JP2002032356A - Recursive discrete fourier transform device - Google Patents

Abstract

PROBLEM TO BE SOLVED: To conduct fast-Fourier transformation processing on a data string, including sampling data that are sequentially supplied within a single sampling period. SOLUTION: With regard to this Fourier transformation device, when N pieces of the latest data are acquired among pieces of data that are sequentially supplied and temporarily stored, while eliminating old data, a data-updating part 1 supplies the value of difference between the latest supplied data value and a data value to be eliminated; the supplied data value and the latest FFT operation results temporarily stored in a memory part 3 are supplied to a recursive DFT operating part 3; these values are calculated with a prescribed method; and FFT operation results to the N pieces of the latest data values are outputted in real time.

Description

DETAILED DESCRIPTION OF THE INVENTION

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to an arithmetic device for Fourier transform, and more particularly to an arithmetic device for performing a Fourier transform by a simple arithmetic process and obtaining an arithmetic result of the Fourier transform in a short time.

[0002]

2. Description of the Related Art Conventionally, Fourier transform techniques used for frequency analysis of time-series data strings are not limited to signal signal analysis in the field of sound signal processing, image data processing of medical equipment, and the like, but also include sound signals and image signals. And widely used as modulation and demodulation techniques in the communication field.

In the Fourier transform technique, a data sequence sampled as a digital quantity is treated as a group of N (N is an integer value, for example, 1024), and a time interval in which the N data sequences exist is defined as a window period. In addition, the window period is defined as the fundamental frequency, and the signal components of the data string existing in the window period are obtained as the real part component and the imaginary part component of the harmonic signal of the fundamental frequency.

[0004] The data sequence handled in this manner is treated as a discrete data sequence sampled at predetermined intervals, and a method of performing Fourier transform on the discrete data is a discrete Fourier transform (DFT). Transfo
rm), and its discrete Fourier transform technology, for example, obtains the state of the manufacturing process by discrete data and analyzes the obtained data to maintain the best process quality and reduce the non-defective rate of the manufactured product. Its application fields are expanding year by year, such as being used as an analysis technique in control techniques such as improving.

In the discrete Fourier transform technique performed in this manner, a supplied signal is sampled at regular time intervals, a voltage value obtained by the sampling is obtained as sampled data, and the obtained data is sampled. A set of N data obtained at a predetermined time t is x (t), x (t + 1), x (t + 2),..., X (t + N−2), x (t
+ N-1), the discrete Fourier transform value X (k, t) obtained for the N pieces of data is defined by the following equation.

[0006]

(Equation 2)

As can be seen from this equation, the Fourier transform is performed by convolving a specific basis function for each point to be obtained with respect to a supplied data string, and the operation of convolving the basis function is performed by a number of multiplication processes. I'm trying to do it.

In this way, the multiplication process is performed by a dedicated multiplication circuit or a DSP (Digital Signal Process).
r) etc., these multiplication circuits,
It is known that the load on hardware used for operations such as a DSP is very large.

The burden of the multiplication processing requires 4N ² multiplications in the case of the conversion formula represented by the above-mentioned equation (1). For example, when N is 1024, the number of multiplications is about 4.2 million. Therefore, the scale of the circuit for multiplying the number of times becomes large, the load of the arithmetic processing becomes extremely large, and when the number N of points handled as a data string increases, the number of times of the multiplication increases by a factor of 2. Is not preferred.

[0010] Therefore, usually, an FFT (Digital Fourier Transform), which uses the fact that the basis function is formed of a periodic function and focuses on the regularity thereof and transforms the matrix to improve the computational efficiency, is used. Fast Fourier Transform (Fast Fourier Transform) has been used.

In the FFT, an operation method called a butterfly operation is used.
A simple integer value, for example, 2 is defined as a radix, and complex arithmetic operations of addition, subtraction, and multiplication are performed once for each supplied binary complex data, and binary complex data is output. It is composed.

Therefore, an N-point FFT is composed of log ₂ N stages and (N / 2) log ₂ N butterfly operations, and is performed by the number of (2N) log ₂ N multiplication processes. Is used as a Fourier transform with high operation efficiency, such as being able to obtain the operation result of

Usually, FFT or DFT (Discrete Fourier Transform) performed in this manner is used, and a Fourier transform is performed on a data sequence that is sequentially sampled and supplied at fixed time intervals. The Fourier transform is sampled,
While temporarily storing the sampled data sequence in the memory circuit, when the number of data temporarily stored in the memory circuit becomes N, the Fourier transform process for the N data is started. .

During the conversion process, the data temporarily stored in the memory circuit is subjected to the Fourier transform while maintaining the stored state, and when the arithmetic process is completed, new data is again generated. After the data is supplied to the memory circuit and temporarily stored therein, the next conversion process is started after N pieces of predetermined amount of data are stored.

However, since the data is continuously supplied even during the Fourier operation processing, the data processing to be continuously supplied is provided as a separate system by providing a memory circuit for storing N data strings. , Every time N data is supplied, a temporary storage process and an arithmetic process are alternately performed, and a Fourier transform process is continuously performed on the time-series data.

[0016]

The Fourier transform performed in this manner performs an arithmetic process on N temporarily stored data strings, that is, while treating the data strings in block units. In the Fourier transform process performed, a delay time corresponding to at least N data strings is generated, and it is not possible to obtain a result of the transform process in real time. Therefore, although the data sequence is sequentially supplied, the result of the Fourier analysis is obtained only at every N sampling time intervals.

On the other hand, a Fourier transform process is performed on a sequentially supplied N-point data string including new data to be sampled, and the result of the Fourier transform process every time the sampled data is supplied is calculated. In order to obtain it, it is necessary to perform N-point Fourier transform processing within the one sampling period, and even when using the FFT operation method developed for such high-speed operation processing, the FFT operation is continuously performed from the FFT. In order to obtain the calculated Fourier transform result, an operation processing speed of N times is required, and it is usually difficult to perform such an ultra-high-speed FFT and supply the obtained operation result.

In the Fourier transform, an FFT operation processing method is generally used. In the FFT operation processing, a sampling frequency is quantized by fs, and an N-point data string supplied is usually supplied with a frequency of fs / N. Perform arithmetic processing at intervals.

