The primary advantage of Wavelet Transform (WT) over Fast Fourier Transform (FFT) is its ability to preserve temporal information while analyzing frequency. While FFT effectively breaks down signal frequencies, it loses the "when"—the specific timing of events. WT uses multi-scale analysis to provide both time and frequency features simultaneously, which is critical for interpreting the complex, non-stationary nature of human movement.
Human gait is rarely constant; it shifts abruptly based on terrain and intent. Wavelet Transform excels by capturing these sudden changes—such as a slip or a stumble—that Fast Fourier Transform often misses by averaging frequencies over time.
Analyzing Non-Stationary Signals
The Nature of Human Movement
Human movement signals are typically non-stationary, meaning they change unpredictably over time. A soldier running on flat ground produces a different signal profile than one climbing rocky terrain.
The Limitation of FFT
FFT assumes signals are stationary or repetitive over the analysis window. It provides excellent frequency resolution but fails to tell you when a specific frequency occurred.
The Wavelet Solution
WT treats the signal as a dynamic entity. It allows engineers to analyze how frequency components evolve over time, providing a complete picture of the user's movement.
Capturing Transient Events
Detecting Sudden Hazards
In industrial and tactical environments, the most critical data points are often transient events. These are short-lived anomalies, such as a sudden slip, a trip, or a rapid change in direction.
Multi-Scale Analysis
WT functions as a multi-scale tool. It can look at the "big picture" of the gait cycle while simultaneously zooming in on fine details.
Precise Localization
Because WT maintains temporal localization, it can pinpoint the exact moment a transient event occurs. This capability is ideal for identifying the instant traction is lost.
Enhancing Classification Precision
Locating Abnormal Nodes
When processing data from complex terrain, simply knowing that an abnormality occurred is not enough; you must know where it happened. WT accurately locates these abnormal movement nodes within the gait cycle.
Superior Feature Extraction
By providing joint time-frequency features, WT offers a richer dataset for classification algorithms. This significantly improves the system's ability to distinguish between normal walking and potentially dangerous anomalies.
Understanding the Trade-offs
Computational Intensity
While WT offers superior detail, it is mathematically more complex than FFT. This can demand more processing power, potentially impacting the battery life of low-power embedded systems found in footwear.
Complexity of Implementation
FFT is a standard, distinct algorithm. WT requires the selection of a specific "mother wavelet" effectively suited to the signal shape, adding a layer of complexity to the design phase.
Making the Right Choice for Your Project
To determine which transform method is best for your smart footwear application, consider your specific end-user requirements.
- If your primary focus is basic cadence or steady-state monitoring: FFT provides a computationally efficient solution for general activity tracking where temporal precision is not critical.
- If your primary focus is safety, slip detection, or tactical maneuvers: WT is the necessary choice to capture the transient, non-stationary events required for high-precision anomaly detection.
By selecting the right feature extraction tool, you transform raw sensor data into reliable, real-time safety intelligence.
Summary Table:
| Feature | Fast Fourier Transform (FFT) | Wavelet Transform (WT) |
|---|---|---|
| Signal Type | Best for stationary/repetitive signals | Excels with non-stationary/dynamic signals |
| Time Localization | No (Loses the 'when' of events) | Yes (Preserves specific timing of events) |
| Detail Level | Global frequency average | Multi-scale analysis (Big picture + Fine detail) |
| Application | Basic cadence & activity tracking | Safety, slip detection, and tactical maneuvers |
| Complexity | Lower computational demand | Higher mathematical/processing complexity |
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References
- Eghbal Foroughi Asl, A. Jalali. Statistical Database of Human Motion Recognition Using Wearable IoT—A Review. DOI: 10.1109/jsen.2023.3282171
This article is also based on technical information from 3515 Knowledge Base .
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