Introduction to ADC testing I

Definition of basic parameters

Ján ŠaligaDept. of Electronics and Telecommunications

Technical University of Kosice, Slovakia

Agenda

Introduction Deterministic and probabilistic

models Basic static parameters Basic dynamic parameters Other parameters

A/D converter – A/D interface

ADC

A/D interface

Timing and control circuit

Signal condi-tioning

Reference and power sources

Buffer

S&H(optional)

ADCADCx

Qx

roundk

ADC parameters (characteristics & errors)

Static (quasistatic) parameters – derived from transfer characteristic Point (gain, gain error, offset, missing code, ...) Function (transfer characteristic, INL, DNL, ...)

Dynamic parameters – characterize a behavior of ADC at time-varying signals SINAD, ENOB, SNR, SFDR, THD, IMD, ...

ADC parameter testing requires extraordinaire accuracy E.g.: 12-bit ADC: detetermination of transition

level with uncertainty < 1% →uncertainty of measurement < 1/(100*4096) ~ 0,00025%=2,5ppm of ADC FS

Accuracy versus precision

ADC transfer characteristicInputcode k

011

010

001

000

111

110

101

100 -4 -3 -2 -10 1 2 3 4

Input analogue value x(t)

[Vfs/Q]IdeIdealal AADCDC

ReRealal AADCDC

Gain (slope) error

Missingcode

Error in monotonicity

Non-linearity

Offset error

Ideal and real straight lines

Vfs - full scale rangeVfs = Vref(2N-1)/(2N)

QTTV Nnom

NnomN

N

fsn

211222

2

T[k] - transition level (thresholdof code k),W[k]= T[k]- T[k-1] – code bin width

N – nominal resolution (number of bits) of ADC

22

112

Nnom

Nnom

nom

TTQ

Gain and offset + their errors Fitting the straight line:

End points straight line - connecting the two end code transition or code midstep values

Least-square fit straight line according a least-square fitting algorithm

Minimum-maximum straight line - the line which leads to the most positive and the most negative deviations from the ideal straight line

ADC transfer characteristic

Deterministic model Stochastic model

00 11 1,1,55 22

PP((kk ||xx))

11

DeterministicDeterministicdefinitiondefinition

StochasticStochasticdefinitiondefinition

11 22

101101

100100

OutputOutput codecode kk

InputInput analanalogueoguevvaluealue xx((t) t)

[[VVfsfs/2/2NN]]

InputInput analogueanaloguevaluevalue xx((t) t)

[[VVfsfs/2/2NN]]

Channel profileChannel profile

OutputOutput codecode kk

analanalooggueue InputInput

valuevalue xx((t) t) [[VVfsfs/2/2

NN]]

011011

010010

001001

000000

111111

110110

101101

100100

-- -- --4 4 3 3 2 2 -- 1 0 1 1 0 1 2 3 4 2 3 4

== NN22 ...,..., 1,1, 0,0,kk -1-1

Conditional probability 5,0: TESTTESTTESTTESTTEST kTkkPkTkkPkT

DNL and INL Differential non-linearity

Integral non-linearity

[[ ]][[ ]]

nonomm

nonomm

QQ

QQkkWWkkDNLDNL

--==

[[ ]][[ ]] [[ ]]

nomnom

nomnom

QQkkTTkkTT

kkINLINL--

==

kDNLkINL

iDNLkINLk

i

10

Dynamic parameters I Bandwidth (BW) - the band of frequencies of input

signal that the ADC under test is intended to digitize with nominal constant gain. It is also designated as the Half-power Bandwidth, i.e., the frequency range over which the ADC maintains a dynamic gain level of at least 3 dB with respect to the maximum level.

Gain flatness error (G(f)) - the difference between the gain of the ADC at a given frequency in the ADC bandwidth, and its gain at a specified reference frequency, expressed as a percentage of the gain at the reference frequency. The reference frequency is typically the frequency where the bandwidth of ADC presents the maximum gain. For DC-coupled ADCs the reference frequency is usually fref = 0.

Quantisation noise and errors

Caused by rounding in quantisation process (and ADC non-linearity)

Power of quantisation noise for ideal ADC (2

eq, 2rms)

Is it dependent/independent on input signal? Is the value Q 2/12 correct? Distribution?

