Why does this phase response wrap so strongly within the passband?
I would expect a composite phase response to wrap near the Nyquist frequency, but this response begins wrapping at much lower frequency:
The evalresp output for this response shows that the datalogger FIR filters are asymmetric:
CB CD2 00 BHZ 2007,182,00:00:00 2599,365,23:59:59 SEED units: In="COUNT", Out="COUNT" Calc_sens=1.002796E+00 (reported=1.038180E+09) @ 5.000000E+00 Hz Calc_delay=3.533534E-01, Correction_applied=0.000000E+00 Est_delay=0.000000E+00, Final_sample_interval=1.000000E-02(sec/sample) Stg 3: FIR_ASYM H0=9.999992E-01 32 Coefficients SInt=4.656613E-06 Sd=1.000000E+00 Stg 4: FIR_ASYM H0=9.999992E-01 83 Coefficients SInt=3.125000E-05 Sd=1.000000E+00 Stg 5: FIR_ASYM H0=9.999539E-01 89 Coefficients SInt=5.000000E-04 Sd=1.000044E+00 Stg 6: FIR_ASYM H0=9.976119E-01 133 Coefficients SInt=5.000000E-03 Sd=1.002751E+00
This means that the order in which the coefficients are listed matters. A symmetric filter plots in the time domain as:
An asymmetric FIR filter with coefficients listed in forward order – with the largest amplitude of the filter plotting to the left (small-numbered coefficients) – appears as:
The phase spectrum of this filter shows wrapping occurring near the high-frequency rolloff or Nyquist frequency:
Plotting stage 5 FIR filter for the channel in question shows that its asymmetric FIR coefficients are listed in reverse order – with the largest amplitudes plotting to the right (large-numbered coefficients):
This results in a different phase spectrum that begins wrapping at lower frequencies than the same filter listed in forward order:
Cascading multiple asymmetric FIR filter stages with coefficients listed in reversed order results in a phase spectrum that begins wrapping well within the passband. To ensure that this phase response will be interpreted as it was applied in the datalogger, this this metadata needs to be resent with asymmetric FIR filters listed in forward order.