Ep 18 — Spectral Processing Basics: Baseline Correction, Smoothing, Normalization

Series: Infrared Spectroscopy Encyclopedia: From Principles to Practice
Section: Part 2 · Elementary — Entering the Lab
Target Audience: High school/undergraduate/graduate students, lab technicians entering the lab
Prerequisites: Ep 16 (Sample Preparation), Ep 17 (Instrument Operation)
Reading Time: ~38 minutes

Introduction: Thoughts Triggered by an "Ugly" Spectrum

Intern Xiao Wang just completed her first KBr pellet spectrum. Excitedly, she printed it and handed it to her supervisor. The supervisor frowned: "This spectrum—baseline tilted by 0.5, noisy, and a distinct shoulder peak… how can this be used?"

Xiao Wang said meekly, "But I just turned on the instrument, collected the background, and followed the preparation protocol…"

The supervisor sighed: "The 'raw' spectrum output by the instrument is never the 'final' spectrum. A raw spectrum is like a rough gemstone that needs to be 'polished' to reveal true beauty—but over-polishing can ruin the original stone."

This is the "Spectral Processing" stage of infrared spectroscopy—a critical step between raw data and final analysis. Processed well, the spectrum is clear, readable, and suitable for quantitative and qualitative analysis; processed poorly, not only is the data unusable, but it can also introduce "false peaks" that mislead conclusions [1][2].

The core objectives of spectral processing can be summarized in four points: Denoise, Deform, Normalize, Resolve [1][2][3]:

• Denoise: Smoothing and filtering to improve SNR
• Deform: Baseline correction to eliminate scattering and absorption deviations
• Normalize: Normalization to make spectra comparable
• Resolve: Derivative to separate overlapping peaks

But every process comes at a cost—over-processing distorts the spectrum and can even create 'false peaks' that were not originally present [1][2]. This episode systematically explains the principles, parameter selection, application scenarios, and risks of the four major processing methods, enabling you to master the art of "just the right amount" of processing.

💡 Episode Focus: Ep 17 taught you how to acquire a spectrum; this episode teaches you how to "make the spectrum look good and usable." Ep 19 and Ep 20 then cover qualitative and quantitative analysis based on processed spectra.

1. Why Spectral Processing is Needed?

In an ideal world, FTIR spectra would have clean bell-shaped peaks and a flat baseline. But reality is never ideal. Raw spectra typically have the following issues [1][2][3]:

1.1 Baseline Tilt and Curvature

Causes [1][3][4]:

• Sample scattering: Rayleigh/Mie scattering due to particles or uneven pellets
• KBr moisture absorption: Water ghost peaks at 3400 and 1640 cm⁻¹ drag down the overall baseline
• CO₂ interference: The 2350 doublet not fully subtracted
• Instrument drift: Changes in source and detector temperature
• Sample residue: Residuals in liquid cells or ATR crystals

Typical manifestation [1][3]:

Absorbance
   ↑
1.5│   ▓▓                 ▓▓▓▓▓ ▓▓   ← High wavenumber baseline high
1.0│   ▓▓▓               ▓▓▓▓▓▓▓    
0.5│   ▓▓▓▓▓▓▓▓▓      ▓▓▓▓▓▓▓▓▓▓▓  
0.0│────────────────────────────→ ν
   4000  3000  2000  1000  500
           ←─────tilt─────

Figure 1: Typical baseline tilt spectrum (baseline higher on left or right, or vice versa)

1.2 High Noise

Causes [1][2][3]:

• Insufficient number of scans (poor SNR)
• Detector noise (MCT warming up, DTGS aging)
• Unstable source
• High resolution (weak signal)

Typical manifestation [1][3]: High-frequency jitter in the spectrum; weak peaks buried in noise

1.3 Non-comparable Intensities

Causes [1][3]:

• Different sample amounts in preparation (KBr pellet sample amount, ATR contact pressure)
• Different optical path lengths in liquid cells
• Different instruments or conditions
• Measurements taken at different times

Typical manifestation [1][3]: Two measurements of the same sample show a factor of 2 difference in overall intensity.

1.4 Peak Overlap

Causes [1][3]:

• Complex samples (multicomponent mixtures)
• Similar functional groups (e.g., different C=O)
• Broad peaks masking narrow peaks

Typical manifestation [1][3]: A single broad peak that actually consists of two overlapping peaks.