Answer: see the simulation

1022

22 211

121

k

Nq kJ

kQ

ADC noise and distortion ADC output random noise – random signal:

Quantisation noise - uniform Noise generated in input analogue circuits - Gaussian Noise caused by sampling frequency jitter and aperture

uncertainty (Kobayashi) Spurious – unwanted deterministic spectral

components uncorrelated with input signal (e.g. 50Hz) Total noise – any deviation between the output

signal (converted to input units) and the input signal, except deviations caused by linear time invariant system response (gain and phase shift), harmonics of the fundamental up to the frequency fm, or a DC level shift.

Distortion – new unwanted deterministic spectral components correlated with input signal

Noise floor determines the lowest input signal power level

which is reliably detectable at the ADC output, i. e., it limits the ultimate ADC sensitivity to the weak input signals, since any signal whose amplitude is below the noise floor (SNR < 0 dB) will become difficult to recover.

max

max

12/

,,1

22

22

2

221

hhh

M

MYkY

NFl

M

hJkJkk

Dynamic parameters IISignal to noise and distortion ratio

SINAD: for a pure sinewave input of specified amplitude and frequency, the ratio of the rms amplitude of the ADC output fundamental tone to the rms amplitude of the output noise, where noise is defined as to include not only random errors but also non-linear distortion and the effects of sampling time errors, i.e., the sum of all non-fundamental spectral components in the range from DC (excluded) up to half the sampling frequency (fs/2).

12/

,1

222

22

221

2

log10M

Jkk

dBM

YNFlKY

NFlJYSINAD

Dynamic parameters IIISNR

Signal to noise ratio (SNR) - harmonic signal power (rms) to broadband noise power ratio excluding DC, fundamental, and harmonics

12/

,,1

22

max

2

22

221

1

log10M

hJkJkk

dBM

YNFlhkY

NFlJYSNR

Dynamic parameters IVTHD, THD+noise, IMD

THD

THD+noise = 1/SINAD

Intermodulation distortion (IMD) - for an input signal composed of two or more pure sinewaves, the distortion due to output components at frequencies resulting from the sum and difference of all possible integer multiples of the input frequency tones.

A

HTHD

A

HTHD i

ADCii

ADCi

dB

22

,log20

IMtoneA

IMD

Dynamic parameters VEffective Number of Bits

Effective Number of Bits (Nef, ENOB) - for a sinusoidal input signal, Nef is defined as:

where rms is the rms total noise including harmonic distortion and eq the ideal rms quantisation noise for a sinusoidal input. (SINADdBFS = SINADdB - 20log(SFSR)) SFSR – signal to full scale ratio

Nef can be interpreted as follows: if the actual noise is attributed only to the quantisation process, the ADC under test can be considered as equivalent to an ideal Nef-bit ADC insofar as they produce the same rms noise level.

02.676.1

12loglog 22

dBSINAD

QNNN

dBFS

nom

rms

q

rmsef

Spurious-free dynamic range (SFDR) - expresses the range, in dB, of input signals lying between the averaged amplitude of the ADC's output fundamental tone, fi, to the averaged amplitude of the highest frequency harmonic or spurious spectral component observed over the full Nyquist band, for a pure sinewave input of specified amplitude and frequency, i.e., max{|Y(fh)| , |Y(fsp)|}:

where: Yavm is the averaged spectrum of the ADC output, fi

is the input signal frequency, fh and fsp are the frequencies of the set of harmonic and spurious spectral components.

|)(||)(max{|

)(log20)(

spavmhavm

iavm

fYfY

fYdBSFDR

Dynamic parameters VISFDR

Dynamic parameters VII Experimental demonstration

Measurement setup (run generator first and then demonstration)

NI USB 6009ADC: 12 bits, 10kHz,

differential

AI1 (DUT) USB

Software (LabVIEW):

1. Sinewave generator = Sound card

2. Control: AI1 = DUT (FS, record)Data processing and visualisation

Sound out

Other parameters Various electrical parameters, e.g. input

impedance, power requirements, grounding, …

Time parameters, e.g. clock frequency, conversion time, sampling frequency, …

Digital output: data coding, levels (logic), serial/parallel, error bit rate, …

…

Introduction to ADC testing IIBasic standardized test methods

Agenda

Standardization Static test method Histogram test Dynamic test with data processing

in time domain Dynamic test with data processing

in spectral domain

Standardization IEEE Std. 1057 - 1994, "IEEE Standard for Digitizing Waveform Recorders", IEEE Std. 1241 - 2000, "IEEE Standard for Terminology and Test Methods

for Analog-to-Digital Converters European project DYNAD – SMT4-CT98-2214, „Methods and draft

standards for the DYNamic characterisation of Analogue to Digital converters“http://www.fe.up.pt/~hsm/dynad

