SU1424027A1 - Device for performing fourier transform - Google Patents

Abstract

The invention relates to the field of automation and computer technology and can be used in control systems for vibration testing of technical objects, measuring equipment. radio engineering and telecommunications to perform forward and inverse Fourier transforms of continuous and discrete, deterministic and random signals in real time. The purpose of the invention is to expand the functionality by performing the inverse Fourier transform. This goal is achieved due to the fact that the device includes an analog-digital converter 2, a clock pulse generator 3, a frequency divider 4, a pseudo-random number generator 5, a counter 6, a block of this memory 7, a comparison block 8, accumulating accumulators- subtractors 9 and 16, two groups of 10 from M comparison units and M totalizer-subtractors, switch 12, pulse distributor 13, element OR 14 and block of elements OR 15. 2 Il. с (f (Л с:

Description

Yu

four

O u

g--:

The simulation relates to automation and computing technology and can be used in control systems of vibration tests for technical objects:), measurement technology, radio .., and telecommunications to perform direct and discrete Fourier transforms continuous and discrete, real-time deterministic and random signals.

The purpose of the invention is to expand the functionality of the device by performing the reverse Fourier transform.

Figure 1 shows a block diagram of an apparatus for performing a Fourier transform; Fig. 2 shows timing diagrams explaining the operation of the device in the reverse Fourier transform mode;

The device contains information input 1, an analog-to-digital converter (ADC) 2, a generator of 3 clock pulses, a divider 4 frequencies, a generator of 5 pseudo-random numbers, a counter 6, a block of 7 permanent memory, a block of 8 comparisons that accumulate sum-players 9 , two groups JO;): b, | shackles of comparison and M adders - 1 h1 readers, information inputs 11 for direct Fourier transform, switch 12, distributor 13 pulses, element OR 14 and block of elements OR 15 accumulating sum-tor-reader 16 and an output 17 of the device for the inverse Fourier Ani.

The pnOfvrncT device in two modes: mode. , y transform and D mode inverse transform; Fourier type.

In the direct conversion mode, the switch 12 is set to the lower position (FIG. 1), and the input analog signal is fed to the input of the ATP 2. The clock pulses from the output of generator 3 are received through divider 4 with a division factor of 2M (M is the number of detected harmonics a) to the control input of block 2, at the information output of which digital samples of the input signal are formed, to the input of the generator 5 pseudo-random numbers, the output of which is formed by the step; firstness of pseudo-random numbers (p), and through counter 6 to the address input of the block ka 7, at the outputs of which sequences of numerical codes are formed, corresponding to the values of the filter functions 3 "; (p) for the first group of 10 blocks and C"; (p) for the second group 10. Herewith

S,; (n)

. 2 sin ni;

0

(12)

 (n) cos - ni,

where N is the number of samples of the input Si1

Nala;

n is the serial number of reference 5 ne 1.

m is the sequence number of the filter function m l, M;

1 is the number of the Fourier coefficient to be determined

0 iiLN / 2.

Comparison blocks compare the numbers coming from the outputs of block 7 and generator 5. If the number received at block 8 is equal to 5 ° NIN from block 7, for example, it is greater than the number received from generator 5, then the output of this block compares permitting the addition operation to be performed in the corresponding from M na0 accumulating adders-subtractors 9, if the specified condition is not fulfilled, the code permitting the execution of the subtraction operation. At the time of discretization X (p), the values of the signal under investigation in the form of a digital code from the output of block 2 are fed to the information inputs of accumulating adders-subtractors 9. Upon entering the control input of the adder5

In addition, code 9, which allows the execution of the Fold, contains the addition X (p) with the amount accumulated at the preceding sampling times. Otherwise, produced

subtraction X (n). After performing N cycles of sampling the values of the signal under study (conversion cycle), M accumulative totalizers-subtractors 9 of the first group 10 are recorded

By the M values of the coefficients a,, and in the M accumulating totalizer-calculators x 9 of the second rounds 10 are the M values of the coefficients b; ;