2. Baseline Correction

Baseline correction is the first step in spectral processing, aimed at eliminating baseline drift not due to sample absorption [1][3][5].

2.1 Physical Nature of Baseline Drift

Scattering Model [1][3][4]:

$$A_{\text{measured}}(\nu) = A_{\text{sample}}(\nu) + A_{\text{baseline}}(\nu) + A_{\text{noise}}(\nu)$$

Where:

• $A_{\text{sample}}(\nu)$: Pure sample absorption (desired part)
• $A_{\text{baseline}}(\nu)$: Baseline drift (to be subtracted)
• $A_{\text{noise}}(\nu)$: Noise

Two Main Forms of Baseline Drift [3][4]:

① Linear Tilt:
$$A_{\text{baseline}}(\nu) = a \cdot \nu + b$$

• Causes: Broad scattering (particles), uneven KBr

② Curved:
$$A_{\text{baseline}}(\nu) = a \cdot \nu^2 + b \cdot \nu + c$$

• Causes: Mie scattering (particle size close to wavelength), refractive index variation near strong absorption bands

2.2 Polynomial Fitting Baseline Correction

Method [1][3][5]:

1. Select "peak-free" regions in the spectrum (baseline points)
2. Fit these baseline points using a polynomial
3. Subtract the fitted curve from the raw spectrum

Polynomial Order Selection [3][5]:

Table 1: Polynomial order selection guide (compiled from [3][5])

Tips for Manual Baseline Point Selection [3][5]:

• Choose regions without significant absorption peaks (e.g., 2200–2500 cm⁻¹ usually has no peaks)
• At least 5–10 points covering the full spectrum
• Avoid CO₂ (2350 cm⁻¹) and water vapor (3400, 1640 cm⁻¹) regions

2.3 Rubber Band Algorithm

The Rubber Band algorithm is the default baseline correction method for Bruker OPUS [5][6]:

Principle [5][6]:

1. Find the "convex hull" of the spectrum
2. Stretch an "elastic band" from below to tighten the spectrum
3. The band automatically attaches to the lowest points
4. The band curve becomes the baseline

Advantages [5][6]:

• Automated, no manual point selection required
• Suitable for complex curved baselines
• Minimal effect on peak shapes

Disadvantages [5][6]:

• May misinterpret broad peaks (e.g., O-H 3400 cm⁻¹) as baseline
• Requires setting a "Rubber Band threshold" parameter

2.4 Other Baseline Correction Methods

① Asymmetric Least Squares (ALS) [5][7]

• Modern baseline correction algorithm
• Insensitive to broad peaks
• Suitable for complex spectra

② ModPoly [5]

• Iterative polynomial fitting
• Automatically excludes peaks, retaining only baseline

③ Polygonal Baseline [3]

• Polygonal baseline (manual point selection)
• Flexible but subjective

2.5 Pitfalls of Baseline Correction

Pitfall 1: Over-correction [1][3][5]

• Polynomial order too high → fits to peak tops, "cutting off" peak intensity
• Manifestation: Peaks become narrower, shorter; quantitative distortion

Pitfall 2: Misinterpreting Broad Peaks as Baseline [5]

• Broad peaks (e.g., O-H 3400, N-H 3300 cm⁻¹) may be mistaken as baseline by Rubber Band
• Solution: Manually select baseline points while avoiding broad peak regions

Pitfall 3: CO₂ Peaks Not Subtracted First [1][3]

• The sharp 2350 doublet can be "dug out" by polynomial, creating false peaks
• Solution: First use CO₂ subtraction function

⚠️ Golden Rule of Baseline Correction: First examine the raw spectrum, understand the baseline shape, then correct. Do not "one-click apply" algorithms [1][3].

3. Smoothing

Smoothing aims to reduce high-frequency noise and improve SNR [1][2][3].

3.1 Mathematical Nature of Smoothing

Moving Average (the simplest smoothing) [3]:

$$A'(\nu_i) = \frac{1}{2m+1} \sum_{j=-m}^{m} A(\nu_{i+j})$$

where $2m+1$ is the window width. For example, when $m=2$, each point is averaged with the two points before and after (total 5 points) [3].