IEC Standard 62008 “Performance characteristics and calibration methods for digital data acquisition systems and relevant software”

Additional and related standards: IEEE Standard on Transition and Pulse Waveforms, Std-181-2003 (IEC 60469-1,

-2) IEEE and IEC standards for DAQ and ADM – in preparation IEC 60748 - covers only static ADC and DAC operations …

Detail overview of standards and standardisation – see the lecture of Pasquale Arpaia: A/D and D/A Standards, CD from SS on DAQ 2005

Standard comparison: Sergio Rapuano: Figures of Merit for Analog-to-Digital Converters: Analytic Comparison of International Standards, In Proc. of IMTC 2006, Sorrento, Italy, pp. 134-139

ADC static test

Standardized method

ADC static test - basic ideas

Yields ADC transfer characteristic Static point and function parameters

can be derived and calculated: Gain, offset, FS, DNL, INL, …

Based on the stochastic model of ADC Simple test setup – DC voltmeter is the

only accurate instrument Time consuming – each T[k] is

determined individually. The total time: 2N x longer than determination of one T [k]

Static test setup (IEEE 1057)

ADC static test - algorithm Start with the code k = 1 Find an input voltage level for which the probability of

codes lower than k in the record is slightly higher than 0.5 – the voltage is below T[k].

Find a bit higher voltage (the usual step is a quarter of Q) for which the probability of codes lower than k is slightly lower than 0.5 – the voltage is above T[k]

Fit these two point by line and calculate the voltage for which the probability of codes smaller than k is 0.5 – this is the transition level of code k – the voltage equal to T[k]

Repeat the procedure for all k = 1, 2, …., 2N-1 – the complete transfer characteristic will be measured out

Uncertainty in the static test

The uncertainty can be reduced by increasing the number of acquired samples (M).

The table shows the measurement precision for a confidence level of 99,87%.Number of acquired samples

(M)64 256

1024

4096

Transition level measurement precision

(% of noise standard deviation)

45% 23% 12% 6%

The main disadvantage of the static testing

The test is long time consuming: Let’s test 16bit ADC with sampling

frequency 10kHz, testing step is Q/4, additive noise: =1LSB, required precision: better than 10%.

The chosen record length: 2000 samples Measurement on one level takes

2000 x 0.1ms = 0.2s Total required time: 0.2s x 2(16+4)= 58.2

hours!!!

Static test Experimental demonstration

Measurement setup (run demonstration)

NI USB 6009ADC: 12 bits, 10kHz,

differentialDAC: 12 bit, static, RSE

AI0 (DUT)

AI1 (Voltmeter)

AO0 (DC source)

USB

1:10

Software (LabVIEW) controls:

1. AO0 = DC test voltage

2. AIO = DUT - FS, record

3. AI1– virtual DC voltmeter with averaging

4. Statistical data processing and visualisation

Alternative static methodwith feedback - IEEE 1241

Alternative static methodwith feedback - IEEE 1241

Some experimental results INI USB 6008 (12 bits, 10kHz, 10000s/T)

Some experimental results IINI USB 6008/9 (10000s/T)

Difference of two following measurements

Switching monitor during the measurement

Histogram (statistical) test

Standardized method

Histogram (statistical) testBasic ideas I

Goal: to determine ADC transfer characteristic (the same as in static test method)

The calibrating signal is a time invariant repetitive signal covering the ADC full scale The stream of ADC output codes is recorded Histogram is built from the record The relative count of hits in code bin k in the

histogram in comparison to the calibrating signal probability density function (or counts for code bin k in cumulative histogram in relation to signal probability distribution function) gives information about the code bin width (or code transition levels)

Histogram (statistical) testBasic ideas II

The best shape would be ramp or triangular signal. Why? Problem?

The basic recommended signal by all standards: sinewave. Why?

