Configuring Moving Average Filter Lengths for Decimated Signal Processing
Matching moving average filter length to the decimation factor eliminates alias leakage by placing transfer function zeros directly on downsampling fold points.
Spectral Zeros
Transfer Nulling
Signal analysis uses the positions in the complex plane where a transfer function goes to zero to define the frequencies that are completely blocked by a system. These spectral zeros correspond to the complex frequencies where the system output becomes zero regardless of the input amplitude. The location of these zeros determines the shape of the stopband attenuation and the phase response of the filter.
Frequency Attenuation
Digital filters employ spectral zeros to suppress unwanted interference at specific frequencies, such as mains power hum. Placing a zero on the unit circle of the z-plane results in infinite attenuation at that exact frequency. The width of the attenuation notch depends on the proximity of the system poles to the zeros.
System Stability
Analog and digital systems must manage the locations of their poles and zeros to ensure stable and predictable performance. While poles determine the stability of the system, the spectral zeros govern the transient response and the phase characteristics. Minimum-phase systems have all their zeros inside the unit circle, which minimizes the group delay of the signal.
In contrast, non-minimum-phase configurations place zeros outside the circle to achieve specific phase equalization. Sensor feedback loops are carefully analyzed to ensure that the zeros do not introduce excessive phase lag, which could cause instability or oscillation under closed-loop control.
Filter Response
Metrological instrumentation uses zero-placement algorithms to optimize the trade-off between filter settling time and stopband rejection. The accuracy of the zero placement is verified by scanning the frequency response with a network analyzer. The measured attenuation depth must meet the specification to guarantee effective noise rejection in the field.