Digital Filtering - CERN

Digital FilteringDigital Filteringin the ATLAS Calorimeter Triggerin the ATLAS Calorimeter Trigger

Jan JongmannsJan Jongmanns

HighRR BiWeekly MeetingHighRR BiWeekly Meeting14.06.201714.06.2017

Part I:Part I:Introduction to Digital FiltersIntroduction to Digital Filters

14.06.2017 Digital Filter 4

-Analogue Filter-Once upon a Time (2 weeks ago...)

● HighRR Hands-On:We looked at a bandpass filter

● Today: Digital Signal Filters


-From Analogue to Digital-The Difference

AnalogueAnalogue DigitalDigitalContinuous signal:

Continuous in time:

Discrete signal:

Discrete in time:

Am

pli

tud

e

Time


-From Analogue to Digital-Digital Definitions 1/2

● Digital processing systems transform series of input values to series of output values

● For purpose of this talk, consider three processing blocks:

++xx

DelayDelay


-From Analogue to Digital-Digital Definitions 2/2

● Note: similar to analogue s-domain, digital circuit can be described in z-domain

● Transfer function is defined as usual

● For this talk: mostly focus on time domain


-Digital Filter-Filter Definition

● A digital filter maps a sequence of input values, to a sequence of output values,

● Define impulse response as filter output for

● Two categories of filters:

- Finite Impulse Response (FIR):

- Infinite Impulse Response (IIR):

FilterFilter


-Digital Filter-FIR Filter Implementation

● Finite Impulse Response Filter:

● Defining the Filter Coefficients

DelayDelay

++

xxxx

DelayDelay

++

xx

DelayDelay

++

xx


-Digital Filter-IIR Filter Implementation

● Infinite Impulse Response Filter:

● Realised via feedback loop:

FIRFIR

DelayDelay

++

xx

DelayDelay

xx

DelayDelay

xx

++++


-Digital Filter-Properties

FIR FilterFIR Filter

guaranteed stable

can have linear phase

no analogue equivalent

less quantisation effects

easier to implement

less effective at same order

IIR FilterIIR Filter

can be unstable

only approx. linear phase

derived from analogue

quantisation effects from feedback

more effective at same order

++

++

++

~~

++++

--

~~

--

--

--

● In general, FIR filter preferred due to stability and linearity

● IIR filter used if FIR would be too large


-Digital Filter-Designing IIR Filter

● Coefficients of IIR filters typically derived from analogue circuit

● General procedure:

- Design analogue circuit with desired bandwidth properties

- Write down transfer function

- Convert to digital transfer function

- Analyse to extract and

Part II:Part II:FIR Noise Filter in ATLAS L1CaloFIR Noise Filter in ATLAS L1Calo


-ATLAS Level-1 Calorimeter Trigger-One-Slide Overview

● ~7200 cables from calorimeterto L1Calo trigger

- Analogue signals give energy deposited in small region of calorimeter

● L1Calo analyses signals

- PreProcessor produces digital information from analogue input

- Object-finding processors analyse depositions to find high- particles

PreProcessorPreProcessor Signal digitisation, identification calibration

ProcessorsProcessors

EMClusters

Jets & Sums


-ATLAS Level-1 Calorimeter Trigger-Input Signals

● Bi-polar signals from calorimeters

- Shaped from triangular ionisation pulse to optimise signal-to-noise

● Typical length 450~600 ns

- Short positive pulse followed by long undershoot

- Sampled at 40 MHz, i.e. T = 25 ns

● Both maximum amplitude and integral of positive part correspond to energy deposited in calorimeter region


-ATLAS Level-1 Calorimeter Trigger-Input Noise

● Distinguish between thermal noise and pile-up noise

- For Run-2, pile-up dominates most calorimeter regions

- Pile-Up strongest in forward region and EM calorimeter


-ATLAS Level-1 Calorimeter Trigger-Peak-Finding

● L1Calo Preprocessor identifies signal by finding peak sample

- Peaks identified by comparison of samples:

- Noise threshold removes peaks with small amplitudes

- Also cuts low energy signals -> filter to improve signal-to-noise


-ATLAS Level-1 Calorimeter Trigger-FIR Noise Filter

● FIR Filter in L1Calo Preprocessor uses 5 samples

- Corresponds to signal peak

- Design coefficients to improve signal-to-noise


-Optimal Filter-Derivation 1/3

● Given:

- Signal amplitude and shape

- Noise contribution

● Find:

- Coefficients that maximise Signal-to-Noise



● Rewrite:

● Introducing Autocorrelation Matrix



● Set derivative to zero to find maximum:

● Solve:

● Rewrite in vectorial form:

● Solution:


-Optimal Filter-Discussion

● The filter coefficients optimise Signal-to-Noise

- Expected signal shape

- Noise correlation matrix

● The structure of the noise dictates the filter coefficients

- For thermal (white) noise, noise samples are uncorrelated

-> is diagonal -> is diagonal -> = Matched FilterMatched Filter

- Pile-up follows signal shape -> pile-up noise strongly correlated

-> non-diagonal -> differs from = Autocorrelation FilterAutocorrelation Filter


-Optimal Filter-Performance 1/2


-Optimal Filter-Performance 2/2


-Summary-

● Digital Filters fall into two categories:

- Finite Impulse Response filters depend only on input signals

- Infinite Impulse Response filters have feedback loops

● IIR filters have higher selectivity at the same order, and are usually designed starting from analogue filter

● FIR filters allow for different type of filtering

- e.g. Signal-to-Noise optimisation in ATLAS L1Calo trigger

- improved signal identification efficiency in high-pile-up environment


-The End--The End-

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Digital Filtering - CERN