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TYPE 34200 STOCHASTICAL ANALVSER

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<strong>TYPE</strong> <strong>34200</strong><br />

STO,CHASTICAL<br />

<strong>ANALVSER</strong><br />

NSA-1000


<strong>TYPE</strong><br />

TYP<br />

346 O<br />

LVSE<br />

"-'<br />

l-ivtta, ,v)~{ .g_+ &tt"'cl -.zeti: 0 JA:-..w.l.J.te>t.~~<br />

( c'j_ "'1..;,.... ' -<br />

E ...-1 {.:.- ,.,...,~ ,,-fr;rrr S../l t!;~V'í.o~ · ~ , ........ t<br />

( ~ 7 J<br />

The Type 34 200 STO CHASTICAL ANALYSER ~ /; !'('{ 1 .)<br />

BASIC ASSEM BLY is a universol equipment for j-eV>.(-(<br />

testing rando m signals. Since, however, the r<br />

basic a ssembly will accommodate measuring ~ { ~\.'i~<br />

unit s other than the four basic ones, a new<br />

stochastical analyser is obtained, which offers<br />

a lorger number of facilities. Moreover, throug h<br />

o combination of the additiono l measuring units,<br />

setups optimolly suited to the actual measurement<br />

task will be obtained. The basic assembly<br />

can be used above ali in the follawing functions:<br />

auto-correlation<br />

cross-correlation<br />

cross-correlation (voltage-pulse)<br />

multi-channel signal averaging<br />

pulse rate time distribution<br />

time interval distribution<br />

omplitude distribution<br />

amplitude density<br />

signal mean and rrns values<br />

digital filtering<br />

pseudo-ro n dom sig na l generation<br />

system identification by pseudo-random<br />

sig no ls<br />

continuous manitoring or single onolysis<br />

generotion of digital sine, cosine, sowtooth<br />

sig no ls.<br />

The individuol odditional units will add the follawing<br />

functions to the above ones.<br />

FOURIER TRA SFO M<br />

E-640<br />

FOURIER TRANSFORMER<br />

real or imoginory port of lineor spectrum<br />

outo-power density function<br />

real or imoginory port of cross-power density<br />

function<br />

multiplication with window function (rectangulor,<br />

Honning, Bortlett)<br />

logarithmic Y output, too<br />

PE 3 67<br />

Dl IT L INTE<br />

Z- 75<br />

CE<br />

MONITOR<br />

visual observotion ond value estimation of<br />

input and output signals<br />

oncitlory for hondling ond servicing the peripherals<br />

.. off-crote" functioning (only +5.8 V/3,5 A).<br />

DIGITAL INTERFACE<br />

readout of chonne11 number and channel<br />

content of basic assembly<br />

readout of channel number ond channel<br />

content of Fourier transforrner<br />

continuous data readout within preselected<br />

limits<br />

interface to printer, tope punch, teletype<br />

optional (under development) interface to<br />

Type 666 programmable colculator


The equipment has been designed with the objective<br />

of providing a range of parameters as<br />

wide as possible, enabling many different types<br />

of measurement. The time schole of 100 ns to<br />

1 s, a resolution of about 1 °/ 0 (corresponding to<br />

100 channels), its facility of continuous manitoring<br />

- ali ore valuable features suiting the<br />

equipment to very wide applications in the<br />

measurements of stochastic signals. The equipment<br />

is a signal analyser ernplaying 100 digital<br />

channels, a storage capacity of 20 bits/ channel,<br />

performing aU computations simultaneously<br />

with the measurement. The basic as·<br />

sembly does not include a result display, but<br />

it can be attached to any conventional type of<br />

oscilloscope or XV plotter. Furthermore, the<br />

principel signals can be obtained from connectors.<br />

The resuhs can be read out at any frequene-y<br />

