Figure 6: Panel (a) shows a portion of the simulated light curve described
in Section 3 of the text. The simulated data possess 64s bins, and noise
is purely due to counting statistics. The squares in panel (b) show the
results of applying the PRH92 reconstruction to the simulated data (using
N=3000 simulated data points. The solid erratic line shows the `real'
simulated signal. Note how well the reconstruction reproduces the `real'
signal during times where data exists, and brackets the signal at other
times.
In order to assess the significance and robustness of the above results,
this section describes the application of this method to simulations. We
tailor our simulation to match the RXTE observation MCG-6-30-15 as
much as possible. EXOSAT showed that the high frequency fluctuations
of MCG-6-30-15 possess a power spectrum of the form 
. We use
this power spectrum with an additional low-frequency cutoff at
:
We then make a (noiseless) simulated continuum light curve, F(t), by
summing Fourier components of random phase between 
and 
, i.e.
where 
is a uniformly randomly distributed in the range 0 to
for each distinct value of f.
Without loss of generality, we assume that the line band flux possesses the same mean normalization as the continuum band light curve. However, in order to mimic the situation found in Section 3 as closely as possible, we assume that there is an additive offset between the continuum band and line band light curves as well as the convolution a transfer function. In other words we compute a (noiseless) line-band light curve using the expression:
Here, 
is the non-zero-lag component of our imposed simulated
transfer function for which we use a Gaussian:
where f is the fraction of the continuum flux that is delayed, 
is
the mean time delay, and 
is the temporal standard-width of the
smearing. For concreteness, we set
This value of f is approximately the fraction of the line-band flux
which originates from the iron line, and hence this simulation crudely
mimics the effect of iron line reverberation with a 
time delay.
Our value of K is set to be similar that found for MCG-6-30-15 above.
From these `perfect' noiseless light curves, we formed Possion sampled noisy light curves assuming a mean count rate of 4cps in both the continuum and line bands, and using 64s bins. The datagap structure of the real MCG-6-30-15 dataset was then imposed on the simulated light curves.
We now examine our realistic, simulated, data in order to assess how well
we can detect the existence of the imposed lag and recover the properties
of using our method.