In the process of data acquisition by a microcontroller unit (MCU), random errors can occur due to various forms of interference. These errors are unpredictable and vary in magnitude and direction when measuring the same quantity under identical conditions. However, they follow statistical patterns over multiple measurements. To reduce the impact of such errors, filtering techniques can be applied either through hardware or software. Digital filtering, in particular, plays a crucial role in measurement and control systems, as it is highly efficient and real-time capable.
Digital filtering offers several advantages over traditional analog methods. First, it does not require additional hardware components, making it cost-effective and reliable. It also eliminates the need for impedance matching. Moreover, digital filters can effectively handle low-frequency signals that analog filters often struggle with. Second, since digital filtering is implemented via software, a single filter program can serve multiple input channels, reducing system overhead. Third, the characteristics of a digital filter can be easily adjusted by modifying its algorithm, allowing for flexible adaptation to different types of noise, including low-frequency interference and random fluctuations.
Commonly used digital filtering algorithms in microcontroller-based systems include limit filtering, median filtering, arithmetic average filtering, weighted average filtering, and moving average filtering.
**1. Limit Filtering Algorithm**
This method compares the difference between two consecutive samples. If the absolute value of the difference exceeds a predefined threshold (A), the current sample is considered invalid, and the previous valid value is retained. Otherwise, the new sample is accepted. This technique is ideal for slowly varying signals like temperature or position. Choosing an appropriate A value is critical and often based on empirical data or experimental results.
**2. Median Filtering Algorithm**
This approach involves taking N consecutive samples (N is usually an odd number), sorting them, and selecting the middle value as the final result. It is particularly effective at removing impulse noise caused by unstable sampling or sudden disturbances. However, it is less suitable for fast-changing signals.
**3. Arithmetic Average Filtering Algorithm**
This method calculates the average of N consecutive samples. The smoothness of the output depends on the value of N: larger N values provide smoother results but lower sensitivity, while smaller N values increase sensitivity at the cost of reduced smoothing. For efficiency, N is often chosen as a power of two to facilitate division using bit shifting.
**4. Weighted Average Filtering Algorithm**
To balance smoothness and sensitivity, this method assigns different weights to each sample. The weights are typically chosen to emphasize more recent samples, improving the system’s responsiveness to changes. The sum of all weights must equal one, ensuring the weighted average accurately represents the signal trend.
**5. Moving Average Filtering Algorithm**
Unlike other averaging techniques, moving average filtering updates the average with each new sample, maintaining a window of the latest N samples. This approach is ideal for real-time applications where continuous data processing is required. A ring buffer structure is commonly used to manage the sliding window efficiently.
**6. Low-Pass Filtering Algorithm**
This algorithm simulates the behavior of an analog RC low-pass filter using a recursive formula:
**Yn = a * Xn + (1 - a) * Yn-1**
Where **Xn** is the current sample, **Yn-1** is the previous filtered output, and **a** is a small coefficient that determines the filter's cutoff frequency. The cutoff frequency can be calculated as **fL = a / (2Ï€t)**, where **t** is the sampling interval. This method is ideal for slow-varying signals but cannot eliminate high-frequency noise above half the sampling rate.
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