520 Chapter 8. Signal Processing
D.1 DetectorSignal.........................
Enhancing the detector signal is one way of increasing the signal to noise ratio. For
example in a PMT the primary photoelectron is multiplied several thousand times
resulting in a large pulse at the anode. This certainly increases the statistical noise
as well but by a lower factor since the statistical noise increases by the square root
of the signal. Neglecting any other noise source, the signal to noise ratio for a signal
of heightNis given by
S/N=N
√
N
=
√
N.
D.2 FrequencyFilters........................
All detection systems contain more than one sources of low frequency noise. Let us
seewhatwecandotoincreasethesignaltonoiseratioinsuchsystems.
Using Band Pass Electronic Filters:Consider a system in which the most
dominant noise has the 1/f behavior. Eliminating sources of such a noise
can be quite challenging since some of them may depend on the design of the
electronics components. In such a situation, a preferable solution is to work
at higher frequencies, if of course the physical detection processes allow that.
Working at higher frequencies requires that the low frequencies are somehow
blocked at some point in the system. This can be done by using ahigh pass
filter, which is an electronic circuit that allows only low frequencies to pass
through. Similarly one can also block higher frequencies using alow pass filter.
In most of the systems, however, it is desired to filter both low and high
frequencies, something that can be achieved by thebandpass filters.Using Software Filters:It is also possible to block certain frequencies in a
system through software. Modern systems are generally hooked to a powerful
central processing unit (CPU), that can perform millions of mathematical op-
erations in a second. It is therefore possible to perform the filtering operations
onlineprovided the CPU is able to handle it. If online processing is not pos-
sible then of course the data can also be filtered offline later on. A commonly
used method of online filtering is through the Fourier Transform of the data.
The steps generally taken are outlines below.
1.Step-1:Take Fast Fourier Transform (FFT) of a block of data. Most of
the FFT algorithms require data points to be exactly 2nin number (n
being an integer) and at least 1024.
2.Step-2:Find peaks in the Fourier spectrum. This can be done by any peak
finding algorithm. These peaks correspond to the dominant frequency
components in the system. For example in a poorly grounded system the
60 Hzpower line noise creeps into the signal and one should see a peak at
60 Hzin the Fourier spectrum of the data.
3.Step-3:Eliminate the peaks by using some interpolation scheme. Gener-
ally it suffices to use the mean baseline value of the output to replace the
peaks.
4.Step-4:Take inverse FFT to obtain the filtered data values.