Turning a Noise Density Figure into Your Own Averaging Window
Square the quotient of specified noise density over target resolution to establish the equivalent noise bandwidth required for averaging filter design.
Boxcar Averaging
Signal Reduction
A signal processing method improves the signal-to-noise ratio of a discrete-time sequence by calculating the arithmetic mean of a specified number of consecutive data points. In practice, boxcar averaging operates as a moving filter that smooths short-term fluctuations to reveal underlying trends. The operation assumes that the noise is zero-mean and uncorrelated with the underlying signal, allowing the variance to decrease proportionally to the number of averaged samples.
Implementation Method
Data flow relies on a sliding window of fixed length that moves through the data stream one sample at a time. This process utilizes a first-in, first-out buffer to update the sum by adding the newest sample and subtracting the oldest. It requires minimal computational overhead, making it suitable for real-time applications on microcontrollers.
Frequency Response
Filter transfer function exhibits a low-pass characteristic with multiple nulls in the frequency domain. These nulls occur at integer multiples of the sampling frequency divided by the window length. This attenuation pattern makes the technique highly effective for suppressing periodic interference.
Performance Limit
Severe distortion of fast transitions involves a loss of temporal resolution. Because the output represents a weighted history, sharp edges in the input signal are smoothed into linear ramps. If the window length is too wide, transient events of interest can be completely obliterated.