Transcript Gamma-Ray Spectroscopy

Digital Signal
Processing
J.P.Martin, Université de Montréal, ILC
EndCap Meeting, Paris, Sept 12-14
2006
1
Selection of an appropriate sequence of transfer function for the processing
Example:
FADC output
1200
Simulated ADC response
ADC gain = 1000
Amplitude (FADC code)
Delta charge injection:
Time
Value
120
0,34
121
0,33
122
0,33
1000
800
600
400
200
160
161
0,2
0,2
0
50
70
90
110
130
150
Sample
Optimized to extract
physical quantities
(charge, etc.)
Processed:
Fn ; n=z,N
<=
170
190
210
230
250
FADCn n=50,250
Original:
FADCn ; n=z,N
transfer function?
J.P.Martin, Université de Montréal, ILC
EndCap Meeting, Paris, Sept 12-14
2006
2
Example:The moving window deconvolution transfer function
For an arbitrary window of L samples :
F[n]
=

With deconvolution, 24-point window
ai * FADC[n-i]
1200
i=0,N
L
a0 = 1
1000
ai = 1/TAUpreamp i = 1, L-1
Corrected amplitude
800
(TAUpreamp in units of the sampling period)
aL = -1 + 1/TAUpreamp
Properties
Transforms an exponential into
a rectangular function of L points.
600
400
200
0
50
100
150
200
250
-200
Time (nsec. X 10)
J.P.Martin, Université de Montréal, ILC
EndCap Meeting, Paris, Sept 12-14
2006
3
Simplified implementation in favorable cases
In the previous example,
ai = 1/TAUpreamp i = 1, L-1

The term with identical ai’s,: G[n] =
(equal weight factors)
ai * FADC[n-i]
i=1,L-1
Add the new element at the head
Reduces to :
G[n] = G[n-1] + a * (FADC[n-1] – FADC[n-L] )
Remove the out of range element at the tail
Value for the previous point
Hardware implementation:
Accumulator
a * FADC[n-1]
Data In
a * FADC[n-L]
Data Out
A
B
+=
Write address
Sampling Clock
Sampling Clock
Counter
Constant N-1
A
B
Read Address
Dual Port
Memory
G[n]
J.P.Martin, Université de Montréal, ILC
EndCap Meeting, Paris, Sept 12-14
2006
4
Deconvolution in the presence of noise
With deconvolution, 24-point window
1200
Remark:
1000
800
Corrected amplitude
For series noise, the
RMS value of the noise
in the resulting function
is increased by a factor
SQRT(2)
600
400
200
0
50
100
150
200
250
-200
Time (nsec. X 10)
Note: It can be demonstrated that the transfer function shown on the next slide will
yield the best estimate of the trend of the “flat” portion of the deconvolution
J.P.Martin, Université de Montréal, ILC
EndCap Meeting, Paris, Sept 12-14
2006
5
Floating average (boxcar) filter applied to the deconvolution result
Transfer function:
G[n] =

aj * F[n-j];
j = 0, K -1
Example with K = 16;
aj = 1/K
Note parameter K => Peaking time
With 16-point boxcar filter
1200
Filtered amplitude
1000
800
600
G[n]
400
200
0
50
70
90
110
130
150
170
190
210
230
250
-200
Sample
J.P.Martin, Université de Montréal, ILC
EndCap Meeting, Paris, Sept 12-14
2006
6
Some interesting properties of the filter
1- For an input step function,
the resulting shape is a
symetrical trapeze with a
peaking time of K and a
flat-top equal to L - K
3- The S/N ratio is slighly
better than that of an
analog CR-(RC)n or
pseudo gaussian filter
of the same FWHM.
1200
1000
800
Filtered amplitude
2- As long as the charge
collection in the detector
is shorter than L - K, the
pulse shape will reach its
full amplitude.
=> NO ballistic deficit
points in rise
38points
risetime
time
600
400
200
0
110
120
130
140
150
160
170
-200
Sample
K
L ILC
J.P.Martin, Université de Montréal,
EndCap Meeting, Paris, Sept 12-14
2006
7
Performance summary of the « trapezoidal » filter
- The S/N of the trapezoidal signal is a few % better than that of a pseudo-gaussian
analog filter
- For signal rise-times shorter than the parameter K, the filtered signal has zero
ballistic deficit. (Same filtered pulse height for all rise-times)
- The trapezoidal signal has no « tail » . (Good behaviour for pile-up)
Other considerations:
As for its analog counterpart with pole-zero suppression, the transfer function
is not zero for the DC or low frequency components. It requires the equivalent
of a « baseline restorer », or double sampling.
J.P.Martin, Université de Montréal, ILC
EndCap Meeting, Paris, Sept 12-14
2006
8
Time measurement
Example: the Constant Fraction Discriminator (CFD)
Principle: Compensates for the time walk associated with the pulse height.
Tr
Threshold set at MAX * Fraction:
“Black” Threshold
“Blue” Threshold
Δt
Same for all amplitudes if Tr is constant
If Tr is not constant: Use a “delay line clip” ≤ than the shortest rise time
Tr1
Not Clipped
Tclipped
Clipped
“Black” Threshold
“Blue” Threshold
Δt
Same again! (in the case of a linear rise time)
J.P.Martin, Université de Montréal, ILC
EndCap Meeting, Paris, Sept 12-14
2006
9
Time measurement, digital CFD implementation example
Step 1: Clip the raw data samples:
F[n]
=