Problems [3]:

• Smoothing = low-pass filtering
• Noise (high frequency) is removed
• But narrow peaks (also high frequency!) are also "smoothed out"
• Narrow peaks become broader and shorter

3.2 Savitzky-Golay Filter

Savitzky-Golay filter (SG filter) is the most common smoothing method for infrared spectra, proposed by Savitzky and Golay in 1964 [3][8][9].

Principle [3][8][9]:

• Fit a polynomial within the window
• Take the midpoint value of the polynomial as the smoothed value
• Balancing smoothing and shape preservation

Two core parameters [3][8][9]:

① Window Size:

• Odd numbers: 5, 7, 9, 11, 13...
• Too small (5): limited smoothing effect
• Too large (> 15): peaks are severely distorted
• Recommended: 9 or 11

② Polynomial Order:

• 2 (quadratic): default recommendation
• 3–4: better shape preservation, but weaker smoothing
• Recommended: 2 or 3

SG filter formula [3][8]:

$$A'(\nu_i) = \sum_{j=-m}^{m} c_j \cdot A(\nu_{i+j})$$

where $c_j$ are SG convolution coefficients, determined by the polynomial order and window width [3][8].

3.3 Comparison of Smoothing Effects

Original spectrum (high noise):

Absorbance
0.5│   ··  ··  ···  ··  ···  ··  ← high noise
0.3│   ··  ··  ···  ··  ···  ··  
0.1│   ··  ··  ···  ··  ···  ··  
0.0│────────────────────────────→ ν

After SG smoothing (window 9, order 2):

Absorbance
0.5│      ▓▓       ▓▓▓           
0.3│   ▓▓  ▓▓  ▓▓  ▓▓▓  ▓▓▓     
0.1│   ▓▓  ▓▓  ▓▓  ▓▓▓  ▓▓▓     
0.0│────────────────────────────→ ν
   ← Noise greatly reduced, peak shape preserved →

Oversmoothing (window 21, order 2):

Absorbance
0.5│        ▓                    
0.3│        ▓▓   ▓              
0.1│   ▓▓▓▓▓▓▓▓▓▓▓▓▓▓           
0.0│────────────────────────────→ ν
   ← Peaks become shorter and broader, small peaks disappear →

Figure 2: Spectrum comparison under different smoothing parameters

3.4 Risk of Smoothing: Creating "False Peaks"

Sinc oscillations (Gibbs phenomenon) [3][5]:

• At the edges of strong peaks, excessive smoothing can produce oscillating "ghost peaks"
• They look like real small peaks, but are mathematical artifacts

Identification [3][5]:

• Real peak: stable position, reasonable width
• False peak: position at the edge of a strong peak ±20 cm⁻¹, abnormally narrow width

Countermeasures [3][5]:

• Do not oversmooth (window < 15)
• Compare before and after smoothing to confirm peak positions remain unchanged
• Use SG order ≥ 2 to avoid excessive distortion

3.5 Alternative: Increase Number of Scans

Important principle [1][3]: Smoothing is "remedy after the fact", not as good as "prevention before the fact". If the spectrum SNR is poor, prioritize increasing the number of scans rather than oversmoothing.

Table 2: Comparison of SNR improvement methods (compiled from [1][3])

💡 Professional advice: Increase scans until SNR > 1000:1 before considering smoothing. When SNR is already sufficient, do not smooth just for "aesthetics" [1][3].

IV. Normalization

Normalization aims to make spectra "comparable" — spectra from different samples, times, or conditions can eliminate intensity differences through normalization [1][3].

4.1 Maximum Normalization

Method [3][5]:

1. Find the absorbance of the spectrum's strongest peak $A_{\text{max}}$
2. Divide all data points by $A_{\text{max}}$

$$A'(\nu) = \frac{A(\nu)}{A_{\text{max}}}$$

Advantages [3]:

• Simple
• Convenient for visual comparison

Disadvantages [3]:

• The strongest peak may not be a meaningful reference peak
• Different samples may have different "strongest peaks", leading to inconsistent normalization baselines

4.2 Peak Area Normalization

Method [3][5]:

1. Calculate the total integrated area of the spectrum
   $$S = \int A(\nu) \, d\nu$$
2. Divide all data points by $S$
   $$A'(\nu) = \frac{A(\nu)}{S}$$

Advantages [3]:

• Not affected by the intensity fluctuation of a single peak
• Suitable for multi-component comparison

