Noise Calculations

We keep learning more about the history of noise calculations. It seems that the topic of the noise of a spectrum in the constant-detector-noise case was addressed more than 50 years ago [1], Not only that, but it was done while taking into account the noise of the reference readings. The calculation of the optimum absorbance value was performed using several different criteria for optimum . One of these criteria, which Cole called the Probable Error Method, gives the same results that we obtained for the optimum transmittance value of 32.99%T [2], Cole s approach, however, had several limitations. The main one, from our point of view, is the fact that he directed his equations to represent the absorbance noise as soon as possible in his derivation. Thus his derivation, as well as virtually all the ones since then, bypassed consideration of the behavior of noise of transmittance spectra. This, coupled with the fact that the only place we have found that presented an expression for transmittance noise had a typographical error as we reported in our previous column [3], means that as far as we know, the correct expression for the behavior of transmittance noise has still never been previously reported in the literature. On the other hand, we do have to draw back a bit and admit that the correct expression for the optimum transmittance has been reported. 

Checking for the absence of photometric noise by using a suitable reflectance standard (e.g. white reflective ceramic tiles or reflective thermoplastic resins, such as Teflon). The reflectance standard should be scanned in accordance with the recommendations of the spectrophotometer s manufacturer and peak-to-peak photometric noise calculated over a specified wavelength region. The amount of photometric noise should be consistent with the spectrophotometer specification. ... 

In recent years questions with regards to noise from Safety Relief Valves (SRVs) have been increasing. Until not so long ago, end users only required noise calculation on control valves. SRVs were considered silent sentinels that opened only very occasionally - or preferably never. This, however, changed several years ago, primarily for four reasons ... 

Luckily, most current SRV sizing programs include a noise calculation. However, it is perhaps interesting to know in detail some methods used in the industry. Standard methods are available for calculation of valve noise heard at a certain distance. 

Different papers have been written on this subject, but the reality is that SRV noise calculation is very complex because ... 

Using the spectra obtained in question 4, and assuming no noise, calculate the data matrix that would be obtained. Perform PCA on this matrix and explain why there are considerable differences between the results using this design and the earlier design, and hence why this design is not satisfactory. 

We realize that, as for the DM noise calculation, from the viewpoint of the noise envelope and its required attenuation, only the fundamental harmonic really counts. The current caused by this is... 

Most mass spectrometers suffer from white noise (Johnson noise and shot noise), RF interference (i.e., radio stations, fluorescent light ballast supplies, switching power supplies, quadrupoles, etc.), and chemical noise (chemical interference peaks). Generally, the noise level reported for signal/noise calculations should be reported as root-mean-square (RMS) of the white noise, but this value can sometimes be difficult to determine if the experiment has much chemical noise. RF noise is not usually dense enough to be a major problem. Regardless, if SNR values are reported, it is important to report exactly how noise is calculated. 

How big can a vacuum gap be for tunnel current to be detected This depends upon the bandwidth required aud the iuput capacitauce of the device recording the current. For example, if this input capacitauce was 1 pF (a small value, quite hard to achieve) and the required baudwidth. A/ was 5 kHz, theu the curreut-to-voltage couverter equivaleut resistauce could uot be larger thau 3 x 10" Q (calculated from aRC= 1 at the -3 dB point of 5 kHz). The associated Johnson noise, calculated from... 

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