55

AH

a, X (p) F sin -, - p1- (p);

3)

BUT

B; Y; X (p) F cos. (P) ()

R

With the rapier distribution law P (n) n P1yh (the cast sequence of the generator 5 pseudo-random numbers F (n) at the outputs 11 of the adders of the reader 9 appears the corresponding values of the discrete Fourier transference coefficient:

one

I, N ZX (n) - in-N-i5

 12 i

b; G, Z X (n) cos - ni,

N

N

15

of block 7, for example, more than the number of generators stalled from the output of this block is a code that resolves at the appropriate addition from the M adders-subtractors; if not, the code allowing subtraction operations (fig.2d) means subtraction, ny - addition). Since the inputs of the summators 9 are not supplied, they are not changed by mine, and the corresponding codes for summation are stored in the corresponding registers of the totalizer-subtraction. On arrival from the pulse distributor (Fig. 2b) these codes n are read from the registers of the readers 9 hours through an element (Fig. 2e), the control input of the adder-subtractor 1 2g is received temporarily with the reading of the control codes from the adders-subtracted are alternately read and xp

BUT

in them, the coefficients a; and b ;, go through the unit 1D to the information input from the calculator 16. After performing the cycles in the accumulator, the subtractor 16 (FIG. 2g) renders the following sum written

20

thirty

with the coefficient of trust, depending on the time of the summation interval (averaging), since the average value of F, for example, for S (n) is equal to

F (n) Jp (n). (7)

In the Fourier transform mode, the switch 12 is set to the upper position (Fig. 1). The totalizers 9 of the first group 10 store the values of the Fourier coefficients a, and, in the adders 9 of the second group 10, the values of the coefficients

1e | , which were obtained during the direct P1-) formation of Fourier. Summator 16 is in the zeroed state.

Clock pulses from the output of the generator 3 through the switch 12 to the input of the distributor 13 pulses, and through the divider D frequency with a period ut (Fig.2A) to the inputs of the counter 6 and the generator 5 pseudo-random numbers. The output of the latter is formed after the succession of pseudo-random numbers (p), (Fig. 2b), and the output of counter 6 forms an address code, which in turn goes to the address input of block 7. At the outputs of the last, sequences of numeric codes are formed, corresponding to the values of the synthesizing functions S (p) for the first group of 10 blocks and Cn; (p) for the second group of 10, which, like the Filtering functions, ° and in the subtractor 16 are described by relations (1) and (2 ) (on figg depicted S, (n) and (p) for the 1st and 5th harmonics).

35

X (

 , 1-1- (1)

 , R 2tg.

one

40

45

This sum is read from the subtractor 16 (Fig. 2k) n 17 (2M + 1) pulse reads of the distributor 13 pulses, and with the same pulse the subtractor 16 is zeroed.

With the arrival of the next deducer for them 4 frequencies through At, the cycle of the device operation is repeated

is recorded next

X (2) 21 ja; rfsin-l 2- i-.f (2: .- g (2) 1

Comparison blocks for the pulse with de-, h 4 frequencies, compare the number: 1, coming from the outputs of the 7th generator of the generator 5. If the number arrives. G.}; and Slok 8 compared with

ten

15

block 7, for example, is greater than the number received from generator 5, then a code is generated at the output of this comparison block that allows execution of the addition operation in the corresponding M accumulating adders-subtractors 9, if this condition is not fulfilled - the code allowing execution of the subtraction operation (Fig .2d), zero level means subtraction, one;, i-th - addition). Since nothing is supplied to the information inputs of adders 9, their contents do not change, and the received control codes for summation or retrieval are stored in the corresponding registers of adders-subtractors 9. These codes are received from the distributor 13 alternately read from the registers of adders-subtractors 9 hours through the element OR 15 (Fig. 2e) are fed to the control input of the adder-subtractor 16. 2g temporarily reading control codes from the adders-subtractors 9 are alternately read and stored with

