SU468246A1 - Apparatus for calculating Fourier coefficients - Google Patents

Description

(54) DEVICE FOR CALCULATION OF FOURIER COEFFICIENTS

The invention relates to computing and can be used in the construction of digital analyzers of random signals. Devices are known for calculating Fourier coefficients containing a multiplication unit, a sine-cosine register whose input is connected to the first input of the device and an output connected to the first input of the multiplying unit, the adder whose first input is connected to the second input by devices, an intermediate register. The purpose of the invention is to simplify the device. This is achieved by the fact that the device contains the first switch, two inputs of which are connected to the output of the adder and a third input to the device, and two outputs are connected to the first output of the device and the input of the intermediate register., An additional register whose input is connected to the output of the intermediate register, the second switch, three inputs of which are connected to the fourth input of the device and the output: I will give intermediate and additional registers, and the output is connected to the second input of the multiplication unit, element AND, two inputs; yes, which are connected to the output of the additional register and the fifth input of the device, the subtraction unit, the first input of which is connected to the output of the element I, and the output connected to the second input of the adder, the third switch, two inputs of which are connected to the output of the multiplication unit and the sixth input of the device, and two outputs connected to the second input of the subtracter and the second output of the device. The drawing shows a device for calculating Fourier coefficients. It contains multiplication unit 1, reg. Sine-cosine register 2, switch 3, intermediate register 4, additional, register 5, switch 6, subtraction unit; 7, element 8, adder 9, switch 1O, device inputs 11-16. The outputs of the device are 17 and 18. The device works as follows. To calculate the coefficients a and in the decomposition in the Fourier series of a signal, represented by a set of ordinates, the discrete Fourier transform is used:; 2 2Tl O. URSOB j fcjо 5Г, Vjj 7. - ,. (1 ,,,. V the list of samples sampled by Ur is discredited: "p; r, go signal. N is the number of discrete samples. It is assumed that N is where is a positive integer. In the device, the modified algorithm, have the form () UU,., Vfci -5-bK (Stni5 K) UJ. 2P114 J where U values are defined as follows: Un 0 Ui 5 / (Uj 2CcoS K). one . J Z, 3 .... Calculation of the coefficients a and in the device in N steps. In the initial state in the intermediate register 4 the value U, Y is stored, in the additional register 5 - the value y O, and in the sine-cosine register 2 the value rnQ.32Lk N In the first step, the multiplication unit 1 is accessed one cycle in switch 6 (which is equivalent to multiplying by 2) is fed to the input of subtraction unit 7. To the second input of subtraction unit 7, UQ output comes from the output of auxiliary register 5, which is subtracted from the previously received product. The resulting difference enters the adder 9, in rum is summed with the value of y, received at input 11. The obtained value and from the output of the adder 9 is written to. the intermediate register 4, and the value of y on the intermediate retaster 4 is rewritten into the additional register 5. Subsequent steps are similar to those described by Y, 4 | In the (IN -1) -th step occurs; (an accurate calculation of the coefficient a.; in this step, the value of U, w. stored 5 In intermediate register 4, is multiplied in multiplication unit 1 by the COS tRK. By the signal at input 14, switch 6 passes i ® work without input delay block, : As subtraction 7 and subtract the value of 10 I from Uij.q. The resulting difference goes to the adder 9, where it is summed with i: the value of W. As a result, at the output: i of the adder 9, the value of the coefficient i is obtained. signal on |. 1 passes the value. and to output 118, and in intermediate register 4 writes zero. The value of U from intermediate .po 4 is transferred to the additional -peri cTp; 5i at the end of this step, the value Sin-K,: N: is written to the blue-cosineus 2 register: In the Nth step, the coefficient 25 is calculated. In this step, the switch 3 passes the value from input extension 5 to input multiplier D, where it is multiplied by the value A and output N of multiplication block 1, the value of coefficient c is obtained. The switch 6 on the signal: to the input 14 passes the value in on - the output 17, and the input to the subtraction unit 7 receives a zero. The second input of the subtraction unit 7 also receives a zero, since, according to a signal at the input 16, the element 8 and 8 zack passes information. As a result, the value of y arriving at input 11 is. 40; ; ;, „From the next sample passes through the sum; g g changes AND is written to | intermediate register 4, and zero from this register is overwritten into additional register 5. At the end of this step, the value of the TG is written to the sine-cosine register 2, the scheme is | the initial state and is ready for calculating the coefficients a and b for the next; ь1 of the ordinate of the signal under study. one; DESIGN OF THE INVENTION, gg | ; A device for calculating Fourier coefficients containing a multiplier.

register: sine-cosine, the input of which is connected to the first input of the device, and the output is connected to the first input of the block; Multiply, the adder, the first input of which pits the KO to the second input of the device fg-va, intermediate register, o and t and h- o; right now; that, in order to simplify the device, it contains the first switch-i torus, two inputs of which are connected to the output of the adder and the third input of the device, and two outputs are connected to the first output of the device and the intermediate input; it register, additional register,:. the input of which is connected to the output of the intermediate register, the second switch, f 15

Three inputs are connected to the fourth;

Gtoma device input and outputs inter-; exact and additional registers, and you-; The input is connected to the second input of the block cleverly, the element I, whose two inputs are connected to the secondary input of the additional register: the fifth input of the device, the subtraction unit, the first input of which is connected to the output; And, and the output is connected to the second input of the adder, the third switch, two, whose I inputs are connected to the output of the multiplication unit and the sixth input of the device, and two outputs connected to the second Apple input of the calculator and the second output of the device.

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