Signal-to-Noise Enhancement Exercise #1

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Introduction

Exercise #1 is designed to familiarize the student with the effect of noise on the detectability of a signal. This exercise is designed to be completed with the Signal Noise Exercise spreadsheet. This spreadsheet allows the user to create an ideal chromatographic separation containing up to three peaks, which represent three different compounds.

The height of each peak is proportional to the amount of analyte being separated. A noise component may be added to the ideal separation in order to simulate data that could be acquired in an actual separation.

Table of Spreadsheet Parameters

The table below describes all of the parameters on the spreadsheet needed to complete the exercise below. Parameters with a light yellow background may be adjusted. Parameters with a light green background may not be adjusted.

Parameter	Definition
S/N (signal-to-noise ratio)	This figure of merit indicates the magnitude of the signal with respect to the noise level at the 95% or 99% confidence level.
Peak Intensity	This value controls the height of the analyte peak. A value of zero indicates no analyte present.
Mean	This value controls the position of the maximum peak intensity. Values are restricted between 0.5 to 4.5 minutes
Standard Deviation (Std Dev)	This value controls the width of the peak. Values are restricted between 0.001 and 0.250 minutes
Noise	This value controls the amount of noise added to the plot. Since it is based on Excel's RAND function, it appears as high-frequency noise superimposed on the analyte peaks. This is also known as the peak-to-peak noise.
Offset	This value is used to raise or lower the baseline of this plot. It is most effective when the plot has large peaks on a noiseless baseline.
RMS Noise	This value is the magnitude of the noise (Max Signal — Min Signal) divided by 5.16 or 3.92 (±zσ), where z = 2.58 or 1.96 (99% or 95% confidence level). Dividing the RMS noise into the peak intensity provides the S/N for that analyte.
Peak + Noise	This cell represents the sum of the peak intensity and the superimposed noise.

Part 1: Spreadsheet Orientation

Familiarize yourself with the Signal Noise Exercise spreadsheet. Observe changes to the plot when:
1. The peak parameters are adjusted (peak intensity, mean, standard deviation)
2. The magnitude of the noise is increased from zero
3. The magnitude of the offset is increased from zero
Answer the following questions
1. Which parameter(s) control the signal level?
2. Which parameter(s) control the noise level?
3. Which parameter(s) or concept(s) control the character of the instrumental response?

Part 2: Evaluating Baseline Noise

Start with a flat baseline by eliminating all traces of signal and noise.
1. How would you accomplish this?
2. Which parameter would you adjust if you can’t see the flat baseline?
Calculating Noise Magnitude
1. Based on the discussion of noise in this e-module, if the peak-to-peak noise (V_N) is 1.0 μV, calculate the RMS Noise at the 99% confidence level.
2. Increase the noise level to 1.0 μV on the spreadsheet and look at the RMS Noise. Does your answer agree with the spreadsheet?
3. Repeat the RMS Noise calculation at the 95% confidence level. Is the RMS Noise smaller or larger? Explain this difference based on your knowledge of population distributions.

Part 3: Evaluating Signal-to-Noise Ratios

Enter the following signal parameters into the Signal Noise Exercise spreadsheet
1. Peak 1
  1. Peak Intensity = 10 μV
  2. Mean = 1 minute
  3. Standard Deviation = 0.1 minute
2. Peak 2
  1. Peak intensity = 5 μV
  2. Mean = 2 minutes
  3. Standard Deviation = 0.1 minute
3. Peak 3
  1. Peak Intensity = 1 μV
  2. Mean = 3 minutes
  3. Standard Deviation = 0.1 minute
Change the peak-to-peak noise level on the spreadsheet to 1.00 μV.
1. Look at the S/N ratio for each peak and determine which peaks are below the detection limit (S/N < 3)
2. Record the "Peak+Noise" magnitude for each peak.
3. Obtain replicate data by pressing F9 to refresh the spreadsheet. Record the new magnitude for each peak.
4. For each analyte peak, calculate the percent relative error range and average percent relative error introduced by adding 1.00 μV peak-to-peak noise to the simulated signal.
5. As the S/N decreases, comment on any trends regarding the effect of noise on the accuracy and precision of the signal
Increase the peak-to-peak noise level on the spreadsheet to 5.00 μV and determine which peaks are now below the detection limit.
Based on your results, what role would signal-to-noise enhancement have in analyte detection?