In general, data is taken into another buffer memory during the Fourier transform process so that the Fourier analysis process is continuously performed on the time series data supplied during the arithmetic process. While the data temporarily stored in the buffer memory is being processed, the data supplied to the other buffer memory is fetched, and when the fetching of N pieces of data is completed, the calculation processing and the data fetching processing are switched to perform a Fourier calculation processing. However, in this case, two sets of buffer memories and FFT operation processing means are required, which is not an economically preferable method.

Further, in this method, since the block processing handles the supplied N time series data collectively, the Fourier transform result for the fetched N point data is output after N sampling times. The analysis result obtained at that time is output only as a Fourier transform processing result for every N samples.

As described above, it is impossible to output the Fourier transform result for the latest N-point data including the data newly sampled and supplied sequentially in real time. Although Fourier transform processing is necessary for each sampling period as described above, performing Fourier transform continuously at one sampling time interval is not realistic because the amount of calculation per unit time is enormous.

On the other hand, Japanese Patent Application Laid-Open No. 1-59454 entitled "Fourier Transform Apparatus and Fourier Transform Method" has been proposed as a method for continuously obtaining Fourier transform operation results.
This publication describes a method of performing a Fourier transform on a sampled and supplied vibration waveform value.
The transform method calculates a difference value between a newly supplied vibration waveform value and an old vibration waveform value already supplied and used for Fourier calculation processing, and obtains a newer value than an old complex amplitude value already obtained by calculation processing. A complex amplitude value is obtained every time a sampling value of a vibration waveform is supplied.

However, a technique for continuously performing Fourier transform is disclosed in Japanese Patent Application Laid-Open No. 1-59454, entitled "Fourier Transform Apparatus and Fourier Transform Method". A frequency analysis or the like can be considered as the application that has been performed. However, when such an application is considered, there is a demand for analyzing an arbitrary frequency band at an arbitrary resolution.

Japanese Unexamined Patent Publication (Kokai) No. 3-63875 discloses a "discrete Fourier transform calculation method using a cyclic technique".
And discloses a discrete Fourier transform for performing an energy spectrum calculation in an ultrasonic diagnostic apparatus, which is continuously calculated using a sampling data filter by a cyclic filter operation. Describes the discrete Fourier transform.

However, in the invention disclosed herein, a method of realizing a circuit configured with complex data as input is described. However, the invention is directed to a signal supplied as time-series data used in the field of frequency analysis and the like. No cyclic Fourier transform method with a simple configuration for performing a conversion process and supplying only a real number signal is considered.

Accordingly, the present invention provides a recursive discrete Fourier transform apparatus for constructing a Fourier analysis for a supplied real number signal in a simple manner, and a frequency analysis for performing the transformation with a desired arbitrary resolution. It is an object of the present invention to provide a recursive discrete Fourier transform device suitable for the following.

[0027]

The present invention comprises the following means 1) to 6) to solve the above-mentioned problems. That is,

1) Times t, t + 1, t + at constant intervals
2, t + 3,..., T + N−1, t + N, (N is a positive integer of 1 or more) data values x (t), x (t + 1), x (t + 2), x
(T + 3),..., X (t + N−1), x (t + N) are supplied, and N data values supplied from time t with respect to the supplied data value are defined as a data string. Order k obtained by performing a complex Fourier transform on the data sequence
(K is 0 or a positive integer smaller than N) as its Fourier coefficients, its real part Xr (k, t) and its imaginary part Xi
In the discrete Fourier transform apparatus for obtaining (k, t), the time t + N
Data sequence x (t), x supplied from time t at −1
(T + 1), x (t + 2), x (t + 3), ..., x (t
+ N−1) first temporary storage means (11)
And a discrete Fourier operation means (3) for obtaining complex Fourier coefficients Xr (k, t) and Xi (k, t) of the data sequence temporarily stored in the first storage means. Second temporary storage means (4) for temporarily storing the obtained complex Fourier coefficients Xr (k, t) and Xi (k, t), and the discrete Fourier calculation means is supplied at time t + N A subtraction unit (12) for obtaining a data value of a difference between the data value x (t + N) to be obtained and the data value x (t) temporarily stored in the first storage means; On the other hand, a constant multiplication unit (31) for obtaining a signal of a predetermined amplitude by multiplying by a constant value A for giving a predetermined amplitude, a signal of a predetermined amplitude obtained from the constant multiplication unit, The real value of the complex Fourier coefficient Xr (k,
t) or an imaginary value Xi (k, t) is added to an addition unit (36) for obtaining an addition signal, an addition signal obtained from the addition unit, and the second temporary storage unit. Real value Xr (k, t) or imaginary value Xi (k, t) of the temporarily stored complex Fourier coefficient
And the other signals are subjected to arithmetic processing using constants based on the base frequency to obtain complex Fourier coefficients Xr (k, t + 1) and Xi (k, t + 1) at time t + 1. A recursive discrete Fourier transform device comprising a function operation processing unit (30).

2) Times t, t + 1, t + at constant intervals
2, t + 3,..., T + N−1, t + N, (N is a positive integer of 1 or more) data values x (t), x (t + 1), x (t + 2), x
(T + 3),..., X (t + N−1), x (t + N) are supplied, and N data values supplied from time t with respect to the supplied data value are defined as a data string. Order k obtained by performing a complex Fourier transform on the data sequence
(K is 0 or a positive integer less than N) as its Fourier coefficients, its real part Xr (k, t) and its imaginary part Xi
In the discrete Fourier transform apparatus for obtaining (k, t), the time t + N
Data sequence x (t), x supplied from time t at −1
(T + 1), x (t + 2), x (t + 3), ..., x (t
+ N−1) first temporary storage means (11)
And a discrete Fourier operation means (3) for obtaining complex Fourier coefficients Xr (k, t) and Xi (k, t) of the data sequence temporarily stored in the first storage means. A second temporary storage means (4) for temporarily storing the obtained complex Fourier coefficients Xr (k, t) and Xi (k, t), wherein the discrete Fourier calculation means (3) Fourier coefficient Xr
A recursive discrete Fourier transform apparatus characterized in that (k, t + 1) and Xi (k, t + 1) are calculated and obtained by the following equation.