even during the measurement. ln addition<br />

to the conventional integreting-type averaging<br />

(single analysis), "forgetting" type integration<br />

(continuous monitoring) is also feasible. Both<br />

the number of averagings and the " forgetting"<br />

time constant ore variable over a wide range.<br />

The equipment can be used for the onolysis of<br />

continuous signals (AC or DC) and pulses. The<br />

width of its time channels can be selected between<br />

100 ns and 1 s (in correlation modes);<br />

thus it is equally suitable for the investigatien<br />

of very fast and very slow processes. ln amplitude<br />

analyses, the maximum sampling freque n­<br />

ey is 5 kHz (otherwise 0.5 M Hz). The f unction<br />

generator provides digitaily generated sin, cos,<br />

pseudo-random and sawtooth sionals with<br />

frequencies adjustable over wide limits. The<br />

time functions of the basic assembly in multichannel<br />

signal averaging and correlation modes<br />

e-an be studied by aid of the Fourier transforrner<br />

in the frequency range, too. For a better<br />

i'llustration, the number of frequency pointscan<br />

be increased. Thus, tagether with the cycle time,<br />

the frequency resolütion can be varied over<br />

wide limits (from 1.25 mHz to 100 kHz). Focil1-<br />

ties ore provided for using time w indows other<br />

then the square-form, vis. multiplication by<br />

Honning and Bartlett weighting function. The<br />

real or the imaginary ports of the functions<br />

within the particulor range can be fo rrned in<br />

succession. Like in the basic a ssembly, the data<br />

outputs deliver analog as weil as d igita l signals<br />

moreover, the analog Y output can be switched<br />

over to logarithmic display, too. The Manitor<br />

unit performs mainly ancillary functions -visual<br />

observation of signals, the estimation of their<br />

values, setting the test setup, facilitating a servicing<br />

and handfing of peripherals (e. g. the use<br />

of Z modulation at peak searching}. Plugged in<br />

alternatively, the M anitor and the D igital Interface<br />

will take over the manitoring function of<br />

the power supply. IM PORTANTI The Manitor is<br />

suitable for "off·crate" functioning, too, only a<br />

power supply of +5,8 V/3,5 A is required. The<br />

Digital Interface enables the variaus functions<br />

(recorded by the basic assembly) and, in expanded<br />

configuration, the frequency spectra<br />

(provided by the Fourier transformer) to be displayed<br />

digitaily or recorded on o tape punch,<br />

o printer or teletype - of course, either for o<br />

given point o r for a ny arbitrary section.<br />

GENERAl SPECIFICATIONS OF THE<br />

BASIC ASSEMBLY<br />

mains data : voltage 220 V ± 10 Ofo<br />

(127 or 110 V by re-connection)<br />

frequency : 50/60 Hz<br />

power consumption: 250 VA<br />

- dimensions: height 316 mm<br />

widttl 505 mm<br />

d epth 600 mm<br />

weight : 36 kg<br />

warm -up time : 15 minutes


o HE IC S E BLV<br />

@<br />

Cabinet<br />

C rate (wi red frame)<br />

Front panel covering two blank ponels<br />

(i<br />

CE,<br />

0<br />

0<br />

Measuring uni ts :<br />

type 34 630 Sam pl ing unit NE-630<br />

type 34 631 1Processor NE-631<br />

type 34 632 Mulii-channel integretor NE-632<br />

type 34 633 Function generator NE-633<br />

IllUllliUl IUlfill IIIIC AlUilU<br />

"" lll·-<br />

+mn<br />

1111 llllllliT<br />

l \<br />

type<br />

®<br />

34 252 Power supply NB-252<br />

®<br />

0<br />

type 34 252/ 111. law-current unit<br />

®<br />

type 34 252/IV. capacitor unit<br />

