Calculating Group Delay in Delta Sigma Converters
Delta-sigma converter group delay equals the phase derivative across decimation filter stages, calculated as K times M minus one divided by twice the modulator clock for sinc filters.
Half Band Fir Delay
Temporal Property
Specific latency value associated with a finite impulse response filter where every second coefficient is zero. The half band fir delay is a fixed interval determined by the number of taps and the sampling interval. It is exactly half of the total filter order because the impulse response is symmetric around the center tap.
Computational Efficiency
Reduction in the number of required multiplications makes these filters ideal for decimation and interpolation stages. The half band fir delay remains constant regardless of the signal content, providing a predictable phase response. This architectural choice simplifies the design of multi rate systems by allowing for easier alignment of parallel processing paths in high speed hardware.
Metrological Calibration
Measurement of this lag is performed by comparing the input signal to the output in the time domain. This comparison yields a precise value for the half band fir delay that can be used in synchronization algorithms.
Delay Stability
Stability of the half band fir delay depends entirely on the precision of the system clock. If the sample rate varies, the absolute delay in seconds changes even though the sample count remains fixed. Integration of these filters into a control loop requires compensation for this latency to prevent instability in the feedback mechanism.