To achieve a required accuracy a relative long record (or records) is required

Faster than the static test Requirement: an accurate generator with

an extremely high accuracy (low distortion, high linearity, high spectral purity)

Histogram (statistical) testGeneral test setup

Ramp signal (IEEE 1241)

T[k]=C+G.HC[k-1]/S for k=1, 2, .... , (2N- 2)G is a gain factor, C is an offset factor,The code bins 0 and 2N-1 are usually excluded from data processing (why?)

noiseandtynonlinearirampbygiven:yuncertaint

221

kDNL

1221

22

11

N

N

i

j

iC

SkH

QkTkT

STT

GTCiHSiHjHN

Sinewave signal(All standards) – theoretical background I

Signal: Density

of probability: Distribution of probability:

ftAtx 2cos

22

1arccos

21

dd

.2xAA

xx

xp

,

2.21

arcsin2.2

arcsin1

d1

11

2

2

2

2122

1

1

1

N

Nfs

N

Nfs

kV

kV

AkV

AkV

xxA

kPN

Nfs

N

Nfs

Sinewave signal(All standards) – theoretical background I

Ideal theoretical histogram:

DNL:

Transition levels:

N

Nfs

N

Nfs

id AkV

AkVM

kH2

21arcsin

22

arcsin11

kH

kHkHkDNL

id

id

12,,2,1

121

cos

NN

c

c kforH

kHACkT

Sinewave signal(All standards) – theoretical background II

Problem in praxis: what are the sinewave parameters – A, C →Hid[k]?

Various ways of estimation, e.g Dynad: Incorrect

estimation →error ingain and offset

12

22cos

120

cos

1~

12~

~

,

1222

cos12

0cos

1222

cos1~

120

cos12~

~

NC

NC

NC

C

N

NC

NC

NC

C

NC

NC

NC

CN

HH

HH

TTA

HH

HH

HH

TH

HT

C

Sinewave signalTest conditions I

The total record must contain exactly an integer number J of sinewave cycles

R partial records can be used instead of one long record

Total recorded number M of samples must be relatively prime with J, i.e. they have no common factor

Then the sampling and sinewave frequency are:

si fMJ

f

si ffrJMr

r

,

21

Sinewave signalTest conditions II

The number of samples (M) to acquire in the histogram test, depends on: The noise level in the measurement system, The required tolerance (B is measured in LSBs)

and confidence level () and the M is different if DNL (quantization interval) or INL (transition levels) it to be determined.

The specification of tolerance for an individual transition level or code bin width, or for the worst case in all range.

1BQTTBQTP MEASrealMEAS

Sinewave signalTest conditions III

The equation generally used to determine the number of records to acquire is:

J=1 for INL, J=2 for DNL, is the standard deviation of noise level in volt for the INL determination and the smaller of the values of and Q/1,1 for the DNL determination.

deK

MTTV

c

cTT

cB

KJR

NS

N

N

0

1

21

2

2erf2

11221

2,0112

1,12

Sinewave signalSimulation

Simulation = (see the simulation): Form of histogram for various test

signals Error caused by limited number of

samples Error caused non-coherent sampling Error caused by noise in input signal Error caused by higher harmonics …

Histogram test Experimental demonstration

Measurement setup (run generator first and then demonstration)

NI USB 6009ADC: 12 bits, 10kHz,

differential

AI1 (DUT) USB1:2

Software (LabVIEW):

Sinewave generator = Sound card

AI1 control = DUT - FS, record

Data processing and visualisation

Sound out

Results of experimental testsComparison generators (USB 6009)

Stanford DS 360 (20-bits, 100 mil. samples)

Agilent 33220A (14-bits, 100 mil. samples)

Histogram (statistical) test

Some non-standardized methods

Non standardized histogram tests Basic ideas

Reasons: To use signals that are closer to real signal

digitized by ADC in common applications To use signal that can be simply generated

with required precision Common signals:

Gaussian noise Exponential signal Uniform noise, small sinewave or triangular

with DC steps, …

Non standardized histogram test Gaussian noise I

Martins, R. C., Serra, A. C.: ADC Characterisation by using Histogram Test stimulated by Gaussian Noise. Theory and experimental results, Measurement, Elsevier Science B. V., vol. 27, n. 4, pp. 291-300, June 2000

The noise is centred within ADC input range and overlap the whole ADC range

Problem generate the noise with really precise Gaussian distribution – convenient methods for low resolution ADCs and very high and very low frequencies where it is difficult to generate sinewave with required purity