typE 34 252/ 11. high -current unit<br />

®<br />

@)<br />

®<br />

@<br />

type 34 252/V low-valtage<br />

type 34 252/VI. law-voltage<br />

type 34 252/VII. low-valtage<br />

unit<br />

unit<br />

unit<br />

- type 34 657 Po wer control unit NZ-657<br />

..<br />

®<br />


G<br />

<strong>TYPE</strong> 34630 SAMPLING UNIT NE- 630<br />

. ~<br />

UIPLII5 IIIT<br />

NE830<br />

~ · · c>l<br />

.:> .<br />

OlGITAl OUT<br />

CHACNJ!<br />

HT.P !..Ol<br />

the second 100-channel correlation<br />

can also be recorded by aid of the<br />

computationai delay<br />

function<br />

built-in<br />

~ further (external) delays may be added through<br />

the rear panel connector<br />

(! analog pre-processing: ca libroted ga in and DC<br />

offset (independent at both inputs) ;<br />

selection of the appropriate input channel;<br />

selection of DC, G N D, A C;<br />

overdrive indicatien in compliance with the<br />

+3 V window;<br />

peak detection<br />

4& um<br />

4<br />

HL-level trigger pulse output correspo nding to<br />

the actual mode of triggering, for d riving other<br />

instruments<br />

pseudo-random or sawtooth signal connection<br />

MAIN TECHNICAL DATA<br />

- Input coupling: DC, GND, AC<br />

- Input voltage range : 0.1 to 15 V p-p<br />

- DC offset : ±5 V (resolution 10 mV)<br />

- Max. input voltage: ± 20 Vp<br />

- Input impedance : 100 kohms // 30 pf<br />

- Bandwidth : DC to 1 MHz (-3 dB) or<br />

1 Hz to 1 MHz (-3 dB)<br />

- G ain : in ó steps (with a continuous coverage of 1 :3<br />

within each step)<br />

- Precomputational delay : zero, external, 100 L:,t<br />

- Pulse counting : max. 15/ L:, t (max. 5 M Hz)<br />

- A/D conversion, in channel A: ± 3 V in steps of 200 mV<br />

in channel B': 1 bit (related to the reference<br />

voltage)<br />

- Max. voltage of reference input: ± 5 Vp


<strong>TYPE</strong> 34631 PROCESSOR NE-631<br />

STOCH 'ST ICA L A.NA LY!ER<br />

(NIA IOOOJ<br />

CIOCK<br />

IIIARNING:<br />

H CI. OCK IS<br />

OlY ID EO &T<br />

MoH .2 0 M~ z<br />

UJ CI O C~ l PUT<br />

. ~ o<br />

o<br />

[IMI"t<br />

PUlSfS OU T<br />

RFMIJTE COliT t<br />

12 measuring modes<br />

2 operotion modes<br />

®<br />

a new meosurement cycle may be triggered by<br />

the end of the previcus cycle or by o voltage<br />

level of the input signal or by on externol signol<br />

the red LED is illuminated if a trigger is selected<br />

incansistent with the actual measuring<br />

mode<br />

• SYSTEV MFKI<br />

.,..,,<br />

NAOE IN HO HSA~Y<br />

principel signals (controlling the operotion of<br />

the onalyser). Remete control of trigger ond<br />

measuring modes<br />

®<br />

output used for triggering processes synchronous<br />

with the measuring cycles, for operotion<br />

in the onalyser system<br />

MAIN TECHNICAL DATA<br />

Modes ol measurement<br />

- Auto-correlation: to i n put A or B<br />

- Cross-correlation : input A or B delayed, or B delayed,<br />

pulse A, anologue B<br />

- Multi-channel signal averaging<br />

- Pulse rate time d istribution<br />

- Time intervol distribution<br />

- Amplltude distribution function<br />

- Ampiitude density function<br />

- Sig nal mean value<br />

- Signal rms value<br />

M odes ol operotion<br />

- Cleoring the register contents<br />

- Measurement process<br />

- Data starage (after measurements)<br />

Sompling ol delay eyeles<br />

- ln correlation measurements: 0.1 /Js to s {in 22 steps)<br />

- ln PHA : 0.2 ms to 1 s (in 12 steps)<br />

- ln t he rest of functions : 2 us to 1 s (in 18 steps)<br />

Clock pulse: 10 MHz (accurocy, ± to-lt, at +25°C)


