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.
Discrete Time Frequency Response
System Analysis
Analytical function describing the steady state output of a sampled system relative to a sinusoidal input. The discrete time frequency response characterizes how a digital sensor or processor alters the magnitude and phase of signals across the Nyquist interval. It is derived from the z transform by evaluating the transfer function on the unit circle.
Periodic Nature
Symmetries in the mathematical representation result in a periodic behavior that repeats every sample rate increment. Evaluation of the discrete time frequency response reveals potential aliasing issues where high frequency components fold back into the primary signal band. Engineers use these plots to verify that attenuation at the folding frequency meets the required rejection specifications for the application.
Measurement Protocol
Laboratory verification involves injecting digital sequences and recording output vectors. The discrete time frequency response is sensitive to quantization, requiring high bit depth test equipment.
Operational Limit
Performance varies based on the coefficients loaded into the processing hardware and the stability of the external oscillator. A stable discrete time frequency response ensures that gain remains predictable across the entire operating temperature range. Deviations occur if the sample clock drifts or if internal arithmetic overflows cause non linear behavior in the feedback loops.