[0030]

(Equation 3)

3) Times t, t + 1, t + at constant intervals
2, t + 3,..., T + N−1, t + N, (N is a positive integer of 1 or more) data values x (t), x (t + 1), x (t + 2), x
(T + 3),..., X (t + N−1), x (t + N) are supplied, and N data values supplied from time t with respect to the supplied data value are defined as a data string. The data sequence is subjected to a complex Fourier transform using a plurality of orders k (k is 0 or a positive integer smaller than N), and a real part Xr of each coefficient is obtained as a plurality of sets of complex Fourier coefficients.
In a discrete Fourier transform apparatus for obtaining (k, t) and an imaginary part Xi (k, t), a data sequence x (t), x (t + 1), x (t + 2) supplied from time t at time t + N−1 , X (t +
3) The first to temporarily store x (t + N-1)
And the respective complex Fourier coefficients Xr (k, t) and Xi (k, t) corresponding to a plurality of k values in the data sequence temporarily stored in the first storage means. ), And their respective k
Second temporary storage means (4) for temporarily storing each of a plurality of sets of complex Fourier coefficients Xr (k, t) and Xi (k, t) obtained by the discrete Fourier calculation means corresponding to the value of And each of the plurality of discrete Fourier calculation means is provided with a data value x (t + N) supplied at time t + N,
And a subtraction unit (12) for obtaining a data value of a difference from the data value x (t) temporarily stored in the storage means, and for giving a predetermined amplitude to the obtained data value of the difference. A constant multiplication unit (3
1), a signal of a predetermined amplitude obtained from the constant multiplication unit, and a real value Xr (k, t) or an imaginary value Xi (k, k) of a complex Fourier coefficient temporarily stored in the second temporary storage means. t), an addition unit (36) for obtaining an addition signal, an addition signal obtained from the addition unit, and a real value Xr () of a complex Fourier coefficient temporarily stored in the second temporary storage unit. k, t) or the other signal of the imaginary value Xi (k, t) is supplied, the signal is subjected to arithmetic processing using a constant based on the base frequency, and a complex Fourier coefficient for a predetermined k at time t + 1 is calculated. A recursive discrete Fourier transform apparatus comprising: a basis function operation processing unit (30) for obtaining Xr (k, t + 1) and Xi (k, t + 1).

4) Times t, t + 1, t + at constant intervals
2, t + 3,..., T + N−1, t + N, (N is a positive integer of 1 or more) data values x (t), x (t + 1), x (t + 2), x
(T + 3),..., X (t + N−1), x (t + N) are supplied, and N data values supplied from time t with respect to the supplied data value are defined as a data string. The data sequence is subjected to complex Fourier transform using a plurality of orders k (k is 0 or a positive integer smaller than N), and a real part Xr of each coefficient is obtained as a plurality of sets of complex Fourier coefficients.
In a discrete Fourier transform apparatus for obtaining (k, t) and an imaginary part Xi (k, t), a data sequence x (t), x (t + 1), x (t + 2) supplied from time t at time t + N−1 , X (t +
3) The first to temporarily store x (t + N-1)
And the respective complex Fourier coefficients Xr (k, t) and Xi (k, t) corresponding to a plurality of k values in the data sequence temporarily stored in the first storage means. ), And their respective k
Second temporary storage means (4) for temporarily storing each of a plurality of sets of complex Fourier coefficients Xr (k, t) and Xi (k, t) obtained by the discrete Fourier calculation means corresponding to the value of And each of the plurality of discrete Fourier calculation means is provided with a data value x (t + N) supplied at time t + N,
And a common subtraction unit (1) for obtaining a data value of a difference from the data value x (t) temporarily stored in the storage unit, and a predetermined difference data value obtained by the subtraction unit. A common constant multiplication unit (31) for obtaining a signal of a predetermined amplitude by multiplying by a constant value A for giving an amplitude, a signal of a predetermined amplitude obtained from the common constant multiplication unit, and the second temporary storage An adding section (36) for adding one of the real value Xr (k, t) or the imaginary value Xi (k, t) of the complex Fourier coefficient temporarily stored in the means to obtain an addition signal; Second temporary storage means (4) for supplying the other signal of the real value Xr (k, t) or the imaginary value Xi (k, t) of the obtained complex Fourier coefficient, and an addition signal from the addition unit, And the real value Xr (k, t) or the imaginary value Xi (k, t) of the complex Fourier coefficient from the second temporary storage means.
Are supplied, and these signals have their respective k
Is performed using a constant based on the base frequency corresponding to the value of, and a plurality of sets of complex Fourier coefficients Xr (k, t + 1) and Xi (k, t +) for each order k at time t + 1.
A recursive discrete Fourier transform device comprising a basis function calculation processing unit (30) for obtaining 1).

5) The plurality of complex Fourier coefficients corresponding to the respective k values are configured to output complex Fourier coefficients corresponding to N k values. 3) or 4). ). The recursive discrete Fourier transform apparatus according to the above item.

6) A positive constant value A for giving an amplitude value for a value of the difference between the x (t + N) and the x (t) is:
The recursive discrete Fourier transform apparatus according to any one of 1), 2), 3) and 4), wherein a value such as 1, a square root of N, or N can be selectively set.

[0035]

DESCRIPTION OF THE PREFERRED EMBODIMENTS Preferred embodiments of a recursive discrete Fourier transform apparatus according to the present invention will be described below with reference to preferred embodiments. FIG. 1 schematically shows the configuration of a recursive discrete Fourier transform apparatus according to the embodiment, which will be described with reference to FIG.

The recursive discrete Fourier transform apparatus is supplied with data sampled at fixed time intervals, and includes a data update unit 1 for temporarily storing the latest N (N is a positive integer) supplied data, A base frequency setting unit 2 for setting a base frequency for performing a Fourier transform;
It comprises a recursive DFT operation unit 3 for performing an FT operation and a memory unit 4 for temporarily storing the calculated data.

Next, the operation of the recursive discrete Fourier transform device configured as described above will be described. First, the supplied data is sampled at fixed time intervals by a sampling circuit (not shown), and the discrete data sampled and quantized is supplied to the data updating unit 1.

The sampling circuit operates at times t, t + 1, t + 2, t + 3,...
The data values supplied at t + N (N is a natural number) are sampled, and the data values supplied at that time are taken as data values x (t), x (t + 1), x ( t + 2), x (t + 3), ...
.., X (t + N−1) and x (t + N) are generated.