Disadvantages [3]:

• Heavily influenced by baseline (high baseline leads to inflated area)
• Requires baseline correction first

4.3 Internal Standard Normalization

Method [3][5]:

1. Add a known amount of internal standard (e.g., KSCN at 2050 cm⁻¹)
2. Normalize using the internal standard peak intensity
   $$A'(\nu) = \frac{A(\nu)}{A_{\text{standard}}}$$

Advantages [3][5]:

• Gold standard for quantitative analysis
• Eliminates sample preparation errors (e.g., KBr pellet thickness)

Disadvantages [3]:

• Requires an internal standard
• The internal standard peak must not overlap with sample peaks

4.4 ATR Correction (a Type of Normalization)

ATR correction is essentially a wavenumber-dependent normalization aimed at eliminating the morphological differences between ATR and transmission spectra [3][5][10].

Principle [3][10]:

In ATR spectra, peak intensity is proportional to penetration depth $d_p \propto \lambda \propto 1/\nu$:

$$A_{\text{ATR}}(\nu) \propto \frac{1}{\nu}$$

Correction formula [3][10]:

$$A_{\text{corrected}}(\nu) = A_{\text{ATR}}(\nu) \cdot \nu \cdot \frac{\nu_{\text{ref}}}{\nu_{\text{ref}}} = A_{\text{ATR}}(\nu) \cdot \nu$$

Actual algorithms also include refractive index correction (to eliminate peak shifts caused by anomalous dispersion) [3][10].

Correction effect [3][10]:

Table 3: Intensity ratios of ATR to transmission spectra before and after correction (polystyrene data, references [3][10])

After correction, all peak intensity ratios are close to 1.0, essentially consistent with transmission spectra [3][10].

🔗 Further reading: Detailed peak positions for polystyrene and alkyl C-H can be found at ftir.fun alkyl C-H functional group page.

4.5 Application Scenarios for Normalization

| Multicomponent Analysis | Peak Area Normalization |
| KBr Pellet Quantification | Internal Standard Normalization (KSCN) |
| ATR vs. Transmission Comparison | ATR Correction |
| Time Series Monitoring | Internal Standard or Fixed Parameters |

Table 4: Application scenarios of normalization methods (Compiled from [1][3][5])

5. Derivative

Derivative is a powerful tool for resolving overlapping peaks [1][3][11].

5.1 First Derivative Spectrum

First derivative [3][11]:

$$D_1(\nu) = \frac{dA(\nu)}{d\nu}$$

Properties [3][11]:

• Peaks in original spectrum → zero-crossing points in first derivative
• Shoulders in original spectrum → peaks in first derivative
• First derivative crosses zero at original peak position, with maximum positive on the left and maximum negative on the right

Advantages [3][11]:

• Completely removes constant baseline
• Removes linear tilted baseline
• Enhances visibility of shoulder peaks

Applications [3][11]:

• Finding hidden peaks
• Precise peak position determination (zero-crossing points)

5.2 Second Derivative Spectrum

Second derivative [3][11]:

$$D_2(\nu) = \frac{d^2A(\nu)}{d\nu^2}$$

Properties [3][11]:

• Peaks in original spectrum → negative peaks in second derivative
• Overlapping peaks in original spectrum → separated negative peaks in second derivative
• More sensitive to peak shape changes than first derivative

Advantages [3][11]:

• Resolves overlapping peaks: narrow peaks under broad peaks become visible
• Removes baseline and linear tilt (more thoroughly)
• Enhances shoulder peak identification

Example: Protein amide I band analysis [11][12]

• 1650–1700 cm⁻¹ overlaps multiple secondary structure peaks (α-helix, β-sheet, turn)
• Original spectrum: a broad peak, unclear details
• Second derivative: separates multiple negative peaks corresponding to different secondary structures

5.3 Savitzky-Golay Derivative

Direct numerical derivation amplifies noise [3][11]. Savitzky-Golay derivative combines smoothing and differentiation:

Principle [3][8][11]:

• Fits a polynomial within a window
• Differentiates the polynomial directly
• Both smooths and differentiates, SNR-friendly

Parameters [3][11]:

• Window width: 9–15
• Polynomial order: 2–4
• Derivative order: 1 or 2

5.4 Risks of Derivative

① Noise amplification [3][11]

• Derivatives are sensitive to high-frequency noise
• Must use SG derivative, not direct numerical differentiation

② False peaks [3][11]

• Derivative oscillations appear at the edges of original peaks
• Resemble small peaks but are mathematical artifacts
• Countermeasure: compare first and second derivatives to identify real peaks

③ Difficulty in intensity interpretation [3][11]

• Derivative peak intensity does not directly correspond to original peak intensity
• Cannot use derivative peak height for quantification (peak height ratios may be reversed)

⚠️ Golden rule of derivative: Derivative is an "identification tool" not a "quantification tool". Used for peak finding, not for quantification [3][11].

