Spectral Analysis
Question: What are the dominant periodicities and cyclical patterns in the selected metric? Data: daily historical series with trend and cyclical components. Method: FFT (Fast Fourier Transform) with detrending, windowing, and spectral peak detection to identify characteristic frequencies and their corresponding periods.
Dataset
FMCG 2022-2024
Daily aggregated sales and quantity
1. Analysis Name
Spectral Analysis via FFT
This page identifies dominant frequencies and periodicities in the selected business metric using Fast Fourier Transform, revealing cyclical patterns that may not be obvious from time-domain inspection alone.
2. Problem Context
What problem this page answers
Understanding the cyclical structure of a metric helps identify recurring business patterns and seasonality. Spectral analysis transforms the signal into the frequency domain to uncover hidden periodicities and separate signal from noise.
3. Time-Domain Representation
Observed series and detrended components
The original metric with its long-term trend, and the detrended version that isolates cyclical behavior.
Signal Statistics
4. Spectral Analysis Workflow
From time domain to frequency domain
The workflow detrends, windows, applies FFT, and identifies peaks to reveal dominant frequencies and their corresponding periods.
Detrend signal
Remove long-term trend to isolate cyclical components.
Apply windowing
Use Hann window to reduce spectral leakage at signal edges.
Compute FFT
Transform to frequency domain and compute power spectrum.
5. Frequency-Based Prediction
Signal reconstruction and 90-day forecast
The signal is reconstructed from the top 20 dominant FFT frequency components (dotted line). The forecast repeats the most recent annual cycle forward 90 days — showing what the series looks like if the observed seasonal pattern continues unchanged.
Spectral Summary
Top Frequencies
6. Dominant Periodicities
Characteristic time scales detected
Key Findings