Non standardized histogram test Gaussian noise II

Holub J., Komárek M., Macháček J., Vedral J.: STEP-GAUSS STOCHASTIC TESTING METHOD APPLICATION FOR TRANSPORTABLE REFERENCE ADC DEVICE, Proc. 8th IWADC 2003, Perugia, Italy, pp. 223-226

Gaussian noise with a small standard deviation is moved within the ADC input range by adding a DC voltage (mean) in small steps so that the results will be the same as using uniform noise overlapping the whole ADC full scale

Discussion: is really possible in praxis to fulfil the requirement of the limit with finite DC steps with acceptable precision?

01

,lim0

kG kpdf

Non standardized histogram test Small amplitude sinewave or triangular with a DC component

Michaeli L., Serra A.C., ..: In: IEEE transactions on instrumentation and measurement, Measurement, proc. of IMTC, IMEKO – IWADC

Idea: multistep test with fractional histograms (and INLs) acquired at small signal (sinewave, triangular) covering only a few tens/hundreds of codes shifted within ADC FS by known DC voltage

Advantage: the quality of test signal may be much worse than those of signal covering the whole FS of ADC

Disadvantage: connecting the partial histograms to build the final histogram

Non standardized histogram test Exponential signal

Holcer R., Michaeli L., Šaliga J.: DNL ADC testing by the exponential shaped voltage, In: IEEE transactions on instrumentation and measurement, Vol. 52, no. 3 (2003), pp. 946-949.

Šaliga J., Holcer R., Michaeli L.: Noise sensitivity of the exponential histogram ADC test, In: Measurement, Vol. 39, no. 3 (2006), pp. 238-244

We will continue with a new PhD. Student next year

Exponential signal is simple to generate – native signal in electronic circuit

Problem: distortion by other exponential with different time constant and keeping the final value of the signal known and constant.

Bt

BFStx

exp

Non standardized histogram test Small signals with a DC component

Measurement setup (run generator first and then demonstration)

NI USB 6009ADC: 12 bits, 10kHz,

differential

AI0 (DUT) USB1:21:10

Arbitrary generator = Sound card

DC shift = AO0

AI0 = DUT (FS, record)

Data processing and visualisation

Sound out

AO0 (DC shift)

Software (LabVIEW):

Histogram testConclusions

Histogram versus static test: histogram test gives usually better – more reliable results because: Faster = the test conditions are “constant”

and measurement of any T [k] is distributed and repeated in time over the all testing time

Disadvantage: an precise generator is needed Non standardised test procedures can

bring simplifying in test setup and decrease the requirements on instrumentation precision.

ADC dynamic testing

Dynamic testIntroduction

Goal: Determination of various dynamic ADC

parameters such as SINAD, ENOB, SNR, THD, IMD SFDR, …

Two ways of data processing: Time domain – directly SINAD, ENOB Spectral domain (DFT test): SINAD, ENOB,

SNR, THD, IMD SFDR, … No way can be generally supposed to be

the best one

Dynamic testGeneral test setup

Dynamic testRequirements

Coherent sampling – the same as for sinewave histogram test - the precise coherence is not necessary

Minimal size of record:

Record can consist of a few partial records Sinewave must cover the ADC input range

as much as possible (more than 90 – 95%) but must not overload it.

NM 2min max

min 12

DNLM

N

Dynamic test

Data processing in time domain

Dynamic testData processing in time domain I

See the following lectures by prof. Kollár and prof. Händel

Basic idea: to calculated the noise in the record (residuals) as the deference between the input signal – sinewave (analogue samples) and the record (digitized samples).

Knowing the noise the SINAD and ENOB can be calculated according the definitions

xyη ~

Dynamic testData processing in time domain II

Difficult task and question: the input signal must be precisely know – how to do it?

Common solution: recovering the input signal from the record by a fitting method (LMS) Three-parameter fit (A, C, ) Four-parameter fit (A, C, , f)

Question: is the recovered fitted signal really the origin input signal?!