6. Other Common Processing

6.1 CO₂ Removal

The 2350 cm⁻¹ CO₂ doublet often remains due to CO₂ concentration differences between background and sample collection [1][3].

Removal methods [3]:

• Software "CO₂ Removal" function
• Fit CO₂ standard spectrum to data near 2350 and subtract residual
• Also subtract CO₂ bending peak near 667 cm⁻¹

6.2 Water Vapor Removal

Similar to CO₂ removal [1][3]:

• Software fits water vapor standard spectrum
• Subtracts residual water peaks at 3400, 1640, etc.
• Suitable for KBr moisture absorption or environmental humidity changes

6.3 Truncation

Truncation: Remove noisy data at both ends of the spectrum [3]:

• e.g., truncate 4000–400 cm⁻¹ to 3800–450 cm⁻¹
• Removes ghost artifacts at boundaries

6.4 Peak Detection

Peak detection algorithms [3][11]:

• Threshold method (absorbance > a certain value considered a peak)
• Second derivative method (minima in D2)
• Curvature method

Output: peak position, peak height, peak area, full width at half maximum

7. Processing Workflow: From Raw to Finished

7.1 Standard Processing Workflow

Raw spectrum
   │
   ▼
1. Check spectrum quality
   │ SNR > 1000:1?
   │ Main peak 0.3–1.5?
   │ Water ghost peak < 0.05?
   │ CO₂ peak < 0.05?
   │
   ├─ Fail → Re-acquire spectrum (increase scans, change parameters)
   │
   ▼ Pass
2. Export data (save raw data separately)
   │
   ▼
3. CO₂ removal (if residual)
   │
   ▼
4. Water vapor removal (if residual)
   │
   ▼
5. Baseline correction
   │ Select algorithm (polynomial / Rubber band / ALS)
   │ Select baseline points (manual or automatic)
   │ Apply and check peak shape
   │
   ▼
6. Smoothing (if necessary)
   │ SG window 9–11, order 2
   │ Apply and compare peak positions
   │
   ▼
7. ATR correction (if ATR data)
   │
   ▼
8. Normalization (if needed for comparison)
   │ Maximum / Peak area / Internal standard
   │
   ▼
9. Derivative (if needed for resolving overlapping peaks)
   │ SG second derivative
   │
   ▼
10. Save processing parameters (store with raw data)
    │
    ▼
Processing complete

Figure 3: Standard spectrum processing flowchart (Compiled from [1][3][5])

7.2 "Honesty" Principles Before Processing

Key principles [1][3]:

• Always preserve raw data (do not overwrite original files)
• Processing parameters should be traceable (save processing history)
• Avoid processing for aesthetics (processing should be based on analytical needs)
• Export processing parameters (so others can reproduce)

7.3 "Honesty" Check After Processing

Check if processing is reasonable [1][3][5]:

• Compare spectra before and after processing; are peak positions consistent?
• Is peak width after processing reasonable? (not abnormally narrow)
• Have "new peaks" appeared? (false peaks introduced by processing)
• Is the second derivative reasonable? (no excessive oscillations)

⚠️ Warning against dishonest processing: When presenting spectra in papers or reports, processing parameters and how raw data were obtained must be stated. Hiding processing steps is unscientific [1][3].