<strong>TYPE</strong> 34632 MULTI-CHANNEL INTEORATOR NE-632<br />

CD<br />

from the attainment of the averaging number<br />

selected, the red LED is illuminated (i. e. indicating<br />

the campletion af the measurement or<br />

the beginning of the formatien of on uncolibroted<br />

result)<br />

generation of + 40 V norrow pulses for each<br />

channel (or far every 100 chonnels) for the monitor<br />

or oscilloscopes<br />

0)<br />

the integretor may also be operated from on<br />

external digital source, thus e. g. o digital filtering<br />

con be realized in exponentiol averaging<br />

&Oa unt<br />

M~Df IH HUNU~Y<br />

MAIN TECHNICAL DATA<br />

M odes of operot ion<br />

- Exponential averaging<br />

(the ,.forgetting" time canstal)t depend s on the m'Ode<br />

of measurement ond the sampli ng or delay cycle)<br />

- linear averaging with preset display<br />

- linear averoging, w ith o utomotic stopping upon ottoinment<br />

of o p reset value<br />

Number of o veragings: 2K where K = 4, 6, 8, 10, 12, 13,<br />

14, 15,<br />

Data outputs<br />

- Output X (channel number) : 7 bits binory and ± 3 V<br />

analog<br />

- Output Y (channel content : 20 bits binary (with sig n),<br />

± 3 V analog (the 7-bit portion of the 20 bits<br />

te be read out can be selected in 8 steps for<br />

the D/A converter)<br />

Readout modes<br />

- For each channel, w ith manual Iriggering<br />

- Fast readout, e. g. for oscilloscope<br />

- Slow readout, e. g. for XV platter (0.2 Ht to 10 Hz)<br />

- Slow readout from external clock pulse


<strong>TYPE</strong> 34633 FUNCTION GENERATOR NE-633<br />

FUNCI IDN<br />

lElEIATil<br />

ti.:<br />

o . -<br />

LJ<br />

o<br />

It<br />

o<br />

(-)<br />

OlGilAl lll<br />

•O<br />

G) providing signols in step with the repetition of<br />

o pseudo-rondom signal<br />

@ the binory output may provide signal trains re•<br />

turning or not returning to zero<br />

0 in the case of coding or decoding, it will provide<br />

o signal if a ditference is found between<br />

the initici word and the coded one<br />

&Or; neu<br />

lo


u<br />

<strong>TYPE</strong> 34640 FOURIER TRANSFORMER NE-640<br />

.SJO(II.A.$'f1Cll AMAlfi El<br />

't' OUf<br />

u r tLO t<br />

..<br />

10<br />

the data loading and camputation processes<br />

can be started by a · toggle switch except<br />

when the automatic method is applied<br />

®<br />

the weighting function is generated by the<br />

Function Generator (the Fourier t ransfarmer<br />

providing the clock pulse only)<br />

any quarter of the transforrned function can be<br />

magnified by varying the display sensitivity<br />

4<br />

the readout cycle is slow (here fixed<br />

manual or external, similor to the<br />

sem b ly<br />

®<br />

1 Hz), fast,<br />

basic ossimilor<br />

to the Multi-channel lntegrotor, the 8-bit<br />

part of the 20 bits to be read out can be selected<br />

in 4 steps for the output D/ A converter<br />

MAIN TECHNICAL DATA<br />

- M öde: real or imaginary part of spectrum<br />

- N umber of f requency' points: 50, 100, 200, 400 where<br />

the respective frequency resolutions ore L,f, /:::,.f/ 2,<br />

/::,f/4, l:,f/8 (l:,f= 1/100l:,t)<br />

- Frequency range : DC to 5 MHz<br />

- Weighting window : rectang ular, cosine (Honning) ond<br />

Bartlett<br />

- Input data loading : manual or outomotic<br />

- Data output: analog X, lin Y or X, log Y<br />

d igital X, Y (in binary code)