The operation of this sampling circuit is the same as the operation of an A / D converter for converting a supplied analog signal to a digital signal, and the analog signal voltage supplied at a constant time interval given by the reciprocal of the sampling frequency. The value is converted to a digital signal value, and the converted digital signal value is a voltage having a similar relationship to an analog voltage that provides a pulse amplitude modulation signal, or the voltage value is represented by a binary digital value. Or something to do.

As described above, the data updating unit 1 stores the sampling data x (t) sampled at the time t, x (t + 1) at the time t + 1,..., And the time t + N-1.
X (t + N-1) at time t, and x (t + N) at time t + N. ,

The data update unit 1 temporarily stores N data (N is a positive integer) of the latest supplied data among the supplied data while updating the data. That is, the supplied data starts from x (t), x (t + 1), x (t + 2), x
When supplied as (t + 3), supplied data
x (t), x (t + 1), x (t + 2), and x (t + 3) are all temporarily stored, and the operation of the temporary storage is continued until data x (t + N−1) is received, and x (t + N) When the data of -1) is received, the total number of data becomes N and the data area of the data update unit becomes full.

In such a state, the next data x (t + N)
Is supplied, since the total number of data is N + 1, the data updating unit 1 subtracts x (t) from x (t + N),
The data obtained by the subtraction is supplied to the recursive DFT operation unit 3 and the oldest data x (t) is deleted from the memory unit, and the data update unit 1 executes x (t + 1), x (t + 2), x (t t +
3) N data of x (t + N−1) and x (t + N) are temporarily stored.

Similarly, when the next data x (t + N + 1) is supplied, the data updating unit 1 outputs the data x (t + N + 1).
−x (t + 1) is obtained and supplied to the recursive DFT operation unit 3, x (t + 1) is deleted from the memory, and the latest N pieces of supplied data are temporarily stored in the data update unit 1. .

Thus, the N data temporarily stored is supplied to the recursive DFT operation unit, and the recursive DF
The T operation unit 1 stores the 1 temporarily stored in the memory circuit 4 according to the frequency resolution information set by the base frequency setting unit 2.
The result of the FFT operation before the sample is supplied to the recursive DFT as recursive data, the recursive discrete Fourier transform operation is performed by a method described later, and the operation result is output.

Next, the recursive discrete Fourier calculation processing method will be described in more detail with reference to the conventional Fourier calculation processing. FIG. 2 schematically shows a relationship between a data value obtained by sampling a supplied signal waveform in a sampling period ts and a DFT operation on the data value.

In the figure, N real data values sampled during a fixed sampling period ts from time t, x (t), x (t + 1), x (t + 2), x (t + 3),.
..., A set of x (t + N−1), and N real data values obtained by sampling from time t + 1, x (t +
1), x (t + 2), x (t + 3), ..., x (t + N-
1), a set of x (t + N) is shown.

Then, the value X (k, t) of the discrete Fourier transform obtained for the data sequence of N real number data values sampled from the time t is defined by the following equation (2). .

[0048]

(Equation 4)

An arbitrary time t defined in this way
Sampling data string supplied from x (t) to x (t +
The conversion of the real part X _r (k, t) and the imaginary part X _i (k, t) of N−1) is defined as in equations (3) and (4).

[0050]

(Equation 5)

The conversion formula for the sampling data sequence supplied from time t is defined as described above. Next, the conversion formula for the sampling data sequence supplied from time t + 1 will be described.

That is, the sampling data sequence supplied from the time t + 1 is x (t + 1), x (t + 2), x (t +
3),..., X (t + N−1) and x (t + N), which are deleted from the data sequence supplied from time t, New data x (t +
N) is added, the conversion of the real part is
In addition, the expression (5) is expanded as follows.

[0053]

(Equation 6)

Here,

[0055]

(Equation 7)

Is as follows. So, the oldest data, x
If (t) is deleted and the newest data x (t + N) is incorporated, it becomes possible to represent Y _r (k, t + 1) using X _r (k, t), and similarly, Y _i ( k, t + 1) to X _i (k,
It can also be expressed as t).

As a result, equations (6) and (7) are written as follows.

[0058]

(Equation 8)

Next, regarding the conversion formula (4) of the imaginary part,
Expand similarly. That is, when new data x (t + N) is supplied, the conversion of the imaginary part is performed in the same manner.

[0060]

(Equation 9)

Therefore, based on the relations of equations (8) and (9), equations (5) and (10) can be written as follows.

[0062]

(Equation 10)

As described above, the discrete Fourier transform at time t + 1 uses the discrete Fourier operation result at time t recursively, and uses the newly acquired sample value.
Using the data value of the difference between x (t + N) and the sample value x (t) to be deleted, it can be obtained by calculation according to equations (11) and (12).

The discrete Fourier transform obtained here is essentially an FIR that performs processing on a finite number of samples N.
Although it is a filter (a non-recursive digital filter), as is clear from the conversion equations of the above equations (11) and (12),
This means that the discrete Fourier transform at the current sampling time is realized by using an IIR filter (recursive digital filter) that derives using the result of the discrete Fourier transform obtained at the previous sampling time.

In the method of realizing this DFT by the IIR filter, the hardware configuration for the operation can be simplified as compared with the case where the DFT is configured by the FIR filter. In the case of performing the recursive discrete Fourier transform, new data sequentially sampled is supplied at the sampling time interval as shown in FIG. A high Fourier transform can be performed.

Now, in this way, cos (2πk / N),
And sin (2πk / N) can be used to perform a Fourier operation, but those base frequencies are set as Γc, Γs (gamma c, gamma s), and 1 / (N Letting A be the square root, equations (11) and (12)
Can be expressed as follows.

[0067]

[Equation 11]

In this way, the Fourier transform operation can be performed by using the equations (13) and (14). Next, the configuration of a recursive discrete Fourier transform apparatus for realizing it will be described.

That is, equation (13) is obtained by converting the real part X _r (k, t + 1) of the Fourier coefficient at time t + 1 to the time t + N and the time t + N.
X (k, t + N), x (k, t) supplied at
And the real part X _{r of} the Fourier coefficients obtained at time t
It is shown that by using (k, t) and the imaginary part X _i (k, t) recursively, the desired base frequencies に お い て c and Γs can be obtained.

Equation (14) is similarly calculated at time t + 1
It is shown that the imaginary part X _i (k, t + 1) of the Fourier coefficient can be obtained. Next, a recursive discrete Fourier transform apparatus that operates according to such an arithmetic expression will be described.

