HPC Tier Module
FFT Spectral Analyzer with GeoNum Precision
Radix-2 FFT spectra with windowing, a Parseval energy check, and a GeoNum drift gauge on the butterflies.
See it run - a worked example, 100% in this browser tab
The problem
Spectral analysis tools often hide their assumptions: the sample-rate labeling, the leakage from windowing, and the round-off accumulated through the transform are easy to get silently wrong.
The local-first solution
This analyzer runs a cited radix-2 Cooley-Tukey FFT/IFFT in your browser, surfaces the sample rate it used, applies named windows with their gains, verifies energy with a Parseval residual, cross-checks against a naive DFT, and reports a GeoNum drift gauge on the butterfly sums. Deterministic f64 math, nothing uploaded.
What it does
Radix-2 decimation-in-time FFT and inverse FFT (FFT(IFFT) identity to round-off)
Magnitude, phase, power spectrum, and one-sided PSD with Welch normalization
Bin-frequency mapping f[k]=k*fs/N with the sample rate always echoed back
Rectangular, Hann, and Hamming windows with coherent and power gains reported
Parseval energy identity reported as a near-epsilon residual
Naive O(N^2) DFT cross-check plus a GeoNum drift verdict on the butterfly accumulations
Honest scope
EXACT: the radix-2 FFT/IFFT, the spectral formulas, the window gains, and the Parseval identity, all cited f64 arithmetic. The sample rate fs is a user input that the bin frequencies depend on - it is always echoed back. NOT modeled: non-power-of-2 lengths (zero-padded and flagged), multi-channel transforms, RFFT packing, overlap-averaged Welch segmenting, or anti-alias filtering; frequencies above fs/2 alias. A signal-processing tool, not measurement-grade metrology.
Authorities cited
- Cooley, J. W. & Tukey, J. W. (1965). An Algorithm for the Machine Calculation of Complex Fourier Series. Mathematics of Computation 19(90), 297-301. DOI 10.1090/S0025-5718-1965-0178586-1. (The radix-2 FFT factorization.)
- Oppenheim, A. V. & Schafer, R. W. (2010). Discrete-Time Signal Processing, 3rd ed., Prentice Hall. Ch. 8-9 - the DFT X[k]=sum x[n] e^{-i 2 pi k n / N}, its inverse, and FFT algorithms.
- Harris, F. J. (1978). On the Use of Windows for Harmonic Analysis with the Discrete Fourier Transform. Proceedings of the IEEE 66(1), 51-83. DOI 10.1109/PROC.1978.10837. (Hann/Hamming windows; coherent and power gain.)
- Parseval/Rayleigh energy theorem: sum_{n} |x[n]|^2 = (1/N) sum_{k} |X[k]|^2 (DFT form) - Oppenheim & Schafer Eq. for the DFT, conservation of energy between time and frequency domains.
- Welch, P. D. (1967). The Use of Fast Fourier Transform for the Estimation of Power Spectra. IEEE Trans. Audio Electroacoustics 15(2), 70-73. DOI 10.1109/TAU.1967.1161901. (One-sided PSD normalization S=2|X|^2/(fs*sum w^2).)
- Higham, N. J. (2002). Accuracy and Stability of Numerical Algorithms, 2nd ed., SIAM. Sec. 24 - the O(eps log2 N) round-off error bound of the radix-2 FFT (the basis for the GeoNum drift gauge). DOI 10.1137/1.9780898718027.
Analyze a spectrum you can trust
Run the transform in your browser with nothing uploaded, then save the spectra and Parseval/drift report to a Sandbox workspace or attach them to a Worklog case.