<strong>TYPE</strong> 34641 CRT MONITOR NE-641<br />

STt:rCH4 llf l ~HÁLY Ifi<br />

in ,.off-crate" operation, the connector can be<br />

driven by o power supply of + 5.8 V source<br />

voltage (providing 3.5 A)<br />

input sensitivity controls matched to the basic<br />

assembly<br />

LED takes over the function of the power control<br />

unit (blinking at about 1 Hz to indicate the<br />

failure of any one of the supply voltages)<br />

switch, for switching the Manitor on or off, separately<br />

MAIN tECHNJCAL DATA<br />

- Input coupling: DC, GND, AC<br />

- Sensitivity: 2, 1, 0.5 V/div.<br />

- Input impedonce : 100 kohms ll 30 pF<br />

- Max. i n put voltage: 63 V<br />

- Bandwidth: DC or 0.3 Hz to 1 MHz (-3 dB), for X<br />

omplifier<br />

DC or 0.3 Hz to 1.5 MHz (-3 dB), for Y<br />

omplifier<br />

- Z medulotion (with AC coupling) : min. +s V<br />

max. + 4o V


<strong>TYPE</strong> 34675 DIGITAL INTERFACE NZ-675<br />

STOCMAS tiC&l att.\ l TUR<br />

DIGITU liTERrACE<br />

NE-875 l<br />

Q) the place of the first p. c. board is blank for<br />

· the option<br />

the data ore receíved from the Multi-channel<br />

Integretor and the Fourier transforrner through<br />

four 20-pole connectors<br />

triggering or stopping of readout by a toggle<br />

switch<br />

unblanking signal output for the monitor<br />

34 675<br />

IN HUNGARY<br />

@ LED takes over the function of the power control<br />

unit (blinking at about 1 Hz to indicate the<br />

failure of any one of the supply voltages)<br />

MAIN TECHNICAL DATA<br />

- Function: displaying the function values of the basic<br />

assembly or the Fourier tronsförmer<br />

- Channel volue indication: sign + 4 digils (decima!)<br />

ond a 2 diglt exponent (wlth sign) of o blnary base<br />

- Display of channel number : 3 d igils<br />

- Channel number selection: by 2x3-digit thumbwheel<br />

switches (initio! and final volues)<br />

- Peripheral interfoces<br />

tope punch :<br />

T-105 Model (mgde in Polond), MOM EC 7191-01<br />

(EP 36) or 4070 Focit (with selector)<br />

code: 8-bit ASCII, porollel data transfer<br />

teletype:<br />

ASR, KSR, RO (Data Dynamics),<br />

GPO or V- 24 interface<br />

code: 8-bit ASCII, se ri ol data transfer<br />

p rinter :<br />

TR-1872 (type 14892)<br />

code : ASCII reduced to 6 bits, porollel data transfer<br />

- Optional (under development) Interface to the type 666<br />

programmable colculator; with this facility incorporated,<br />

the remete control functlons of the basic assembly,<br />

the Fourier t ransforrner ond the Digital interface<br />

os weil os the control functions of data delivery<br />

will be perforrned by the calculotor.


CIPAL D TA OF OTH<br />

U TS<br />

<strong>TYPE</strong> 34252 PO WER SUPPL V<br />

NB-252<br />

Nominal output voltoges and current s:<br />

+40 V/70 mA<br />

+ 15 V/0.5 A<br />

+ 12 V/0.5 A<br />

-12 V/0.9 A<br />

+ 5.8 V/16 A<br />

- 6 V/0.5 A<br />

<strong>TYPE</strong> 34657 POWER CONTROL UNIT<br />

N Z-657<br />

ln the event of a breakdown of + 5.8 V, + 15 V,<br />

+ 12 V, -6 V stabilized and +40 V unstobilized<br />

voltoges, it will deliver a blinking signal of obout<br />

1 Hz.<br />

<strong>TYPE</strong> 34604 SERVICE UNIT<br />

NE-604<br />

It enables the measuring units to be operated<br />

" off-crote".<br />

EQUIPMENT RECOMMENDED FOR PERIPHERALS<br />

<strong>TYPE</strong> 14892 PRINTER TR-1892<br />

Printing rate:<br />

· Column copocity:<br />

Set of characters :<br />

Data input:<br />

1 line/s (asynchronous)<br />

20<br />

64 different c haracters<br />

(7-bit ISO code reduced to<br />

6 bits)<br />

parallel BCD coded, TTL level<br />

positive logic<br />

<strong>TYPE</strong> 79812 X-Y RECORDER NE-240<br />

Se nsitivity:<br />

Applicoble chart size:<br />

20 mV/cm to 10 V/cm<br />

297x420 mm (A/3 format)<br />

Possthrough speed (average): min. 50 cm/s<br />

Controllable pen lift


<strong>TYPE</strong> <strong>34200</strong> ASS EMB lES OF THE <strong>STOCHASTICAL</strong> ANAL YSER<br />