FIG. 3 shows a recursive discrete Fourier transform circuit constituting a main part of the recursive discrete Fourier transform apparatus.
FIG. 4 is a diagram showing the basis function calculation processing section in FIG. 3 in further detail, and will be described with reference to these figures.

In FIG. 4, the recursive discrete Fourier transform circuit includes a delay circuit 11 and a subtractor 12 constituting a data updating unit 1, a plurality of multipliers 31 to 35 constituting a recursive DFT operation unit, and It comprises a plurality of adders 36 to 38 and delay circuits 41 and 42 constituting a memory section.

Next, the operation of the recursive discrete Fourier transform circuit configured as described above will be described. First, supplied input signals are time t, t + 1, t + 2, t + 3,..., T at a constant interval by a sampling circuit (not shown).
+ N−1, t + N (N is a natural number) is sampled, and the level of the input signal at that time is sampled as a data sequence x (t), x (t)
+1), x (t + 2), x (t + 3), ..., x (t + N)
−1), x (t + N) discrete data
Supplied to

In the data updating unit 1, one of the supplied data is supplied to the delay unit 11 and the other is supplied to the subtractor 12. The delay unit 11 delays the signal for a time corresponding to the period of the N sampling clocks. That is, the delay unit 11 has a function of temporarily storing the data of the number N of data supplied most recently while updating the data.

Here, when the supplied data starts from x (t) and is supplied as x (t + 1), x (t + 2), x (t + 3), the delay unit 11 outputs the supplied data x (T),
All of x (t + 1), x (t + 2) and x (t + 3) are temporarily stored, and the operation of the temporary storage is continued until data x (t + N-1) is received, and data of x (t + N-1) is stored. Is received, the total number of data becomes N, and the data area of the delay unit 11 becomes full.

In such a state, the next data x (t + N)
Is supplied, the total number of data becomes N + 1,
The delay unit 11 supplies the oldest data x (t) to the subtractor 12, and the subtractor 12 subtracts the oldest data x (t) from the supplied data x (t + N) and obtains the result by subtracting it. [X (t + N) −x (t)] is supplied to the recursive DFT operation unit 3.

The recursive DFT operation unit 3 performs multiplication and addition of the signals thus supplied. First,
In the multiplier 31, the supplied signal [x (t + N) -x (t)]
Is multiplied by the aforementioned constant value A, and the multiplied signal is supplied to the adder 36.

The adder 36 receives the signal supplied from the multiplier 31 and the signal obtained by delaying the real part of the output signal of the recursive discrete Fourier operation circuit by one sampling period by the delay unit 41. The added signals are supplied to respective multipliers 32 and 33.

In one of the multipliers 32, the supplied signal is multiplied by a base frequency Γc = cos (2πk / N), and the signal obtained by the multiplication is supplied as one input signal of the adder 37, In the multiplier 33, the supplied signal is multiplied by the base frequency −−s = −cos (2πk / N), and a signal obtained by the multiplication is supplied as one input signal of the adder 38.

As the other input signal of the adder 37, one of the signals obtained by delaying the imaginary part of the output signal of the recursive discrete Fourier operation circuit by one sampling period by the delay unit 42 is used by the multiplier 34. Γs = cos (2πk / N)
And the other input signal of the adder 38 described above is multiplied by the multiplier 35 with the other of the signals delayed by one sampling period by the delay unit 42.
A signal multiplied by c = cos (2πk / N) is generated, and the generated signal is supplied.

The signal thus added by the adder 37 is supplied as the real part signal X _r (k, t + 1) of the output signal of the recursive discrete Fourier operation circuit, and a part of the signal is supplied. The aforementioned delay circuit 4 as a recursive signal
1 and the signal added by the adder 38 is supplied as an imaginary part signal X _i (k, t + 1) of the output signal of the recursive discrete Fourier operation circuit, and a part of the signal is a recursive signal. Is supplied to the delay circuit 42 described above.

Here, the respective multiplication coefficients Γc and Γs given to the multipliers 32 to 35 are set by the base frequency setting unit 2 shown in FIG. 1, and this recursive discrete Fourier operation circuit is Based on the set frequency,
N is set according to the target resolution, and the coefficients of the discrete Fourier transform according to the N are calculated and output.

In this manner, the supplied data string x
(T), x (t + 1), x (t + 2), x (t + 3), ...
·, Complex Fourier transformation for x (t + N-1) and x (t + N)
Exchange result X _r(K, t + 1) -jX_i(K, t + 1)
it can.

In the above equations (11) and (12),
Let cos (2πk / N) and cos (2πk / N) be Γc and Γs, respectively.
In the above, the operation of the recursive DFT operation circuit shown in FIG. 4 has been described. However, these Γc and Γs indicate the base frequency, and the recursive DFT operation circuit shown in FIG. D for the base frequency defined by
Since the module performs FT operation, N modules can be connected in parallel to form a DFT operation circuit for all base frequencies at N points.

FIG. 5 shows a configuration of an N-point recursive DFT calculator composed of calculation modules using N base frequencies. Γc and Γs in each module shown in FIG.

[0086]

(Equation 12)

The value of k in Γc and Γs of each module of the N-point recursive DFT calculator is 0
It is set so that N different base frequencies satisfying ≦ k ≦ N−1. As a result, a recursive DFT operation unit that processes the N-point Fourier transform by parallel operation can be realized.

The operation in the recursive DFT operation unit realized in this manner is performed for each sampling period ts by the above-described equations (11) and (12), and the value of k used in the operation is calculated as follows: By changing the value from 0 to N-1, a Fourier transform result at each base frequency can be obtained.

The recursive DFT operation performed by using these transformation formulas does not use the Fourier transform values of other points, ie, depends on each other, in order to calculate the Fourier transform value of a predetermined specific point. , And Fourier transform values can be obtained independently.

As described above, the fact that the Fourier transform value at a predetermined frequency can be obtained independently is, for example, when focusing on a specific frequency point, that is, when k is selected to a specific value, The value of the expression of the trigonometric function shown in (11) and (12) is a constant.

In order to compare this with the conventional DFT operation, the conventional DFT is defined by the above-described equation (1), and the butterfly operation in which the value of the trigonometric function indicating the basis function changes with the value of k is used. Is performed by the conventional FF
In T, it is difficult to calculate a specific point. However, in the method based on the recursive DFT operation shown here, since the value of the expression represented by the trigonometric function is a constant, it is easy to calculate the Fourier coefficient for the specific point. Is different.

