JPH07175636A - Digital trigonometric function generating circuit - Google Patents

Abstract

PURPOSE:To reduce the capacity of a memory for storing a trigonometric function by forming a domain phase angle signal and a fragment phase angle signal from an input phase angle and performing trigonometric function generation processing corresponding to the domain phase angle signal. CONSTITUTION:In the case of a sine function over the range of a phase angle thetafrom 0 deg. to 45 deg., the condition of the phase angle theta=fragment phase angle phiis established because of a domain phase angle alpha=0 deg.. Since a function value over the range of the phase angle from 0 deg. to 45 deg. is stored in a ROM 5 as a sin table, the sin theta can be provided as it is by inputting the fragment phase angle phi=0 deg.-45 deg. like sintheta=sinphi. Next, the sin function value can be calculated by using a cos table inside a ROM 6 over the range of theta=45 deg.-90 deg.. Namely, the condition of sintheta=sin(45 deg.+phi)=cos(45 deg.-phi) is established. Concerning the ranges of the phase angle theta=90 deg.-135 deg., theta=135 deg.-180 deg., theta=180 deg.-225 deg. and theta=225 deg.-270 deg., the sin function can be similarly calculated from the tables in the ROM 5 and ROM 6 as well.

Description

Detailed Description of the Invention

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a digital signal processing device, and more particularly to a trigonometric function generator for generating trigonometric function values from digital signals.

[0002]

2. Description of the Related Art In the NTSC system, a luminance signal and a color signal are transmitted as a color television signal. The television receiver expresses colors by using the three primary colors R (red), G (green), and B (blue) signals of light. In order to demodulate into a primary color signal on the television receiver side, a color difference signal obtained by adding the luminance signal (Y signal) is required. The color difference signal is (RY),
The three signals are (G-Y) and (B-Y). The luminance signal voltage E _Y and the color difference signal voltages E _RY , E _GY and E _BY are 3
It is expressed by the following equation based on the primary color voltage signals E _R , E _G , and E _B.

[0003]

## EQU1 ## E _Y = 0.30E _R + 0.59E _G + 0.11E _B

[0004]

[Equation 2] E _RY = 0.70E _R −0.59E _G −0.11E _B

[0005]

[Equation 3] E _GY = −0.30E _R + 0.41E _G −0.11E _B

[0006]

E _BY = −0.30E _R −0.59E _G + 0.89E _B Among these color difference signals, (RY) signal and (BY)
Since a (G-Y) signal can be created based on the signal, the signals to be transmitted are (R-Y) signal, (B-Y) signal,
Three Y signals are enough.

In the NTSC system, a color difference signal (RY),
(BY) is modified to use I and Q signals. The human eye has excellent color resolution for colors in the orange and cyan directions and poor resolution for the green and magenta directions. Therefore, in the NTSC system, a wide transmission band is provided for orange and cyan systems to transmit fine details, and a wide transmission band is not unnecessarily provided for green and magenta systems. It's meant, so I'm narrowing the bandwidth.

I axis (orange, cyan system) and Q axis (green,
The magenta system is an axis in which the phases are advanced by 33 ° from the (RY) axis and the (BY) axis. In the frequency distribution of the color television broadcast wave in the NTSC system, a color subcarrier (subcarrier) f _sc is placed at a position shifted by 3.579545 MHz from the video carrier. The sine component of the color subcarrier _fsc is used as the I signal and the cos component is used as the Q signal for simultaneous modulation.

The signal E ₁ of the first scanning line of the NTSC signal can be expressed by the following equation.

[0010]

Equation 5] _{E 1 = E Y1 + E I1} sinω c t + E Q1 cosω c t voltage E ₁ is a video composite signal of the first line,
The voltage E _Y is a luminance signal voltage. The voltage E _I is the I signal voltage and the voltage E _Q is the Q signal voltage. The angular frequency ω _c is the color signal angular frequency and is represented by the color subcarrier f _sc such that ω _c = 2πf _sc .

In the color modulation / demodulation circuit for the color signals I and Q signals, it is necessary to generate a sine wave and a cosine wave as the two-phase color subcarriers at right angles. Since the sine wave and the cosine wave are periodic functions, it is sufficient to have a maximum of one cycle of function values as ROM data.

