(Koji, Joe, Yuta)

Motivation:
  We wanted to know more about CDS.

Setup:
  Same as in elog #3829.

What we did:
  1. Made test RT models c1tst and c1nio for c1iscex.
     c1tst has only 2 filter module(minimum limit of a model), 2 inputs, 2 outputs and it runs with IOP c1x01.
     c1nio is the same as c1tst except it runs(or, should run) without IOP.

  2. Measured the time delay of ADC through DAC using different machine, different sampling rate by measuring transfer functions.

  3. c1nio(without IOP) didn't seem to be running correctly and we couldn't measure the TF.
     "1 PPS" error appeared in GDS screen(C1:FEC-39_TIME_ERR).
     It looks like c1nio is receiving the signal as we could see in the MEDM screen, but the signal doesn't come out from the DAC.

TF we expected:
  All the filters and gains are set to 1.

  We have DA's TF when putting 64K signal out to analog world.
    D(f)=exp(-i*pi*f*Ts)*sin(pi*f*Ts)/(pi*f*Ts)  (Ts: sample time)

  We have AA filter and AI filter when downsampling and upsampling.
    A(f)=G*(1+b11/z+b12/z/z)/(1+a11/z+a12/z/z)*(1+b21/z+b22/z/z)/(1+a21/z+a22/z/z)       z=exp(i*2*pi*f*Ts)
  Coefficients can be found in /cvs/cds/rtcds/caltech/c1/core/advLigoRTS/src/fe/controller.c.

/* Coeffs for the 2x downsampling (32K system) filter */
static double feCoeff2x[9] =
        {0.053628649721183,
        -1.25687596603711,    0.57946661417301,    0.00000415782507,    1.00000000000000,
        -0.79382359542546,    0.88797791037820,    1.29081406322442,    1.00000000000000};
/* Coeffs for the 4x downsampling (16K system) filter */
static double feCoeff4x[9] =
    {0.014805052402446, 
    -1.71662585474518,    0.78495484219691,   -1.41346289716898,   0.99893884152400,
    -1.68385964238855,    0.93734519457266,    0.00000127375260,   0.99819981588176};

  For 64K system, we expect H=1.

  We also have a delay.
    S(f)=exp(-i*2*pi*f*dt)   (dt: delay time)

  So, total TF we expect is;
    H(f)=a*A(f)^2*D(f)*S(f)
  a is a constant depending on the range of ADC and DAC(I think). Currently, a=1/4.

  We may need to think about TF when upsampling.(D(f) is TF of upsampling 64K to analog)

Result:
  Example plot is attached.
  For other plots and the raw data, see /cvs/cds/caltech/users/yuta/scripts/CDSdelay2/ directory.
  As you can see, TFs are slightly different from what we expect.
  They show ripple we don't understand at near cut off frequency.

  If we ignore the ripple, here is the result of delay time at each condition;

data file    host    FE    IOP        rate    sample time    delay        delay/Ts
c1rms16K.dat    c1sus      c1rms    adcSlave    16K    61.0usec    110.4usec    1.8
c1scx16K.dat    c1iscex    c1scx    adcSlave    16K    61.0usec     85.5usec    1.4
c1tst16K.dat    c1iscex    c1tst    adcSlave    16K    61.0usec     84.3usec    1.4
c1tst32K.dat    c1iscex    c1tst    adcSlave    32K    30.5usec     53.7usec    1.8
c1tst64K.dat    c1iscex    c1tst    adcSlave    64K    15.3usec     38.4usec    2.5

  The delay time shown above does not include the delay of DA. To include, add 7.6usec(Ts/2).

  - delay time is different for different machine
  - number of filters (c1scx has full of filters for ETMX suspension, c1tst has only 2) doen't seem to effect much to delay time
  - higher the sampling rate, larger the (delay time)/(sample time) ratio

Plan:
 - figure out how to run a model without IOP
 - where do the ripples come from?
 - why we didn't see significant ripple at previous measurement on c1sus?