AND ITS ADDITIONAL UNITS NSA- 1000<br />

Th e un1versal character of<br />

t he measurement system may<br />

be considered frorT' two aspects.<br />

Th e basic assembly<br />

!one is suitable f or a wid e<br />

v ri e ty of measurements;<br />

t he combinations ot t he a d­<br />

ditio nal measu ring llnlts<br />

will furt her Increc se the<br />

number of setups fo r different<br />

p u rposes. 10 dlfferent<br />

setups o re available, six of<br />

which o re totolly self-conta<br />

ined, the rest assuming<br />

the use of an external power<br />

sourc e.<br />

<strong>TYPE</strong> <strong>34200</strong><br />

Conti nuous manitoring of the tests<br />

provid ed by the basic o sembly he<br />

manitor involves lower costs t hon the<br />

permanent use of o generai-purpose<br />

oscilloscope.<br />

<strong>TYPE</strong> 34640<br />

<strong>TYPE</strong> 34640<br />

(-0<br />

It ca n be used<br />

for the invest!-<br />

g ation of fu netions<br />

in the<br />

time domain<br />

over the f requency<br />

range.<br />

There ore special<br />

means (e<br />

g. ascilloscope)<br />

provided for<br />

displaying the<br />

output f unctions.<br />

For the tests provided by the basic a ssembly, but<br />

the resu lts may be led to o printer, o tope punch<br />

or teletype.<br />

r - - - -~<br />

:<br />

l<br />

l<br />

.......__...;;;..__ <strong>TYPE</strong><br />

l l 34641<br />

1-----.J ffi<br />

The above setup is completed with<br />

o n external manitor powe red from an<br />

external power supply C+ S.B V/ 3.5A)


<strong>TYPE</strong> 34641<br />

®<br />

-----,<br />

l<br />

l<br />

-- _<br />

For continuous monitoring. For the<br />

..<br />

combined manitoring of a 100-channel<br />

auto-correlation function and<br />

power density function.<br />

l<br />

l<br />

l<br />

l<br />

'--<br />

l<br />

l<br />

- ..l<br />

An optimum setup<br />

with two external<br />

monitors.<br />

<strong>TYPE</strong> 34641<br />

@<br />

monitoring.<br />

An optimum setup provided a general-purpose<br />

oscilloscope and peripherals<br />

ore available.<br />

An optimum<br />

external monitor.<br />

setup with an<br />

EB<br />

PERIPHERALS<br />

PERIPHERALS<br />

Ci)


10<br />

The principel operotion modes of the equípment<br />

are the generation of correlation functions,<br />

línear or exponentíal averaging thereof<br />

and the investigatien of their behavíour wíthín<br />

the gíven domain. The analyser generates digitaily<br />

a relay correlation functíon, substituting an<br />

i -bit bínary word for the signal coming through<br />

one measuring channel ín the samplíng time<br />

ínstants (substitutíng a 5-bit binary word for<br />

the signal coming through the other measuring<br />

channel). The 1-bít manitoring is made wíth respect<br />

to a pseudo-random auxílíary signa l {also<br />

called .,dither" ). The way of sampling varies<br />

wíth the delay cycle time.<br />

.. t<br />

x(t)<br />

y(t) L__,S,_b",i_,_,_ ts _ _ _ _____, l ~b i t multipl i e r<br />

Sym metrical sampling (SS) in slow modes J<br />

,<br />

'~!<br />

i -bit multlplier<br />

Botch sornpling (BS) in medium-rate modes<br />

l -bit register 1 bit reg ister<br />

x(t)<br />

1-bit<br />

multiplier<br />

Shift sampling (ShS) in fastest modes.<br />

J


ln addition to linear averaging, the other averaging<br />

procedure applied by the analyser enables<br />

the process parameter under test to be studied<br />

continuously over a long period of time. The<br />

exponential .,forgetting" typical of the analogue<br />

RC complex, may be written with the help of<br />

the follawing digital arithmetic procedure:<br />

x. +<br />

l ~<br />

Subtroctor<br />

-~<br />

f ...<br />

1<br />

2K<br />

'r!<br />

Adde r<br />

1 ..<br />

1 Register 1--<br />

Black diogram of exponentiol overogíng, K=4 through 15<br />

r<br />

ln the memory of the basic assembly, the result<br />

function is represented by a function sector<br />

consisting of 100 digital samples. ln the course<br />

of the transformation to be carried out, the initio!<br />

signal is regarded to be the periodic repetition<br />

of that sector: the Fourier series of the<br />

signal is generated. The actual frequency resolutien<br />

to be obtained is equal to be reciprocal<br />

of cycle time; the highest actual frequency ls,<br />

as a rule, a hundred times thereof. To better<br />

illustrate the result of transformation, the<br />

number of frequency points may be selected to<br />

be greater, too.<br />

function<br />

to be transformed<br />

o cosine<br />

multipller function<br />

( 2n) cos N n · m<br />

T = 1\ L t<br />

-----,!'<br />

weighting function<br />

Of N sampled values, M=N/2 freq uency points<br />

can be obtained. The m-th real or imaginary<br />

frequency component can be obtained from the<br />

follawing formulae:<br />

N-1<br />

Am= .2 xlnl)· w(nl)· cos l:._l_l) n·m<br />

n= O \ N N N


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