Dynamic testThree-parameter fit I

Simple calculation = system of linear system of 3 equations is to be solved

CmfAmfA

CffmAf

fmA

CmfACffmAmx

iNiN

s

i

s

i

iNs

i

2sinsin2coscos

2sinsin2coscos

2cos2cos~

22

1

0

2

~E

2sinsin2coscos1

rms

M

miNiN CmfAmfAmy

M

xy

Dynamic testThree-parameter fit II

In matrix form: T,sin,cos CAAP x

11-Msin21-Mcos2

.........

1sin2cos2

101

where,~ T2

iNiN

iNiN

PP

ff

ff

D

DxyDxyxy

yDDDxx

DxyDxy T1TT

0

P

P

PP

Dynamic testThree-parameter fit III

Necessary condition:The input (and sampling) frequency

must be precisely known!!!If not – incorrect results SINAD, …

SEE THE SIMULATION

Dynamic testFour-parameter fit I

Unknown parameters: A, C, , f Difficult calculation = system of non-

linear system of 4 equations is to be solved

The system can be solved only by iteration process

Dynamic testFour-parameter fit II

Let T,,sin,cos iNP fCAA x

T,,sin,cos jiNjjjjjjP fCAA x

12cossin1

12sincos1112sin12cos

............2cossin

2sincos12sin2cos

0101

11

11

11

11

MfMA

MfMAMfMf

fA

fAff

jiNjj

jiNjj

jiNjiN

jiNjj

jiNjj

jiNjiN

j

D

00 iNf0iNfLet the first estimation

is yDDDx T

jjTjjP

1 11 jiNjiNjiN fffRepeat

calculation:

Dynamic testFour-parameter fit III

Problem with convergence – one global minimum and a few local minima

If the first estimation is incorrect the iteration converges to the fault minimum One of best estimations is the estimation from

spectrum within the interval (J-s, J+s):

See the simulation

sJ

sJm

sJ

sJmiN

mY

mYfmf

2

2

~

Dynamic testData processing in spectral domain – DFT test

Dynamic testData processing in spectral domain I

The same test setup, requirements and the first step as for Data processing in time domain

The DFT spectrum is calculated from the record

Using the definitions (see the beginning part of this lecture) the unknown ADC parameters can be estimated

Dynamic testData processing in spectral domain II

Common problem in praxis: incoherent sampling – leakage effect in the record spectrum

Solution: applying a window function (Hanning, 7 term Blackman-Harris, …) to suppress the leakage effect and then correction of results according the window parameters (see the general theory of windowing in DSP) Introduced in detail in DYNAD Rule: the higher the ADC resolution is, the lower the

side-lobes of the window have to be. Nevertheless, lowering the side-lobes results in increasing the main lobe width

Calculation is much more complex

Dynamic testData processing in spectral domain III

Spectrum calculation:

Error in coherency:

1

0

.2

eM

m

Mmi

fj iN

mxmwiY

1

0

2

21

0

2

2

1

0

22

21

0

2

M

n

M

n

T

M

nT

M

n

nw

nw

A

nw

nwA

PG

21

0

1

0

2

M

n

M

n

nw

nwMENBW

Processing gain

Equivalent Noise Bandwidth

Mf

Jf sJi

Dynamic testData processing in spectral domain IV

Changes in formulas: example 1: Noise floor:

maxmax

maxmax

12/

(,1,1

22

2

0,2

)12(2

221

llhh

lhM

MYkY

NFl

M

lJhrndkJkk j

Dynamic testData processing in spectral domain V

Changes in formulas: example 2: SINAD

max

2

2

2

22

max

12/

(,1,1

1

0

22

max

2

2

222

,0

.

and

0with

0,22

122

:where

0log10log10log10

h

h

M

feisj

c

sjrc

j

M

lJhrndkJkk

M

n

sjrc

dB

dttweM

fW

M

fJhfracW

WJhrndYENBWB

ll

nwWM

YNFllkYA

M

fW

WENBW

BA

NFlJYSINAD

sj

j

Dynamic testConclusions

No method of data processing can be suppose to be absolutely the best

Processing in time domain is less sensitive on coherency but the 4-parameter fit can be problematic

Processing in frequency domain gives directly much more parameters but it is very sensitive on coherency

The final conclusions ADC testing is not a simple task Extremely difficult task: to test ADC with

high resolution (more than 20 bits) Methods are in the process = a challenge

for you Another challenge: test procedures for

special ADC, e.g. band-pass for direct digitalization and demodulation of high frequency signals, etc.

Thank you for your attention