Week10

Week 10 Progress: Exponential Moving Average and Trend Detection

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Objective

To apply signal processing techniques to smooth ADC data and detect abnormal trends that may suggest ankle swelling. The techniques include:

1. Short-term smoothing using EMA (Exponential Moving Average)

2. Long-term trend detection by evaluating the slope of consecutive filtered values

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What is EMA?

The Exponential Moving Average is a recursive smoothing filter calculated by:

$$EM{A}_t=\alpha \cdot X_t+(1-\alpha )\cdot EM{A}_{t-\mathrm{1}}$$

Where:

• $X_{t}$ is the current data point

• $\alpha$ is the smoothing constant (0 < α < 1)

A lower α means stronger smoothing but slower response.

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Implementation Details

1. Short-Term EMA (Real-Time Filtering)

• Applied on 200 averaged samples every 2 seconds.
• Removes noise from breathing, minor twitches, or slight sensor jitter.

2. Long-Term EMA (Trend Filter)

• Samples are further passed through another EMA with a lower alpha (0.1) for trend detection.

Trend Detection Logic

When the system is in the STATIONARY state, the firmware tracks the slope of filtered values every 15 seconds.

If three consecutive values form a strictly decreasing sequence, swelling is assumed:

• A trend window is maintained using a sliding array.

• If conditions are met, alarmTriggered = true.

Results

Module	Outcome
EMA filter	Real-time signal became significantly smoother and more stable
Long-term tracking	Allowed safe and low-noise detection of physiological changes
Alarm logic	Only triggered under clear, sustained declines in signal (fewer false positives)