In order to accurately perform color demodulation in the digital color demodulation circuit, it is necessary to increase the number of bits representing the phase angle which is the input parameter to the ROM that stores the trigonometric function value. However, as the number of input bits of the ROM increases, a problem that a large capacity ROM is required arises.

In order to solve the problem, the sin function of 1 cycle is not stored in the ROM and the sin of 0 to 90 ° is maintained.
It has been proposed that a function value for one cycle can be generated only by storing the function value and the cos function value in the ROM.

[0014]

In the digital trigonometric function generator circuit, when the number of bits representing the phase angle of the input is increased,
The ROM capacity for storing the trigonometric function value becomes large.

An object of the present invention is to provide a digital trigonometric function generating circuit which can generate trigonometric function values with a small storage capacity.

[0016]

The digital trigonometric function generating circuit of the present invention has an input terminal for receiving an input signal representing an arbitrary phase angle θ of 0 to 360 degrees, and a sin output terminal for outputting a signal representing sin θ. , Cos output terminal that outputs a signal that represents cos θ, and 45 from the input signal that represents the phase angle θ
By inputting the subdivided phase angle signal φ, a division signal forming means for forming a region phase angle signal α in degrees and a subdivided phase angle signal φ representing an angle of 0 to 45 degrees such that θ = α + φ Phase inversion means for outputting an inverted phase angle signal (45 ° -φ), and a sin function value and a cos function value for 0 to 45 degrees are stored, or a sin function value or a cos function value for 0 to 90 degrees are stored. , A memory for generating two outputs at the same time, a memory input means for inputting a subdivided phase angle signal φ or an inverted phase angle signal (45 ° −φ) to the memory based on the area phase angle signal α, and a area phase angle signal means for selectively inverting the sign of the two outputs from the memory based on α and supplying one output to the sin output terminal and the other output to the cos output terminal.

[0017]

[Function] The area phase angle signal α and the subdivided phase angle signal φ are formed from the input phase angle θ, and the trigonometric function generation processing is performed according to the area phase angle signal α to reduce the memory capacity for storing trigonometric function values. can do.

[0018]

EXAMPLE When the phase angle θ representing the input parameter of the trigonometric function is represented on the xy plane, it belongs to any one of the four quadrants. Since the trigonometric function is a periodic function, if it has a function value in any one of the four quadrants, mapping to the other three quadrants is possible. For example, a function value having a phase angle of 0 to 90 ° representing the first quadrant is RO
If it is stored in M, the phase angle θ = 0 representing all four quadrants
Function values can be generated for ~ 360 °.

Furthermore, a sin having a phase angle θ of 45 to 90 °
The function value is a ROM of the cos function value with a phase angle of 0 to 45 °
Can be generated from the data. This will be clear from the following trigonometric formula.

[0020]

[Mathematical formula-see original document] sin [theta] = cos (90 [deg.]-[Theta]) (6) Similarly, the cos function values of [theta] = 45 to 90 [deg.] Are also [theta] = 0 to 4
It can be generated from ROM data having a sin function value of 5 °.

Therefore, si at a phase angle of 0 to 45 °
An embodiment will be described in which the sin function and the cos function are simultaneously obtained from the input values of the phase angle θ = 0 to 360 ° in one cycle by using the n table and the cos table at the phase angle of 0 to 45 °.

The input phase angle θ is represented by an 8-bit digital signal phase [7: 0] as shown in FIG. θ
= 0 ° is phase [7: 0] = "00000000"
, The signal phase increases as the phase angle θ increases.
[7: 0] also becomes large. Phase angle θ = 36 different for one cycle
0 ° is the same as θ = 0 ° and the signal phase [7: 0] =
It is represented by "00000000".

The signal phase [7: 5] represents the area phase angle α indicating the phase angle θ in the unit of 45 °. Signal ph
When ase [7: 5] = “000”, the phase angle θ = 0 to
It represents 45 °, and the signal phase [7: 5] = “001”.
Then represents the phase angle θ = 45 to 90 °, and the signal phas
If e [7: 5] = “010”, phase angle θ = 90 to 1
It represents 35 °, and the signal phase [7: 5] = “011”.
Then, the phase angle θ = 135 to 180 ° is represented, and the signal ph
If ase [7: 5] = “100”, the phase angle θ = 18
The signal phase [7: 5] = “1” represents 0 to 225 °.
If "01", the phase angle θ = 225 to 270 ° is represented, and if the signal phase [7: 5] = "110", the phase angle θ
= 270 to 315 °, and the signal phase [7: 5]
= “111” represents the phase angle θ = 315 to 360 °.