ai * FADC[n-i] ; (a0=1, aMinTr=-1) = FADC[n] – FADC[n-MinTr]
i=0,N
Step 2: Arm the “find Max” process when F[n] goes above a pre defined threshold
(leading edge)
Step 3: Find the maximum value of F[n]
Step 4: Calculate the constant fraction threshold ( F[Max] * Fraction)
Step 5: Produce a delayed clipped pulse shape
Step 6: Find the two points of F[n] delayed on either side of the threshold level
Step 7: Interpolate the value between the two points
result: 1) Value of the index “n” at the crossover point
2) Time interpolation value (“vernier”) ( precision << sampling period)
=>
“High resolution Time Stamp”
J.P.Martin, Université de Montréal, ILC
EndCap Meeting, Paris, Sept 12-14
2006
10
Timing resolution in the digital CFD
Sources of error in the presence of noise:
Error on the evaluation of the
signal amplitude = Nrms
Error on the evaluation of the
maximum = Nrms
Amplitude
Error on the evaluation of the
fraction threshold = Nrms * Fraction
Tr
S
fraction threshold
Δt
Time
J.P.Martin, Université de Montréal, ILC
EndCap Meeting, Paris, Sept 12-14
2006
11
Timing resolution in the digital CFD (zoom)
Resulting error in the evaluation of time:
Tr
TError_rms = Nrms * (1+Fraction) * Tr/S
error
S
Notes:
- Valid for analog or digital CFD
- independant of digital sampling rate to first order
- Error may be much smaller than the sampling
rate for large signal to noise (S/Nrms) ratios
fraction threshold
Extra source of errors for the discrete sampling:
- linear intrapolation of the rise time function
nominal
Δt
Position of the sample with no noise
Position of the sample with noise
J.P.Martin, Université de Montréal, ILC
EndCap Meeting, Paris, Sept 12-14
2006
12
Characteristics:
The TIG-10 Module
Form factor: VXI-C
Interface :a) Stand-alone: VME-A24D16
:b) System: 200 MHz source
synchronous LVDS
Number of channels:
10
Digitizers : 100 MHz 14-bit
Signal processing:
Raw data
- Trigger latency buffer
- Data sample buffers
Charge Channel:
- Preamplifier decay pole deconvolution
- Trapezoidal filter
- Baseline restorer
Timing channel
- Hit detector
- CFD
- Trigger generate / accept logic
Data flow/control:
- Parameters read/write
- Event builder
- Communication links
J.P.Martin, Université de Montréal, ILC
EndCap Meeting, Paris, Sept 12-14
2006
13
Example 4: the VF48 card, (Rev 0 shown)
48 Differencial Channels
FADCs:
- 10 bit, 20-65 MS/sec
Interfaces
- Serial LVDS
- VME64
Signal processing:
7 Altera Cyclone FPGAs
- Raw data segments
- Hit detection
- Charge calculation
- Time stamp
- Event formatting
Applications:
TPC readout
- ILC prototypes
- TACTIC detector
- PET readout
Silicon and scintillation
detectors readout
ASIC preamp multiplexer readout (ALPHA)
J.P.Martin, Université de Montréal, ILC
EndCap Meeting, Paris, Sept 12-14
2006
14
Properties of the VF48 card
Form Factor
Number of channels
Number of bits
Max sampling frequency
Max number of samples/event
Interface:
: VME 6U
: 48
: 10 (12 bits under development)
: 65 MS/sec.
: 2048 (for each channel)
: 1) VME64X
2) Source synchronous serial, 200 mbits/sec, copper (RJ45)
Common system clock
: From front panel connector or serial link
Local trigger signalling output : Front panel conector or serial link
Trigger accept input
: «
«
«
J.P.Martin, Université de Montréal, ILC
EndCap Meeting, Paris, Sept 12-14
2006
15
Example 3, TIGRESS DAQ architecture
Optional logic signals
Trigger decision
Run control (parameters)
System clock
Master
Communication links
Interface to computers
Sub Events,(one
clover or more)
System concentrators
Communication links
TIG-C
Event fragments,
(one crystal)
Local Collectors
Communication links
TIG-10
720+ Channels
720 Signals + Aux.
Detectors
J.P.Martin, Université de Montréal, ILC
EndCap Meeting, Paris, Sept 12-14
2006
Trigger requests,
Data elements:
-pulse shapes
- charge
- time
- other “features”
16
Example 2, TIG-C serial readout module, PCB, component layer
1 RJ45 master link connector
(820 Mbit/sec. Max)
VME64
12 RJ45 links connector
Altera Stratix FPGA
J.P.Martin, Université de Montréal, ILC
EndCap Meeting, Paris, Sept 12-14
2006
17