Solution: Data Analysis Techniques in Embedded and DAQ Systems

1. Statistical Analysis

Basic statistics summarize acquired data.

Mean

$$\bar{x}=\frac{1}{N}\sum_{i=1}^{N}x_i$$

Variance

$$\sigma^2=\frac{1}{N}\sum_{i=1}^{N}(x_i-\bar{x})^2$$

Other useful measures include minimum, maximum, range and standard deviation.

2. Filtering

Digital low-pass, high-pass, band-pass and notch filters can remove unwanted frequency components.

3. Time-Domain Analysis

Examines how the signal changes with time. Peak value, RMS value, rise time, pulse width and zero crossings may be measured.

For samples $x_i$, RMS is:

$$x_{RMS}=\sqrt{\frac{1}{N}\sum_{i=1}^{N}x_i^2}$$

4. Frequency-Domain Analysis

The FFT (Fast Fourier Transform) converts sampled time-domain data into frequency-domain information. It is widely used for vibration, audio and periodic-signal analysis.

5. Trend Analysis

Long-term trends are examined to detect gradual changes, drift or degradation.

6. Threshold and Event Detection

The system can compare a measurement against predefined limits and generate an alarm or control action.

7. Correlation Analysis

Correlation measures the relationship between two signals or variables and can help identify related system behavior.

8. Feature Extraction

Important features such as mean, RMS, peak, frequency and pulse rate are extracted from raw data for classification or monitoring.

9. Calibration and Error Analysis

Measured values are compared with known references to determine offset, gain error, sensitivity and other measurement errors.

Embedded Implementation

To perform analysis on a microcontroller, efficient algorithms, fixed-point arithmetic where appropriate, buffering and interrupt/DMA-based acquisition may be used.

Conclusion

DAQ analysis combines statistical, time-domain, frequency-domain, filtering, trend, threshold, correlation and calibration techniques to convert raw measurements into useful engineering information.