As described above, in the regression type DFT, by selecting the value of k corresponding to the frequency to be subjected to the frequency analysis, the DFT conversion result at the selected frequency point can be obtained by a simple calculation.

Furthermore, since Fourier analysis can be performed by selecting only a desired base frequency, the number of points handled as in the conventional FFT is an exponential point of 2 (a value indicated by a power of 2; 2, 4 , 8, 16, 32,
64, 128,...), And Fourier analysis can be performed by specifying an arbitrary number of points.

Next, the configuration of a recursive DFT operation circuit in which the operation modules thus constructed are arranged in parallel will be described. In the operation in the N-point recursive Fourier transform shown in FIG. 5 described above, there are constituent parts that perform exactly the same operation in all of the N modules arranged in parallel, and the part that performs the same operation is common. And a simplified Fourier transform circuit.

FIG. 6 shows an example of a shared N
2 shows a configuration of a point recursive DFT transformer. The DFT in the same figure is different from the module shown in FIG.
Parts that perform the same operation are shared, and parts that are not common are configured as submodules.

That is, in the above-described recursive DFT conversion circuit of FIG. 4 constituting the module, a delay unit 11 for accumulating N samples of data sampled and supplied,
From the data value sampled and supplied, the delay unit 11
And a multiplier 31 for multiplying a signal supplied from the subtractor 12 by a predetermined coefficient A are commonly used.

Each of the submodules 1 to (N-1) has the same configuration as that of the modules 1 to (N-1) except that these common components are removed. In (N-1), the signals supplied from the common delay unit 11, subtracter 12, and multiplier 31 are used in common, and the circuit scale, size, and power consumption are reduced.

The recursive discrete Fourier transform apparatus has been described above, but there is a recursive inverse discrete Fourier transform apparatus which reversely converts the signal format. That is, the recursive discrete Fourier transform device described here is a device that converts time series data into frequency sequence data, while a recursive inverse discrete Fourier transform device is a device that converts frequency sequence data into time series data. Yes, a recursive inverse discrete Fourier transform device can be realized by applying the device configuration method described here.

Then, frequency series data is generated as time series data by a recursive inverse discrete Fourier transform device,
When the generated time-series data is converted into frequency-series data by the recursive discrete Fourier transform device, if the conversion is performed using the corresponding parameters, the original frequency-series data is reproduced.

The parameter is a numerical value defining the amplitude value indicated as A in the above-mentioned equations (13) and (14), and this numerical value is a value such as 1, N, or the square root of N. Are allocated and used.

That is, data generated by performing a recursive inverse discrete Fourier transform by using, for example, a numerical value a as a parameter is supplied to a recursive discrete Fourier transform to perform symmetric signal conversion and signal retransformation. When performing the Fourier transform using the parameter A corresponding to the parameter a of the inverse Fourier transform used at that time, data before the transform can be obtained.

When the amplitudes of the signals given by a and A are 1 on the inverse Fourier transform side, the Fourier transform side is N, and when the Fourier inverse transform side is N, the Fourier transform side is 1. When the Fourier inverse transform side uses the square root of N, if the Fourier transform side also gives an amplitude based on the square root of N, the data before the transform can be obtained by performing the Fourier transform on the signal subjected to the inverse Fourier transform. .

This relationship will be described based on the above equations (11) and (12).

[0104]

(Equation 13)

In the description of the recursive DFT conversion circuit shown in FIG. 4 where A is assumed, the value is obtained by defining DFT by the above-described equation (2) and introducing it.
This coefficient exists for adjusting the amplitude of T and its corresponding IDFT.

Therefore, the constant A in the recursive DFT is
As a value corresponding to the constant a on the IDFT side corresponding thereto,

[0107]

[Equation 14]

In addition, a convenient value such as 1 or 1 / N which is complementary to the IDFT side is appropriately selected to constitute the multiplier 3.

The inverse Fourier transform configured in this way is used for an OFDM (orthogonal frequency division multiplexing) signal generating device, and the Fourier transform is used for an OFDM signal receiving device. The receiving side decodes the transmitted signal using Fourier transform, and the constants a and A that determine the amplitude used at that time are the corresponding values as described above. Should be set to.

However, actually generated in this way,
Since the transmitted OFDM signal has many factors that fluctuate the amplitude value (gain of the transmitted signal) in its path, the amplitude value at the time of the discrete Fourier transform almost corresponds to the value at the time of the inverse discrete Fourier transform. The value of A in the discrete Fourier transform may be set by appropriately selecting a value that is easy to incorporate.

The discrete Fourier transform derived by the equations (11) and (12) and the inverse discrete Fourier transform as an application thereof have been described above. The formula for calculating these Fourier coefficients is a simple form using the difference between two data values separated by N samples and the sine and cosine values of the base frequency for the Fourier coefficient values obtained one sample clock before. Can obtain the Fourier coefficient value.

The cosine value Γc and the sine value Γs of the base frequency used in the discrete Fourier transform derived by the equations (13) and (14) are recursively obtained by using mutually orthogonal functions. This shows that a type DFT converter can be configured, and a similar analysis method can be realized using other mutually orthogonal functions, such as exchanging Γc and Γs.

At this time, the relationship between the real part and the imaginary part of the Fourier coefficient used as the recursive signal and the polarity of each signal are also set so that the Fourier coefficient can be obtained by the simplest possible expression. Determine the combination of
It is necessary to derive Fourier coefficients by the defined method.

[0114]

According to the first aspect of the present invention, a complex Fourier transform is performed on a supplied data sequence consisting of N samples, and a complex Fourier transform is already performed based on the sample value of a new sample supplied next. The oldest sample value used to perform the conversion is subtracted to obtain a subtraction value, the oldest sample is deleted, and the N is updated one by one based on the subtraction value and the complex Fourier operation result already obtained. Since the result of discrete Fourier calculation for a number of samples can be obtained, unlike the conventional case where Fourier calculation is performed after data of N samples is supplied, the number of points that gives the required analysis resolution within one sample period This has an effect that a recursive Fourier transform apparatus for obtaining a fast Fourier operation result in N can be configured.

