## Question

### 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: Figure 1. Composite amplitude (top) and phase (bottom) response showing unexpected phase wrapping within the passband.

Why?

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: Figure 2. Time domain plot of FIR coefficients for a symmetric filter.

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: Figure 3. Time domain plot of FIR coefficients for an asymmetric filter whose coefficients are plotted in forward order (larger coefficients listed toward the beginning).

The phase spectrum of this filter shows wrapping occurring near the high-frequency rolloff or Nyquist frequency: Figure 4. Composite amplitude (top) and phase (bottom) response of an asymmetric FIR filter with coefficients listed in forward order.

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): Figure 5. Time domain plot of FIR coefficients for an asymmetric filter whose coefficients are plotted in reverse order (larger coefficients listed toward the end).

This results in a different phase spectrum that begins wrapping at lower frequencies than the same filter listed in forward order: Figure 6. Composite amplitude (top) and phase (bottom) response of an asymmetric FIR filter with coefficients listed in reverse 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.

## Tags

Updated: 07/10/2019
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