Fast Fourier Transform (FFT) analysis

Table of contents

  1. Introduction
  2. How to use
  3. Behavior
  4. Method
  5. References

Introduction

Fast Fourier Transform (FFT) analysis converts a selected spectrum from the Raman shift domain into the frequency domain so periodic or high-frequency structure can be inspected.

How to use

  1. Upload data and finish preprocessing if needed.
  2. Open Analytics Page.
  3. In Select Analytics Plot, choose Fast Fourier Transform (FFT) analysis.
  4. Use Select spectrum for FFT to choose Average or an individual spectrum.
  5. Optionally enable Subtract average value before FFT.
  6. Review the FFT plots and use Download FFT analysis data as CSV if you need the transformed data.

Behavior

Analytics FFT converts the selected spectrum from the Raman shift domain into the frequency domain. The page shows six FFT views in this order: Amplitude and Phase, Power and Real + Imaginary, then Real and Imaginary. It also exports a CSV containing the FFT data. If Subtract average value before FFT is enabled, the selected intensity trace is mean-centered before the transform.

Method

SpectraGuru computes the discrete Fourier transform of the selected intensity values:

\[X_k = \sum_{n=0}^{N-1} x_n e^{-2\pi i kn/N}\]

When mean subtraction is enabled, the signal becomes:

\[x'_n = x_n - \bar{x}\]
Parameter Tunable or fixed Implementation
Select spectrum for FFT Tunable Average or any selected sample column
Subtract average value before FFT Tunable Boolean toggle, default False
Input x-axis Fixed Raman shift column from the current Analytics dataset
Output Fixed Six FFT plots plus downloadable CSV

References

  1. Cooley, J. W., & Tukey, J. W. (1965). An algorithm for the machine calculation of complex Fourier series. Mathematics of Computation, 19(90), 297-301. https://doi.org/10.1090/S0025-5718-1965-0178586-1
  2. NumPy Developers. Discrete Fourier Transform. https://numpy.org/doc/stable/reference/routines.fft.html