Smoothing Operation
Linear digital filtering operations calculate the arithmetic unweighted mean of a sliding window of consecutive data points. A moving average filter smooths high-frequency noise from time-series measurement signals while maintaining a simple finite impulse response structure. Input samples enter a shift register of fixed length N, where the oldest sample is removed as each new sample arrives.
System integration uses this filter when computational simplicity outweighs strict frequency selectability requirements.
Step Response
Time-domain implementation requires adding the newest sample to a cumulative sum and subtracting the oldest sample, dividing the result by window length N. Step response exhibits a constant linear ramp reaching full amplitude after exactly N sample intervals. Sharp signal transitions suffer significant edge blurring, spreading step changes across the filter window width. Impulse response is rectangular with constant amplitude equal to one divided by N over the window duration.
Phase Delay
Phase response exhibits strict linearity, resulting in a constant group delay equal to half the window length minus one sample. Frequency response follows a sinc-like magnitude profile with attenuation nulls occurring at integer multiples of the sampling rate divided by N. Poor stopband attenuation limits filter effectiveness when sharp out-of-band noise cancellation is required. Sidelobes allow high-frequency noise energy to leak into the filtered output stream, requiring secondary filtering stages in precision applications.
Bandwidth Limit
Filter window selection must balance noise reduction goals against allowable time-domain phase delay.