8. Typical Processing Cases

Case A: Polymer KBr Pellet Spectrum Processing

Raw spectrum issues [1][3]:

• Tilted baseline (high at high wavenumbers, low at low wavenumbers)
• Water peak at 3400
• CO₂ doublet at 2350
• Moderate noise (SNR ≈ 500:1)

Processing steps [1][3]:

1. Check raw spectrum → main peak 0.8, SNR 500 → usable but needs processing
2. CO₂ removal → 2350 doublet disappears
3. Water vapor removal → 3400, 1640 reduced
4. Baseline correction (Rubber Band) → baseline flattens
5. SG smoothing (window 9, order 2) → SNR improves to 1500:1
6. ATR correction → not needed (transmission data)
7. Maximum normalization → main peak normalized to 1.0

Result: Clear, comparable spectrum suitable for qualitative identification and library search

Case B: ATR Protein Spectrum Processing

Raw spectrum issues [3][11]:

• Amide I band (1600–1700) is a broad peak, secondary structure not clear
• Aqueous solution background, strong water interference
• ATR data, morphology differs from transmission library

Processing steps [3][11]:

1. Water subtraction (using pure water background) → water peak reduced
2. Baseline correction (manual point selection, avoiding amide peaks)
3. SG smoothing (window 11, order 3) → SNR improved
4. ATR correction → morphology consistent with transmission library
5. SG second derivative (window 11, order 3, second order) → amide I band separates into multiple negative peaks

Result: Separated peaks for α-helix (1656), β-sheet (1632, 1685), turn (1670), etc. [11][12]

Case C: Quantitative Analysis Spectrum Processing

Goal: Quantitative determination of a component in KBr pellet

Processing points [1][3][5]:

• Do not smooth (avoid peak height distortion)
• Do not normalize (except internal standard normalization)
• Baseline correction: manual baseline point selection, polynomial order 2
• Peak area calculation: within fixed integration range (e.g., 1750–1700 cm⁻¹)
• Internal standard peak area: used to eliminate pellet thickness variation

Key [5]: Quantitative analysis must strictly fix the processing workflow, with identical parameters each time. Any variation affects quantitative results.

IX. Warnings of Overprocessing

9.1 The Birth of 'False Peaks'

Case: A novice repeatedly applies the following to a poor SNR spectrum:

1. Heavy smoothing (window 25)
2. Polynomial baseline (order 6)
3. Second derivative

Result [3][5]:

• The spectrum appears 'clean'
• But small peaks that do not originally exist appear
• These small peaks are mathematical artifacts

Verification [3][5]:

• Re-measure with higher quality data
• Real peaks will reappear
• False peaks will 'drift' with changing processing parameters

9.2 The Cost of 'Beautification'

Spectrum processing is similar to a 'beautifying camera' [1][3]:

• Moderate processing → spectrum clear and readable
• Excessive processing → looks pretty but distorted

Common symptoms of overprocessing [1][3][5]:

• Abnormally narrowed peaks (FWHM < 5 cm⁻¹)
• Appearance of 'sharp spikes' (possibly sinc oscillations)
• Baseline 'digging holes' (polynomial order too high)
• Second derivative plot 'all peaks' (noise amplification)

9.3 Processing by 'Subtraction'

Rather than 'adding' processing, perform 'subtraction' operations [1][3]:

Principle of subtraction:

• Instead of smoothing, increase number of scans
• Instead of high-order baseline correction, re-collect background
• Instead of normalization, use internal standard
• Instead of derivative peak discrimination, use higher resolution

Priority [1][3]:

1. Improve measurement (parameters, sample preparation) → first choice
2. Essential minimal processing (baseline, smoothing) → second choice
3. Advanced processing (derivation, normalization) → only when necessary

X. Comparison of Software Tools

10.1 Commercial Software

① Thermo OMNIC [1][4]

• Built-in baseline, smoothing, normalization, ATR correction
• Easy to use, good visualization
• Suitable for routine analysis

② Bruker OPUS [5][6]

• Rubber Band algorithm
• Powerful derivative functions
• Automatic peak detection

③ PerkinElmer Spectrum

• Similar to OMNIC
• Suitable for PerkinElmer users

④ Thermo TQ Analyst

• Designed specifically for quantitative analysis
• Supports multivariate statistics

10.2 Open Source Tools

① Python (NumPy + SciPy) [3]

• Fully controllable
• Suitable for research, custom algorithms
• Steep learning curve

Example code:

import numpy as np
from scipy.signal import savgol_filter

# Savitzky-Golay smoothing
smoothed = savgol_filter(spectrum, window_length=9, polyorder=2)

# Second derivative
d2 = savgol_filter(spectrum, window_length=11, polyorder=3, deriv=2)

② R (hyperSpec package)

• Strong statistical analysis
• Suitable for chemometrics

③ GNU Octave

• MATLAB alternative
• Free

④ Orange3

• Visual programming
• Suitable for non-programmers

Summary of This Chapter

Review Questions

1. You obtain a spectrum with SNR = 200:1, main peaks clearly visible, but small peaks are buried in noise. Design a processing workflow to improve SNR without distorting peak shapes. If instead you could improve instrument operation, what should be prioritized?

