The first CIC Decimator output is always zero

It seems that the first CIC Decimator output is always zero and I don't understand its behavior.

I generated the input data and construct signed 12-bit data.

len_data = 100;
in = randi([-2048 2047], len_data, 1);
a = fi(in,1,12,0)

a = 
         314
       -1721
        1722
        -925
          30
       -1070
        2002
        -265
       -1356
        1127
       -1559
        1843
        1968
       -1457
        1010
         274
        1085
        2039
       -1424
       -1938
        1248
         992
        -205
       -1640
        -141
        -321
        -416
         747
         948
        1956
        -249
        1306
        1615
         510
         932
        2009
         422
        -954
       -1765
       -1385
        -194
        -591
        -525
        -531
        1038
        1434
        1840
         411
         724
         269
         614
         849
        -895
        -303
        1756
       -1494
       -1298
        1522
       -1478
       -1051
        1588
        1048
        1793
        -124
       -1771
       -2006
        -590
         829
       -1563
        -107
         329
       -1741
         677
       -2003
         643
         898
        -422
        1626
        -474
        1419
         448
        1400
       -1416
        -717
         866
        1411
        -441
       -1070
         622
       -1803
       -1481
        -660
       -1824
         630
          61
       -1326
           8
         -57
        1494
        1528

          DataTypeMode: Fixed-point: binary point scaling
            Signedness: Signed
            WordLength: 12
        FractionLength: 0

Then I created CIC filter object with decimation factor of 20, number of stages of 4, and internal bit width of 30-bit, and output bit width of 30-bit.

cicDecimOut = dsp.CICDecimator(DecimationFactor=20,...
                    NumSections=4,...
                    FixedPointDataType="Specify word lengths",...
                    SectionWordLengths=30,...
                    OutputWordLength=30)

cicDecimOut = 
  dsp.CICDecimator with properties:

      DecimationFactor: 20
     DifferentialDelay: 1
           NumSections: 4
    FixedPointDataType: 'Specify word lengths'
    SectionWordLengths: 30
      OutputWordLength: 30

Then I checked the output of the CIC filter.

out = cicDecimOut(a)

out = 
           0
     -372895
     5999117
    32856134
    37682867

          DataTypeMode: Fixed-point: binary point scaling
            Signedness: Signed
            WordLength: 30
        FractionLength: 0

My question is the first output of the CIC filter is always zero no matter the input is and I don't know why.

Answer 1

[Lokesh]

Hi Jay,

I believe that the behavior you are observing where the first output of the CIC decimator is zero is expected due to the nature of how CIC filters operate.

A CIC filter consists of multiple integrator stages followed by comb stages. The integrators accumulate the input signal, and the comb stages perform differencing operations on the accumulated values. So as per my understanding, since there is no previous sample for the first input, the output is zero.

[Jay]

Thanks for sharing the thought, Lokesh.

I also thought in that way. However, there are multiple stages of integrators and combs (e.g., 4 integrators and 4 combs in this example) with 0 being the initial values, then it takes more than one cycle all the initialization values are updated (e.g., input data take multiple cycles for propagation and update the initial status). Until then the CIC ouput is 0. In this case, there is only one zero output even though there are 8 stages of integrators and combs. Am I missed something?