of the STS-2 seismometer for the minimum noise green) and the mode (red) of sensor noise measured at the Conrad Observatory, Austria. The light gray and dark gray bands... 

Seismometer Self-Noise and Measuring Methods, Fig. 2 Self-noise estimates for a strong-motion accelerometer using the single-sensor method (red), the Sleeman (Sleeman et al. 2006) threesensor method (green), and the Holcomb (Holcomb 1989) two-sensor method (blue). For reference the New Low-Noise Model (NLNM) is included (black)... 

Under the assumption that the sensors both have weU-known responses, the instrument corrected output, from the two sensors, should only differ in instrumental self-noise. By estimating the coherent signal between the two records, the coherence signal is removed resulting in the incoherent signal which is attributed to the self-noise. It can be seen from this estimate of the self-noise that it is critical to have well-described transfer functions for both instruments i and j. Since the transfer functions are used in the calculation, errors in the transfer function will produce errors in the self-noise estimates of the instrument. This method was originally proposed by Holcomb (1989), who later characterized error sources (Holcomb 1990). In the latter work, Holcomb also suggested alternative two-sensor methods, under the assumptions that the two sensors... 

Seismometer Self-Noise and Measuring Methods, Fig. 4 Self-noise estimate of the Geotech GS-13 geophone using a theoretical seU-noise model blue) versus the estimated low seh-uoise model of the Geotech GS-13 (red) from 11 seU-uoise... 

It is also important to isolate the instruments from non-seismic noise sources (e.g., temperature variations, pressure variations, locally induced tilt). These noise sources can increase the self-noise estimate of the individual instruments as they generally do not respond coherently to such sources (Anderson et al. 2012). Misalignment of the horizontal components can... 

Seismometer Self-Noise and Measuring Methods, Fig. 6 Self-noise estimates from three horizontal very broadband Metrozet M-2166 seismometers (flat to velocity from 0.0028 tolO Hz) using Sleeman (Sleeman et al. 2006) three-sensor self-noise estimate (solid lines). Single-sensor estimates are in dotted lines. In order to minimize incoherent tilt noise, all three instruments were... 

Tasic 1, Runovc F (2012) Seismometer self-noise estimation using a single reference instrument. J Seismol 16 183-194... 

---