According to the second aspect of the present invention, a complex Fourier transform is performed on the supplied data sequence of N samples, and the sample value of the next new sample to be supplied and the complex Fourier transform Based on the oldest sample value used for performing the conversion and the already obtained complex Fourier operation result, a discrete Fourier operation result is newly obtained for each of the N samples by performing an operation using a predetermined operation expression. Therefore, unlike the conventional method, the Fourier operation is performed after the data of N samples is supplied, and the result of the fast Fourier operation at the number of points N that provides the required analysis resolution within one sample period is obtained. This has the effect that a recursive Fourier transform device can be configured.

According to the third aspect of the present invention, a complex Fourier transform is performed on a plurality of base frequencies with respect to a supplied data sequence including N samples, and a new sample to be supplied next. From the sample values, subtract the oldest sample value already used for performing the complex Fourier transform to obtain a subtraction value, delete the oldest sample, and based on the subtraction value and the complex Fourier operation result already obtained. Since it is possible to obtain a discrete Fourier calculation result for a plurality of base frequencies for the N samples updated one by one, unlike the conventional case where the Fourier calculation is performed after data of N samples is supplied, 1
This has the effect that a recursive Fourier transform apparatus that operates at high speed and obtains Fourier operation results for a plurality of base frequencies within a sample period can be configured.

According to the fourth aspect of the present invention, a complex Fourier transform is performed on a plurality of base frequencies with respect to a supplied data sequence including N samples, and a new sample to be supplied next is obtained. From the sample values, subtract the oldest sample value already used for performing the complex Fourier transform to obtain a subtraction value, delete the oldest sample, and based on the subtraction value and the complex Fourier operation result already obtained. When obtaining discrete Fourier operation results for a plurality of base frequencies for the N samples updated one by one, the first primary storage unit, the subtraction unit, and the constant multiplication unit can be commonly used. Unlike the conventional case where the Fourier operation is performed after data of N samples is supplied, the Fourier operation for a plurality of base frequencies within one sample period is performed. It has an effect capable of constituting a recursive Fourier transform device of simplified construction by sharing the hardware operates at a high speed to obtain a calculation result.

According to the fifth aspect of the present invention, in addition to the effects of the third and fourth aspects, in particular, a recursive Fourier transform apparatus which operates at high speed and obtains Fourier operation results for all N base frequencies is provided. It has an effect that can be configured.

According to the sixth aspect of the present invention, in addition to the effects of the first, second, third, and fourth aspects, the positive constant value A
Can be calculated by an FFT in which values such as 1, N, or the square root of N are appropriately selected and set.
For example, an information signal to be transmitted,
In the case where an FT (Inverse Fast Fourier Transform) conversion process is performed to convert the signal into a time-series signal and transmit the time-series signal, the transmitted signal is supplied to the FFT and the FFT operation is performed to reproduce the information signal. In such a Fourier arithmetic device, for example, 1, N,
Alternatively, a constant value A corresponding to a constant value of a, which is the number of the square root of N, can be used in an FFT operation processing circuit to configure an FFT that operates complementarily to the IFFT to decode the information signal. By using the constant value A corresponding to a used in the IFFT operation in the corresponding system for the signal supplied from the corresponding system, a recursive Fourier transform device having good quality characteristics is configured. It has the effect that can be.

[Brief description of the drawings]

FIG. 1 is a diagram showing a schematic configuration of a recursive discrete Fourier transform device according to an embodiment of the present invention.

FIG. 2 is a diagram schematically illustrating a relationship between a data value obtained by sampling a signal waveform supplied to a recursive discrete Fourier transform apparatus according to an embodiment of the present invention and a DFT operation on the data value.

FIG. 3 is a diagram showing a configuration of a recursive discrete Fourier transform device according to an embodiment of the present invention.

FIG. 4 is a diagram illustrating in detail a configuration of a recursive discrete Fourier transform device according to an embodiment of the present invention.

FIG. 5 is a diagram illustrating a configuration of a recursive discrete Fourier transform apparatus that calculates a Fourier coefficient for an N-point base frequency according to an embodiment of the present invention.

FIG. 6 is a diagram illustrating a configuration of a recursive discrete Fourier transform device that calculates a Fourier coefficient for an N-point base frequency according to an embodiment of the present invention.

[Explanation of symbols]

 Reference Signs List 1 data update unit 2 base frequency setting unit 3 recursive DFT operation unit 4 memory unit 11 temporary storage unit 12 subtraction unit 30 basis function operation processing unit 31 constant multiplication unit 32 to 35 multiplication unit 36 to 38 addition unit 41 temporary storage unit 42 Temporary storage

Claims (6)

