In chromatography software as Chromgate, Chrom Perfect, and others, we will usually find a function time constant or smoothing or perhaps the filter parameters with different name on other software, especially on the menus or function associated with the detector.
By the time we run the method for chromatography data acquisition, these parameters will be sent (upload) by software to HPLC detector of interface box to activate the DSP (digital signal processing) and/or microprocessor or mathematical procedure in software with the parameters specified filters.
These parameters can be set also manually through the digital menu on detector used in HPLC system such as UV-Detector, RI-Detector, Fluorescence detector, and others.
To understand these functions, the following will be explained in a simple sense of time constant or smoothing or filter, contained in software/firmware.
Frequency of peak and sinusoidal wave.
Frequency is the number of waves that occurs in unit of time. The figure below can help us in understanding the concept of simple frequency.
Figure 1. Example of sinusoidal waves.
In the example above, there are 12 wave that occurred within 5 minutes, meaning that the wave frequency is 2.4 per minute, or normal expressed in Hertz: 12/ (5x60) = 0.04 Hertz.
Figure 2. Magnification image of the sine wave in figure 1, it was obvious tha the wave 1 takes about 0.41 minutes or 25 seconds, so that may be expressed f=1/25=0.04 Hz.
Once we understand the concept of frequency, then we can assume the peak in the chromatogram can also be expresses in terms of frequency, and determining the frequency of the same magnitude, the time required for one peak (one wave) can be expressed in terms of Hertz.
Figure 3. Peak width of about 0.25 minutes (15 seconds), f=1/15=0.07 Hz.
The picture above is an example of a chromatographic peak obtained from the analysis by using HPLC, if we “overlay” Figure 3, with a sine wave, then the image will be obtained as follows:
Figure 4. Overlay peak in chromatography with a sine wave.
In figure 4, it was obvious that a peak can be assumed as a sinusoidal wave. Peak in HPLC chromatogram (isocratic HPLC system) will usually be narrow at the beginning of the retention time, while the peak appearing at longer retention will be more broadly. Thos mean that the frequency of peak in the chromatogram is not constant, but varies, usually between 0.1-0.01 Hz, or about 10-100 seconds peak width as shown below:
Figure 5. Example of peaks in the chromatogram.
Noise in the chromatogram.
Noise term was originally derived from a radio technique which mean the existence of unwanted signals, which signal the static sounds in the ears (hiss). In development, the world of science and engineering describe the noise as fluctuation (signal) obtained randomly from the observed continues signal.
Noise in the chromatography may arise from various sources. Pressure fluctuation of HPLC pump typically can provide periodic noise, while noise from electronic components usually are random. The following (Figure 6) is an example of noise in 2 overlay with sinusoidal waves with frequency 10 Hz and 0.4 Hz.
Figure 6. Examples of noise signal on chromatography and we can see correlation both signal with sine wave on top.
In the picture above, look carefully noise waves, we can see the pattern on the two sine wave on top of it. Depending on the way we see, we can assume noise similar with one or two sinusoidal waves on it.
Low Pass Filter.
How filtering works is by reducing the specific frequency on a signal. Generally low pass filter can pass (no filter) peaks in the chromatogram, due the peaks has a low frequency, while signal with high frequency (noise) filtered.
Noise filtering is not possible if there is no difference in frequency between signals (peaks) and noise, as good as any low pas filter that we use, hardware or mathematical formulas.
Passive analog filter made of capacitors and resistors, while the active filter components are made by using the op-amp IC’s (operational amplifier). While the digital filter can be made with the formulation/mathematically procedure in microprocessor or software to process the acquired signals.
Filter Hardware.
In the old of HPLC detectors (analog) there is usually an analog low pass filter by using a series of resistors capacitors.
Figure 7. RC low pass filter.
Order of the filter can be seen from the number of its RC circuit. For example, if a filter has order 4th, there are 4 RC circuit that is placed in series. In the 4th order filter, the signal coming filtered by first filter, then fed to the next filter until 4th filter. At this screening stage, will be much reduced signal due to the resistor components.
Unlike the case with active low pass filter, which is used operational amplifiers as its main component, thus reducing the main signal (not noise) can be avoided.
Digital filter (mathematically procedure in software/firmware).
In the development of electronics, there were already microprocessor with extraordinary ability in executing instructions per unit time, the digital filter alternative to replace the filters are made in the form of hardware (either passive or active filters).
