3.2 Digital Implementation
59
3.2.3.2 Digital Shaper
If a pulse arrives shortly after another one, the latter pulse will have an artificially
higher peak as the pulse is overlaying on the tail of the previous pulse. This is
particularly an issue for Multi-Wire Proportional Chamber (MWPC) where the tail
can be quite long. The purpose of the digital shaper is to shorten the signal pulse and
reduce the effect of pulse pileup. The architecture of the digital shaper is implemented
as cascade of four first order direct-form 2 transposed IIR filters as shown in the top
part of Fig. 3.11. Each stage of the filter is controlled by means of two coefficients,
the zeroes L i and poles K i , that adjust the passband of the filter. The coefficients
are programmed independently and have a precision of 13 bits. In general, the tail of
the signal is shortened with increasing value of the poles, and shortened with higher
value of the zeroes. This implementation corresponds to the following function in
the Z domain:
H (z) =
1 − L 1 z
−1
1 − K 1 z −1 ·
1 − L 2 z
−1
1 − K 2 z −1 ·
L 30 − L 3 z
−1
1 − K 3 z −1 ·
1 − L 4 z
−1
1 − K 4 z −1
S = 0 ∀ 0 ≤ K i , L i < 1
S = 1 ∀ − 1 ≤ K i , L i < 1
(3.2)
Where S selects if the coefficients K i and L i are signed. This is a new feature for the
SAMPA and provides more freedom in the use of the filter, but sacrifices one bit of
precision. In previous implementations, the coefficients were always positive.
If the coefficient L 30 is set to 1 and S = 0, the filter has the same form as what was
present in the S-ALTRO. This was an improvement in the form of less conversion
noise, less power consumption and better accuracy then what was present in the
ALTRO [8], which also only uses only three cascades.
Since GEM detectors do not suffer from long tails, the filter is not needed in the
new ALICE TPC, but is kept as an option for other MWPC based TPCs. As the
cascaded form is best aimed at removing signal tails [9], the filter has been modified
to transform the two last cascades into a 2nd order direct form 2 transposed filter
which can better provide more common filtering options like low-pass, high-pass
and band-pass filtering capability. By setting the coefficients in the two first cascades
two zero, the filter is reduced to only the 2nd order. The transfer function for the
modified filter is shown in (3.3).
H (z) =
1 − L 1 z −1
1 − K 1 z −1 ·
1 − L 2 z −1
1 − K 2 z −1 ·
L 30 + L 3 z −1 + K 4 z −2
1 + K 3 z −1 + L 4 z −1
S = 0 ∀ 0 ≤ K i , L i < 1
S = 1 ∀ − 1 ≤ K i , L i < 1
(3.3)
3.2.3.3 Baseline Correction 2
A second level of baseline correction can be applied to the signal to correct for signal
perturbations created by non-systematic effects. The correction is based on a low-pass
Finite Impulse Response (FIR) filter implemented as a moving average filter using
59
3.2.3.2 Digital Shaper
If a pulse arrives shortly after another one, the latter pulse will have an artificially
higher peak as the pulse is overlaying on the tail of the previous pulse. This is
particularly an issue for Multi-Wire Proportional Chamber (MWPC) where the tail
can be quite long. The purpose of the digital shaper is to shorten the signal pulse and
reduce the effect of pulse pileup. The architecture of the digital shaper is implemented
as cascade of four first order direct-form 2 transposed IIR filters as shown in the top
part of Fig. 3.11. Each stage of the filter is controlled by means of two coefficients,
the zeroes L i and poles K i , that adjust the passband of the filter. The coefficients
are programmed independently and have a precision of 13 bits. In general, the tail of
the signal is shortened with increasing value of the poles, and shortened with higher
value of the zeroes. This implementation corresponds to the following function in
the Z domain:
H (z) =
1 − L 1 z
−1
1 − K 1 z −1 ·
1 − L 2 z
−1
1 − K 2 z −1 ·
L 30 − L 3 z
−1
1 − K 3 z −1 ·
1 − L 4 z
−1
1 − K 4 z −1
S = 0 ∀ 0 ≤ K i , L i < 1
S = 1 ∀ − 1 ≤ K i , L i < 1
(3.2)
Where S selects if the coefficients K i and L i are signed. This is a new feature for the
SAMPA and provides more freedom in the use of the filter, but sacrifices one bit of
precision. In previous implementations, the coefficients were always positive.
If the coefficient L 30 is set to 1 and S = 0, the filter has the same form as what was
present in the S-ALTRO. This was an improvement in the form of less conversion
noise, less power consumption and better accuracy then what was present in the
ALTRO [8], which also only uses only three cascades.
Since GEM detectors do not suffer from long tails, the filter is not needed in the
new ALICE TPC, but is kept as an option for other MWPC based TPCs. As the
cascaded form is best aimed at removing signal tails [9], the filter has been modified
to transform the two last cascades into a 2nd order direct form 2 transposed filter
which can better provide more common filtering options like low-pass, high-pass
and band-pass filtering capability. By setting the coefficients in the two first cascades
two zero, the filter is reduced to only the 2nd order. The transfer function for the
modified filter is shown in (3.3).
H (z) =
1 − L 1 z −1
1 − K 1 z −1 ·
1 − L 2 z −1
1 − K 2 z −1 ·
L 30 + L 3 z −1 + K 4 z −2
1 + K 3 z −1 + L 4 z −1
S = 0 ∀ 0 ≤ K i , L i < 1
S = 1 ∀ − 1 ≤ K i , L i < 1
(3.3)
3.2.3.3 Baseline Correction 2
A second level of baseline correction can be applied to the signal to correct for signal
perturbations created by non-systematic effects. The correction is based on a low-pass
Finite Impulse Response (FIR) filter implemented as a moving average filter using