BUT

in them, the coefficients a; and b; that go through the block of elements OR 1D to the information input of the adder-reader 16. After 2M cycles in the accumulating adder-subtractor 16 (Fig. 2g), the following sum is written

20

thirty

 , ° and in the adder-subtractor 16

° and in the subtractor 16

35

X (

 , 1-1- (1)

totalizer subtractor

 , R 2tg.

one

and in the subtractor 16

This sum is read from the adder-subtractor 16 (Fig. 2k) on B Lac 17, (2M + 1) th read pulse from the distributor 13 pulses, moreover, the same impulse 16 subtracts 16.

With the arrival of the next pulse from the frequency 4 deducer via At (Fig. 2a), the device operation cycle repeats,

The following amount is recorded:

and in the subtractor 16

n etc.

X (2) 21 ja; rfsin-l 2- i-.f (2): .- g (2) 1

+ b, F

I; h cos - N

 In the general case, the following sums are read out from the adder-subtractor 16:

m G G about 1 X (p) J a; F sinyi p- (p) -k 1- L LJ

-t-b; rGso5 1-p- (p) | .

(ten)

With a uniform distribution law P (p) in the output sequence and pseudo-random number generator 5, the expression for the average value can be written as follows:

(n) X (n) as

one

sZi

2 / n. U Sin - ni- -b;

cos - ni),

(eleven)

with the coefficient of trust, hanging from the time of the summation interval (averaging), since the average value of F, for example, for 5 "; (n) is equal to

F (sin ni-fCn)) P (n).

Claims (1)

(12) Claim Formula A device for performing a Fourier transform containing a clock pulse generator, an analog-to-digital converter, a meter, whose information output is connected to an ad hoc cavity, fixed memory blocks, i.e. (il, M, M - number of detectable harmonics) information outputs of the first and the second group of which are connected to the first BXIs of ix blocks. Equals, respectively, of the first and second groups, the outputs of which are connected to the inputs of the mode ix selection of accumulating adders-subtractors of the first and second groups, respectively otorrhea are co tvetstvenno outputs real and imaginary parts of the i-th harmonic spectrum of the device, an information input of which is information input analog to digital converter, and the output of pseudorandom numbers -eneratora sub- |;. for prison to second inputs of the i-x blocks five 0 comparing the first and BTOpoii groups, o t: i and h and DI e so that, in order to extend the functionality by calculating the inverse Fourier transform, a switch, a frequency divider, a pulse distributor, a block of OR elements are introduced into it, the OR element accumulating the adder-subtractor whose output is the output of the inverse Fourier transform of the device, the output of the analog-digital converter is connected to the first information input of the switch, the first output of which is connected to the information inputs ix accumulating The first and second groups of subtractors, a clock generator are connected to the clock input of the frequency divider and the second information input of the switch, the control input of which is the input of the device operation mode, the second switch output is connected to the pulse distributor j-th (j 2K-1, M) the output of which is connected to the clock input of the j-ro accumulating adder-subtractor of the first group, the 1st output (,, M) of the pulse distributor is connected to the clock input of the 1st accumulating adder -vychitatel second group, the output of the frequency divider is connected to the input of analog-to-digital synchronization 5 converter, counting input the counter and the clock input of the pseudo-random number generator, the outputs ix of accumulating adders for the first and second groups are connected respectively to the 1st and (i- -M) -My input of the block of elements OR, the output is connected; the input is an accumulative sum of the torus-nych and- tatel, the input mode selection which  connected to the output of the element 11TI, The i- and () -th inputs of which are connected to the outputs of the selection .ig and ix of adders-subtractors, respectively; - the first and second groups, and the (2M + 1) -th output of the pulse distributor .I-switch to the clock n; -; one value adder-subtract; . 0 0 0 I / one f i 2M ((2 i) I I I I I I I I I I I I I YO m, (r )  R / 7 -% R tf Bs Nf, J Lj