2. In the ATR spectrum of the same polystyrene sample, the peak at 698 cm⁻¹ is much stronger than that at 3082 cm⁻¹. Write the mathematical formula for ATR correction and explain why after correction the intensities become close to those in the transmission spectrum.

3. You suspect that a 'single peak' at 1700 cm⁻¹ in a spectrum is actually two overlapping peaks. Design a verification workflow using second derivative to discriminate peaks. How to distinguish real peaks from mathematical artifacts?

4. A quantitative analysis task requires measuring the intensity of the C=O peak at 1740 cm⁻¹. Explain why smoothing and peak area normalization should not be performed before quantitation? How should the spectrum be processed?

5. Write Python code to perform the following on an infrared spectrum in CSV format (two columns: wavenumber, absorbance): baseline correction (linear), Savitzky-Golay smoothing (window 9, order 2), and maximum normalization. Explain the principle of each step.

References

[1] Griffiths P R, de Haseth J A. Fourier Transform Infrared Spectrometry. 2nd ed. Wiley, 2007. Chapter 9–10. ISBN: 978-0-471-19404-0.

[2] Smith B C. Quantitative Spectroscopy: Theory and Practice. Elsevier, 2002. ISBN: 978-0444511246.

[3] Smith B C. Fundamentals of Fourier Transform Infrared Spectroscopy. 2nd ed. CRC Press, 2011. Chapter 7–8. ISBN: 978-1420069297.

[4] Korte E H, Schrader B. Infrared and Raman Spectroscopy: Methods and Applications. VCH, 1995. Chapter 6.

[5] Bruker Optics. "OPUS Spectroscopy Software: Spectral Processing Manual."
https://www.bruker.com/en/pro…

[6] Liland K H, Rukke E H, Olsen E F, et al. "Customized Baseline Correction." Applied Spectroscopy, 2011, 65(8): 907–915. DOI:10.1366/10-06124.

[7] Eilers P H C, Boelens H F M. "Baseline Correction with Asymmetric Least Squares Smoothing." Leiden University Medical Centre Report, 2005.

[8] Savitzky A, Golay M J E. "Smoothing and Differentiation of Data by Simplified Least Squares Procedures." Analytical Chemistry, 1964, 36(8): 1627–1639. DOI:10.1021/ac60214a047.

[9] Steinier J, Termonia Y, Deltour J. "Smoothing and Differentiation of Data by Simplified Least Squares Procedure." Analytical Chemistry, 1972, 44(11): 1906–1909. DOI:10.1021/ac60319a045.

[10] Thermo Fisher Scientific. "ATR Correction Algorithm." Nicolet FTIR Application Note AN-011.
https://www.thermofisher.com/…

[11] Olinger J M, Griffiths P R. "Quantitative Effects of Finite Bandwidth on the Resolution and Shape of Infrared Bands." Analytical Chemistry, 1990, 62(8): 821–825. DOI:10.1021/ac00207a007.

[12] Byler D M, Susi H. "Examination of the Secondary Structure of Proteins by Deconvolved FTIR Spectra." Biopolymers, 1986, 25(3): 469–487. DOI:10.1002/bip.360250307.

[13] ftir.fun. "Infrared Functional Group Database."
https://ftir.fun/ir/group/alk…

Next Episode Preview: Ep 19 — Introduction to Qualitative Analysis: Library Search and Matching
We will enter the core of infrared spectral analysis—qualitative analysis. Explain the composition of commercial spectral libraries (Sadtler, Aldrich, Hummel), mainstream search algorithms (correlation coefficient, absolute difference, first derivative matching), the meaning of HQI values, mixture search strategies, and the significance and methods of building custom libraries. Also emphasize the risk of misjudgment that "cannot rely entirely on library search."

This article is licensed under CC BY-NC-SA 4.0. Images are from public domain or web resources with attributed sources; copyright belongs to the original authors.