🚀 FFT-Based Motion Detection on STM32F4

Real-time motion classification using frequency-domain analysis on an STM32F4 (Cortex-M4) microcontroller.

Instead of traditional threshold-based motion detection, this project implements a full DSP pipeline using CMSIS-DSP to analyze accelerometer signals in the frequency domain.

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📌 Overview

This project captures accelerometer data from the MPU-6050 over I2C and processes it using an optimized FFT pipeline to classify motion states:

• 🧍 Standing (Idle)
• 🚶 Walking (Low-frequency rhythmic motion)
• 🏃 Running (High-frequency rhythmic motion)

The system leverages the hardware FPU (Floating Point Unit) and DSP instructions available in the Cortex-M4 for efficient real-time signal processing.

🧠 Why Frequency-Domain?

Traditional motion detection often uses simple logic: if(acceleration > threshold) → motion.

The FFT Approach Advantages:

• Periodic Pattern Detection: Differentiates between a random bump and a rhythmic gait.
• Noise Sensitivity: Filters out high-frequency mechanical vibrations.
• Robustness: Enables actual activity classification rather than just "moving/not moving."

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⚙️ System Architecture

🔹 Hardware

• MCU: STM32F4 Series (Cortex-M4)
• Sensor: MPU-6050 (3-Axis Accelerometer) via I2C
• Clock: Configured for maximum performance (At 84MHz)

🔹 Sampling & Buffering

• Sampling Rate: 200–500 Hz
• Buffer Size ($N$): 256 samples
• Overlap: 50% (128 samples shifted) to improve temporal resolution.

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🔬 DSP Processing Pipeline

1. Acceleration Magnitude

To make detection orientation-independent, we calculate the magnitude: $$|A| = \sqrt{A_x^2 + A_y^2 + A_z^2}$$

2. DC Removal & Windowing

• DC Removal: Subtract the mean to remove the $1g$ gravity component.
• Hanning Window: Applied to reduce spectral leakage before the FFT.

  float window = 0.5f * (1.0f - arm_cos_f32((2.0f * PI * i) / (FFT_SIZE - 1)));

3. FFT Execution (CMSIS-DSP)

We use the Real FFT (RFFT) function. Since accelerometer data is real-valued, RFFT is twice as fast and uses half the memory of a Complex FFT (CFFT).

arm_rfft_fast_f32(&fft_instance, fft_input, fft_output, 0);
arm_cmplx_mag_f32(fft_output, fft_mag, FFT_SIZE/2);