In the stereo generator, post interpolation, the pilot is added, subcarrier generated and the MPX signal prepared for output to the DAC. The DAC and subsequent analogue filter produce a degradation of the MPX response, resulting in a bad channel crosstalk specification.
In the stereo generator we go a step further and incorporate a response correction filter after the interpolation filter. There are two deviations from a perfect flat amplitude and linear phase response to be corrected. The maximum output frequency of the MPX signal is 53KHz with a sample rate of 192KHz. Thus the the DAC sincX response will begin to have effect on these upper frequencies that needs to be corrected in order to achieve a good separation of channels. Correction is achieved by introducing an inverse sincX characteristic up to 53KHz on the interpolation filter.
The sinc/x response degradation is a roll off inherent to the digital to analogue (DAC) conversion process. The must be a null at the sample rate used by the DAC. The AD1852 DAC used here has a rolloff of 0.24db at 53KHz for a 192KHz sample rate. The rejection is >100db for frequencies > 120KHz
The second degradation to be corrected is the response of the MPX output filter in the analogue domain after the DAC. This is a low pass active Bessel filter to maximise presevation of the phase linearity. An arbitary high cutofff frequency cannot be used because the spurious frequencies from the DAC have to be removed (Look above the sample rate). Thus there will be a very small frequency droop that needs to be corrected as well. We combine these two correction factors (inverse sincX and inverse Bessel filter) and generate a lowpass filter that compensates for these degradations. Then the filter is converted into an the correction filter format.The sample rate is 192KHz
Again we use FILTERSHOP to design the correction filter. The lowpass filter and a sincX filter are cascaded to produce the overall response. Then we generate an inverse response up to 53KHz. Combining these two items we achieve an absolutely flat response to 53KHz. Having checked that the result is as required we synthesise the correction filter. Using a curve matched linea phase FIR filter we obtain the coefficients required. A simple n = 16 filter was found to be sufficient.
This correction filter was derived by using the mean response of the Bessel Filter. An active Bessel filter with tight tolerance components was used. Even so there will be some deviations from the ideal due to component tolerances and to a lesser extent the layout choosen. A series of Monte Carlo runs allows the magnitude and phase response of the filer to be determined for different component tolerances, operational amplifiers and temperature sensitivity. Once a suitable trade off between component tolerance and cost is obtained we take the mean response of the filter for the purpose of calculating the correction filter.
Since in practice there will always be some variation of the filter we use the sensitivity analysis information to select a component or components to be used as adjustables for final trimming of the stereo generation specification when in production. (0.5% resistors are very cheap but better than 2% capacitors are still expensive.)