How is work (average filter) can be explained mathematically, the data of N will averaged to generate new data. For example average filter output Y[80] (80th data) of 5 points data calculated from data points between X[80] to X[84] can be described mathematically as:
X[80]+X[81]+X[82]+X[83]+X[84]
Y[80] = ----------------------------------------------------
5
Any input data will have weighting factor 0.2. In the world of DSP (Digital Signal Processing) in more complex, used a mathematical equation that is more complicated to calculate the data output Y[n] from average filter with formula as follow:
Y[n] = a0X[n]+a1X[n-1]+a2X[n-2]+a3X[n-3]+…
note the difference with the previous formula, in this formula, each data point has different weighting factor. The sum of all weighting factor a 0..n should be = 1. Because of this reason, DSP has a delay in processing the data, to generate a required data from appeared earlier data’s.
There are many mathematical formulations (name for the person who formulates it) for the purposes of digital filter, among others: Bessel, Chebychev, Savitsky, Hamming, etc.
Represents the filter characteristics.
There are many several ways to describe the characteristics of filter. Among the most widely used is the amplitude response plot, where this plot will provide important information from a filter, among others cut-off frecuency. For example, We will use 0 to 1 Hz frequency signal, which we consider signals with frequency above 1 Hz is the noise. Then the ideal filter for our purposes can be describe as below:
Figure 8. Plot of amplitude response of a low pass filter with the ideal 1 Hz cut-off frequency.
Inthe picture above, the signal with a frequency between 0 to 1 Hz will be passed, while the signal with frequency more than 1 Hz be arrested/filtered. In practice no filter will be found to be perfect as the picture above, the plot will be seen a gradual decline in higher frequencies. Cut-off frequency obtained at the time of the output signal amplitude 70% of the amplitude input signal, which is known as the 3dB point.
Figure 9. Plot of amplitude response of low pass filter with cut-off frequency of 1 Hz. A = 2 poles, B = 4 poles, and C = 8 pole using Bessel filter.
In the picture 9 shows that the number of poles is very important to determine the characteristics of the filter. A filter will be nearly perfect if the number of poles is higher. In analog electronic circuits, pole number indicates the number of install filter circuit in series, as follow:
Figure 10. Six poles Bessel active filter.
Digital filter do not have a pole, but was characterized by number of input data used to calculate the new data output. For example, to generate data Y[1] of 9 input data used the digital filter (Savitzky-Golay) as follows:
Y[1] = -0.090909091 X[1] + 0.060606061 X[2] + 0.168831169 X[3] +
0.233766234 X[4] + 0.255411255 X[5] + 0.233766234 X[6] +
0.168831169 X[7] + 0.060606061 X[8] + -0.090909091 X[9]
It should be noted that the sum of all coefficients is 1. Y[n] is the output data, while X[n] is the processed input data. In general, the performance of the digital filter would be better if more input data processed, but also required the microprocessor/microcontroller with the ability to calculate per unit time is very high.
Filter application in HPLC detector firmware.
In the chromatogram when the noise frequency is different from signal/peak frequency, then based on the previous explanations, we can derive the noise can be muted. By using the correct setting value (cut-off frequency), noise can be attenuated so as to raise the ratio of signal to noise (S/N). Please note once again, that any clever mathematics formula, low pass filter can be apply only if the noise frequency is higher than the frequency of peak/signal.
Figure 11. Filter application on chromatogram.
In the picture above, from to bottom, the filter seting 0.5, 0.02, and 0.002 Hz (or can be expressed as 2, 50 and 500 seconds). Existing narrow peaks at beginning of the chromatogram will change at the filter value 0.005 Hz, while a larger peak barely visible change. Details noise reduction can be seen in the left of figure 11.
In HPLC Detectors, noise filter works well when the ratio S/N is high, without interfering of peak shape itself, the hard part is if the frequency of signal/peaks close to noise frequency.
Depending on the detector manufacturer, usually they recommend the setting of filter value (cut-off frequency) as follows:
KNAUER
Time constant = 1/10 (broad peak) in seconds.
ANTEC LEYDEN
Filter setting = 1/(2 x Peak Width) in seconds.
So for the peak with a width of 10 seconds, the time constant is chosen should be:
KNAUER
Time constant = 1 sec, its mean: Cut-off frequency = 1 Hz.
Antec Leyden:
Filter = 0.05 Hz (20 sec), its mean : Cut-off frequency = 0.05 Hz.
Filter/time constant parameter need to find to be applied in an optimum chromatogram, a peak that is not our target is missing/changed form that appears as noise can be minimized.
In the development of technology, filter value can be programmed according to the time that we want (time event program), because usually the earlier peaks frequency different with the peaks at the end of chromatogram.
Example chromatograms are applying a filter as follows:
Figure 12. Chromatogram using filters to raise the S/N ratio.
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