[Claims] 1. Times t, t + 1, t + 2, t + at constant intervals.
3,..., T + N−1, t + N, (N is a positive integer of 1 or more), and data values x (t), x (t + 1), x ( t + 2), x (t +
3),..., X (t + N−1), x (t + N) are supplied, and N data values supplied from time t with respect to the supplied data value are defined as a data string, The order k obtained by performing a complex Fourier transform on a sequence (k is
Its real part Xr (k, t) and its imaginary part Xi (k, t) as complex Fourier coefficients at 0 or a positive integer less than N).
In the discrete Fourier transform apparatus that obtains, the data sequence x supplied from time t at time t + N−1
(T), x (t + 1), x (t + 2), x (t + 3), ...
, X (t + N-1), and a complex Fourier coefficient Xr (k, t) and Xi (k, t) of a data sequence temporarily stored in the first storage means. ), And second temporary storage means for temporarily storing the complex Fourier coefficients Xr (k, t) and Xi (k, t) obtained by the discrete Fourier calculation means. A subtraction unit that obtains a data value of a difference between the data value x (t + N) supplied at time t + N and the data value x (t) temporarily stored in the first storage unit, A constant multiplier for multiplying the obtained data value of the difference by a constant value A for giving a predetermined amplitude to obtain a signal of a predetermined amplitude; A signal, a real value Xr (k, t) of a complex Fourier coefficient temporarily stored in the second temporary storage means, or an imaginary value An adder for adding one of the values Xi (k, t) to obtain an addition signal, an addition signal obtained from the addition unit, and a complex Fourier coefficient temporarily stored in the second temporary storage means. Real value Xr
(k, t) or the other signal of the imaginary value Xi (k, t) is supplied, the signal is subjected to arithmetic processing using a constant based on the base frequency, and the complex Fourier coefficient Xr at time t + 1 is calculated.
A recursive discrete Fourier transform device comprising a basis function operation processing unit for obtaining (k, t + 1) and Xi (k, t + 1). 2. Times t, t + 1, t + 2, and t + at fixed intervals.
3,..., T + N−1, t + N, (N is a positive integer of 1 or more), and data values x (t), x (t + 1), x ( t + 2), x (t +
3),..., X (t + N−1), x (t + N) are supplied, and N data values supplied from time t with respect to the supplied data value are defined as a data string, The order k obtained by performing a complex Fourier transform on a sequence (k is
0 or a positive integer less than N) as its Fourier coefficients, its real part Xr (k, t) and its imaginary part Xi (k, t)
In the discrete Fourier transform apparatus that obtains, the data sequence x supplied from time t at time t + N−1
(T), x (t + 1), x (t + 2), x (t + 3), ...
, X (t + N-1), and a complex Fourier coefficient Xr (k, t) and Xi (k, t) of a data sequence temporarily stored in the first storage means. ), And second temporary storage means for temporarily storing the complex Fourier coefficients Xr (k, t) and Xi (k, t) obtained by the discrete Fourier calculation means. , The discrete Fourier operation means comprises a complex Fourier coefficient Xr (k,
A recursive discrete Fourier transform apparatus, wherein t + 1) and Xi (k, t + 1) are calculated and obtained by the following equations. (Equation 1) 3. Times t, t + 1, t + 2, t + at constant intervals.
3,..., T + N−1, t + N, (N is a positive integer of 1 or more), and data values x (t), x (t + 1), x ( t + 2), x (t +
3),..., X (t + N−1), x (t + N) are supplied, and N data values supplied from time t with respect to the supplied data value are defined as a data string, The column is subjected to a complex Fourier transform using a plurality of orders k (k is 0 or a positive integer smaller than N), and as a plurality of sets of complex Fourier coefficients, the real part Xr (k,
t) and a discrete Fourier transform apparatus for obtaining an imaginary part Xi (k, t), wherein a data sequence x supplied from time t at time t + N−1
(T), x (t + 1), x (t + 2), x (t + 3), ...
, X (t + N−1), and first and second complex Fourier coefficients Xr (r) corresponding to a plurality of k values in a data sequence temporarily stored in the first storage means. k,
t) and Xi (k, t), and a plurality of sets of complex Fourier coefficients Xr (k, k) obtained by the discrete Fourier calculation means corresponding to the respective values of k.
t) and second temporary storage means for temporarily storing each of Xi (k, t), and each of the plurality of discrete Fourier calculation means is stored at time t
+ N, and a subtraction unit for obtaining a data value of a difference between the data value x (t + N) supplied at + N and the data value x (t) temporarily stored in the first storage means. On the other hand, a constant multiplier for obtaining a signal of a predetermined amplitude by multiplying by a constant value A for giving a predetermined amplitude, a signal of a predetermined amplitude obtained from the constant multiplier, and the second temporary storage Adding one of the real value Xr (k, t) or the imaginary value Xi (k, t) of the complex Fourier coefficient temporarily stored in the means,
An addition unit for obtaining an addition signal; an addition signal obtained from the addition unit; and a real value Xr of a complex Fourier coefficient temporarily stored in the second temporary storage unit.
(k, t) or the other signal of the imaginary value Xi (k, t) is supplied, the signal is subjected to arithmetic processing using a constant based on the base frequency, and a complex Fourier for a predetermined k at time t + 1 A recursive discrete Fourier transform apparatus characterized by comprising a basis function operation processing section for obtaining coefficients Xr (k, t + 1) and Xi (k, t + 1). 4. Times t, t + 1, t + 2, t + at which intervals are constant.
3,..., T + N−1, t + N, (N is a positive integer of 1 or more), and data values x (t), x (t + 1), x ( t + 2), x (t +
3),..., X (t + N−1), x (t + N) are supplied, and N data values supplied from time t with respect to the supplied data values are used as a data string, The column is subjected to a complex Fourier transform using a plurality of orders k (k is 0 or a positive integer smaller than N), and as a plurality of sets of complex Fourier coefficients, the real part Xr (k,
t) and a discrete Fourier transform apparatus for obtaining an imaginary part Xi (k, t), wherein a data sequence x supplied from time t at time t + N−1
(T), x (t + 1), x (t + 2), x (t + 3), ...
, X (t + N−1), and first and second complex Fourier coefficients Xr (r) corresponding to a plurality of k values in a data sequence temporarily stored in the first storage means. k,
t) and Xi (k, t), and a plurality of sets of complex Fourier coefficients Xr (k, k) obtained by the discrete Fourier calculation means corresponding to the respective values of k.
t) and second temporary storage means for temporarily storing each of Xi (k, t), and each of the plurality of discrete Fourier calculation means is stored at time t
+ N, a common subtraction unit for obtaining a data value of the difference between the data value x (t + N) supplied at + N and the data value x (t) temporarily stored in the first storage means, A common constant multiplication unit for multiplying the data value of the difference by a constant value A for giving a predetermined amplitude to obtain a signal of a predetermined amplitude; and a predetermined constant amplitude obtained by the common constant multiplication unit. Signals,
An adder for adding one of the real value Xr (k, t) or the imaginary value Xi (k, t) of the complex Fourier coefficient temporarily stored in the second temporary storage means to obtain an addition signal; The temporarily stored complex Fourier coefficient real value Xr (k,
t) or a second temporary storage unit that supplies the other signal of the imaginary value Xi (k, t); an addition signal from the adding unit; and an actual value of a complex Fourier coefficient from the second temporary storage unit. The other signal of the numerical value Xr (k, t) or the imaginary numerical value Xi (k, t) is supplied, and these signals are subjected to arithmetic processing using a constant based on a base frequency corresponding to each value of k, A recursive discrete Fourier transform apparatus comprising a plurality of sets of complex Fourier coefficients Xr (k, t + 1) and Xi (k, t + 1) for each order k at time t + 1. . 5. The system according to claim 3, wherein the plurality of complex Fourier coefficients corresponding to the respective k values are configured to output complex Fourier coefficients corresponding to the N k values. 5. The recursive discrete Fourier transform apparatus according to 4. 6. A positive constant value A for giving an amplitude value corresponding to a difference value between x (t + N) and x (t) is 1, N
5. The recursive discrete Fourier transform apparatus according to claim 1, wherein a value such as a square root of N or N can be selectively set.