Quantifying Phase Margin Loss from Cascaded Sinc and Boxcar Filter Window Delay
Cascaded sinc and boxcar filter window delays introduce deterministic group delays that subtract directly from control loop phase margin at crossover frequencies.
Boxcar Filter
Window Function
Discrete-time signal processing algorithms calculate the unweighted arithmetic mean of a finite series of sequential data samples. A boxcar filter applies a uniform rectangular window over a moving temporal block to attenuate high-frequency fluctuations. The filter length determines both the noise suppression factor and the time-domain step response delay.
Qualification procedures evaluate the window width against expected signal dynamics to prevent excessive smoothing of true physical transients.
Attenuation Profile
Frequency-domain analysis reveals a sinc-shaped transfer characteristic containing distinct spectral nulls. The first null occurs at an input frequency equal to the sampling rate divided by the window length. Sidelobes decay slowly at a rate of six decibels per octave, allowing significant high-frequency spectral energy to pass through unattenuated.
Mathematical convolution of the rectangular window with the input sequence causes magnitude attenuation in the passband, distorting signal components near the cutoff frequency. Phase response remains strictly linear, preserving temporal symmetry across all transmitted frequencies.
Noise Reduction
Averaging continuous sensor outputs reduces uncorrelated zero-mean white noise by a factor equal to the square root of the sample count. Random voltage fluctuations in strain gauge amplifiers or temperature sensors decrease significantly when processed through long window lengths. Non-stationary noise sources or impulse spikes skew the output mean, introducing broad transient artifacts across the entire window duration.
Median filtering or modified trimmed means offer alternative smoothing when non-Gaussian noise corrupts the primary signal path.
Passband Limit
Systems requiring flat passband transmission must restrict window length to avoid signal attenuation.
Integrating Moving Average Filter Windows with Analog Converter Downsampling Rates
Aligning moving average filter lengths as integer multiples of ADC decimation rates eliminates aliasing foldover and maximizes noise bandwidth reduction.