Comparing the measured and computed bandpass shapes of the digital filters

sep 2002

Links:

The computed band passes.
Comparing the actual spectra with the computed band passes.

Introduction.

The interim correlator input is filtered by 8 analog filters (50 Mhz wide at the 260 Mhz IF... one for each sub correlator). It is then sampled at 100 Mhz using an 8 bit A/D converter. For bandwidths of 25 Mhz and below the real data stream is digitally down converted to complex samples I, Q streams. Each I, Q stream is half band filtered 1 to 8 times (bandwidths 25,12.5,6.26,....195Mhz) and then digitally upconverted back to a real data stream. The resulting data is then converted to 3 or 9 levels and sent to the correlator chips for processing. The figure below shows 1 of the 8 paths:

This is a 50 Mhz anti aliasing filter.
The 260 IF is down converted to 0 to 50 MHz (real signal)
The 8 bit digitizer real samples the 50 MHz bandwidth at 100 MHz sampling rate.
The digital filters down convert to I, Q complex samples and then filter each of these to 25 Mhz.
This is the half band filtering chain applied once for each octave of filtering requested. Every two stages the output bits are shifted by 1 bit to compensate for the reduction in bandwidth.
The I, Q complex samples are filtered and then upconverted back to a real signal.
This last step generates a data stream twice as fast by interpolating the real samples. It is needed for double nyquist sampling. It is done for all bandwidths less than 25 MHz. If double nyquist is not used then every other sample for the output is kept.

Computed band passes.

A the computed band passes are shown in the figure.

The Top figure is the halfband filter bandpass computed from the filter coefficients. The red line is where the signal aliases. At that point the filter is 6 db down from the peak.
The Bottom figure shows different computed filter shapes taking into account how the correlator uses the digital filters. These filters fall off on both sides since the filtering is done on the complex I,Q data streams separately. The different colors are:

Black: This is the unmodified filter shape (same as top figure with a linear scale).
Red: The aliased power is included. The the edges of the spectra now drop to only .55 of the peak. The drop-off is symmetric since the aliasing occurs on the individual I,Q data streams.
Green: This includes the aliased power and an extra application of the filter on the I,Q pair. When upconverting from complex back to real, there is a filter step followed by the frequency shift to get a real band. This extra filter step (on the I,Q data streams) causes the edges on both sides drop to .3 of the peak.
Dark Blue: This has the aliased power, extra IQ filter step, and a final filter application on the real bandpass. It causes the high edge of the bandpass to drop to .1 . The low edge does not change since the filtering is applied after the upconversion to real.
Purple. This is the same as the dark blue line except that there are two applications of the filter on the resulting real bandpass instead of 1.
Light Blue: If you just apply the extra IQ filtering with no aliasing, then both sides of the bandpass drop to .1

On the low frequency side the green, dark blue, and purple lines overlay one another.

processing: x101/digfilter/dfbpcomputed.pro

Comparing the computed band passes with real data.

The plots show the actual spectra with the computed band passes. Data was taken from a noise source in the downstairs IF/LO (so it will not include any ripples from the upstairs if/lo or standing waves from before the horn). The data from correlator board 1 (polA) was used.

The top figure shows the band passes of the data for various configurations of the correlator. All of the 25 Mhz band passes have the same shape. The 12 Mhz bands: 9 level, 3 level, and 3 level interleaved all have a second shape. 12 Mhz 3 level double nyquist has a 3rd shape. These shapes differ in the interpolation stage of the real signal for double nyquist:

25 Mhz: it is not used
12 Mhz double Nyquist: all of the interpolated points are used.
12 Mhz not double Nyquist: every other point from the interpolation is used.

The bottom figure plots one data bandpass from each shape, and the computed bandpass that is closest to it.

Black 25 Mhz. The computed filter has aliased power and the extra IQ filtering.
Blue 12 Mhz 9 level. The computed filter has aliased power, extra IQ filtering, and two applications of the filter on the resulting real bandpass.
Orange 12 Mhz double Nyquist. The computed filter has aliased power, extra IQ filtering, and two applications of the filter on the resulting real bandpass.

The low frequency left edge of all of the band passes is the same and matches the computed bandpasses pretty well. The 25 Mhz band falls off differently but this is probably because of the filter shape of the 50 Mhz analog filter. The right edge drop-off of the 12 Mhz bands follows the computed bandpass. The 25 Mhz drop is a bit steeper than the computed one (again probably because of the analog filter).

All of the bands below 12 Mhz have bandpass shapes identical to the 12 Mhz shape.The interleaved band passes were odd because they jumped between the 12 Mhz and the 25 Mhz shapes for different boards at the same bandwidth (see measured bandwidths less than 25 Mhz). This only happened for bandwidths less than 25 Mhz. It must be the extra interpolation stage at the end that is only done for bandwidths < 25 Mhz that is causing this.

When data is taken without an off position, the computed digital filter band passes can be used to remove the digital filter shapes. This can extended the useable parts of the band pass.

processing: x101/digfilter/dfbpcmpMeasured.pro

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