Solving Issues with a Spectrum Analyzer for Discrete Signals

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SUMMARY

This discussion addresses challenges in analyzing discrete signals using a spectrum analyzer, specifically when comparing results from personal computations to professional software outputs. The user successfully computes valid Fourier transforms using FFT and DFT but struggles with intensity analysis from microphone-captured waves. The recommended approach for calculating intensity involves using the power spectrum formula: intensity(f) = √(R²(f) + I²(f)), where R and I represent the real and imaginary components, respectively. The book "Numerical Recipes in C" is cited as a valuable resource for understanding Fourier transforms and power spectra.

PREREQUISITES
  • Understanding of discrete Fourier transform (DFT) and fast Fourier transform (FFT)
  • Familiarity with complex numbers and their components (real and imaginary)
  • Knowledge of power spectrum analysis
  • Basic proficiency in signal processing techniques
NEXT STEPS
  • Study the power spectrum calculation in detail
  • Explore the contents of "Numerical Recipes in C," particularly Chapter 12 on Fourier transforms
  • Investigate software tools for spectrum analysis, such as MATLAB or Python libraries like NumPy
  • Learn about microphone signal processing and its impact on frequency analysis
USEFUL FOR

Signal processing engineers, audio analysts, and anyone involved in analyzing discrete signals using spectrum analyzers will benefit from this discussion.

bogdan
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I tried to obtain the spectrum of a discrete signal and I had some problems...
If I compute on a PC the discrete Fourier transform (FFT or DFT) I obtain valid Fourier transforms (the same Excel computes...)...
...but how do I analyze a wave obtained using a microphone ? I don't get the same results professional programs do...I tried using as the "intensity" of a frequency the magnitude...I tried using the real component...the complex one...but still no good...
Can you help ?
 
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How about
intensity(f) = [squ](R2(f)+I2(f))
where R is the real component, and I is the imaginary one.
 
You're looking for what is called the "power spectrum." The book "Numerical Recipes in C" is the best place to look (as usual!).

It's available in its entirety, free of charge, at http://www.nr.com

Chapter 12 deals with Fourier transforms and power spectra.

- Warren
 

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