Here are results on a study of using iwave to control closely spaced doublets of sinusoids. This study was conducted on test data at 16384Hz sampling rate, of 100 second duration. The dataset consisted of two sine waves at 27.8 and 27.9Hz, each of amplitude 1, on a background of Gaussian white noise of RMS 0.1. Two iwave configurations were used to try and subtract the two components. In both schemes, iwave was running with a tau parameter of 5 seconds and initial guess frequencies at exactly the line frequencies. Iwave was running in phaselocked mode. The loops on the lower and upper frequency lines were set to close 5 and 6 seconds into the dataset, respectively, although these time delays are unimportant; they could both have been set to zero just as well and I mention them for completeness.

CONFIGURATION 1: the raw data is injected into iwave1 set to track the lower frequency (27.8Hz). The D phase output of iwave1 is subtracted from the raw data, and the result is injected into iwave2, set to track the upper frequency (27.9Hz).  The D phase output of iwave2 is subtracted from the input to iwave2, and the difference is the final output. In other words, the two iwave filters are cascaded.

CONFIGURATION 2: the raw data minus the D phase output of iwave2, set to track the upper frequency line (27.9Hz) is used as the input for iwave1, set to track the lower frequency line (27.8Hz). The raw data minus the D phase output of iwave1 is used as the input for iwave2. In other words, for each iwave, the input is the result of the raw data with the D phase output of the other iwave subtracted. 

The first attached pdf shows the results of studies of the the two configurations; the first two pages are for configuration 1 and the pages 3 and 4 are for configuration 2. In each case, there are three plots - the extracted line amplitudes and frequencies (together on the same page), and amplitude spectral densities of the raw data, the data after the subtraction of the first line, and the the output data after both lines are subtracted. 

The 'cross-subtraction' technique is superior, having much better line attenuation and markedly less sidebands introduced. This is because iwave uses the product of the input data and the Q phase output to sense phase shifts, but when the input data is polluted by a close by line, this causes residual beats between this line and the q phase output in the phase measurement. You can see this on page 1, where both the inferred frequency of the line and its amplitude oscillate at the difference frequency between the two lines, which is 0.1Hz, or a 10 second beat. When each iwave input has the inferred line from iwave outputs on other loud lines removed before input, this distortion goes away. 

I have attached a schematic of the cross subtraction configuration, 2, as a second attached figure, in case the written description above is not clear enough. One detail is, the output of iwave2 which is then subtracted from the input data before injection into iwave1 must be derived from the previous sample of iwave2 output, and hence has to be phase shifted forward by one sample period to accurately subtract the line. This is easy to do using both the Q and the D phase outputs of iwave2, and the cos and sin of the phase shift per sample for the frequency of the line tracked by iwave2.