The signal phase [4: 0] is the above-mentioned 45.
It represents a subdivided phase angle φ = 0 to 45 ° within a unit of °, and corresponds to an input phase angle θ−a region phase angle α. That is, the input phase angle can be represented by θ = α + φ. Subdivision phase angle φ =
0 ° is represented by phase [4: 0] = “00000”,
The signal phase increases as the subdivision phase angle φ increases.
[4: 0] also becomes large.

FIG. 2 shows si at a phase angle of 0 to 45 °.
Phase angle θ = 0 from the function values of the n table and the cos table
It is a graph which shows the procedure which calculates | requires the function value of sin (theta) and cos (theta) of -360 degrees. The sin function value and the cos function value within the range of the phase angle φ = 0 to 45 ° are stored in the ROM, and the si of the phase angle θ = 0 to 360 ° is stored by using this function value.
Find the n, cos function value.

FIG. 2A shows sin θ with respect to the phase angle θ.
It is a graph showing. The phase angle θ of 0 to 360 ° is divided into units of 45 ° as shown by a broken line in the graph for description. This is because the function value can be obtained by the same conversion method within each 45 ° range.

First, the sin function in the range of θ = 0 to 45 ° will be described. In this range, since the region phase angle α = 0 °, the phase angle θ = φ holds. Since the function value in the range of the phase angle of 0 to 45 ° is stored in the ROM as a sin table, sin θ can be obtained as it is by inputting the subdivided phase angle φ = 0 to 45 ° as in the following equation.

[0028]

## EQU7 ## sin θ = sin φ (7) Next, in the range of θ = 45 to 90 °, the cos in the ROM is
The sin function value can be calculated by using the table. The region phase angle α = 45 °, and the sin function value sin θ with respect to the phase angle θ is the subdivision phase angle φ
Can be expressed by the following equation.

[0029]

## EQU00008 ## sin.theta. = Sin (45.degree. +. Phi.) = Cos (90.degree.-45.degree..phi.) = Cos (45.degree .-. Phi.) (8) where (45.degree .-. Phi.) Is 0-45. It is called a reversal phase angle because it is a phase angle that changes opposite to φ in the range of °.

In the range of θ = 90 to 135 °, the area phase angle α = 90 °. Note that the formula 10 is established from the formulas 6 and 9.

[0031]

## EQU00009 ## cos .theta. = Cos (-.theta.) (9)

[0032]

[Mathematical formula-see original document] sin [theta] = cos (90 [deg.]-[Theta]) = cos ([theta] -90 [deg.]) (10) When [theta] is between 90 and 135 [deg.], [Theta] = 90 [deg.] + [Phi],
sin θ can be expressed by the following equation using the subdivided phase angle φ. Therefore, the cos table in the ROM can be used as it is.

[0033]

Sin θ = cos (90 ° + φ−90 °) = cos φ (11) Next, in the range of θ = 135 to 180 °, the area phase angle α
= 135 ° (θ = 135 ° + φ), Equation 13 is established from Equation 12, and the inversion phase angle of the subdivision phase angle φ is 45 °.
Using −φ, sin θ can be calculated from the sin table in the ROM.

[0034]

(12) sin θ = sin (180 ° −θ) (12)

[0035]

(13) sin θ = sin (180 ° -135 ° -φ) = sin (45 ° -φ) (13) In the range of θ = 180 to 225 °, the area phase angle α = 18.
It is 0 °, and sin θ can be expressed by the following expression from Expression 12.

[0036]

[Mathematical formula-see original document] sin [theta] = sin (180 [deg.]-180 [deg.]-[Phi]) = sin (-[phi]) Further, Formula 16 holds from Formula 15, and sin [theta] can be obtained from the sin table in the ROM.

[0037]

## EQU15 ## sin (-. Theta.) =-Sin.theta .... (15)

[0038]

## EQU16 ## sin θ = -sin φ (16) In the range of θ = 225 to 270 °, the area phase angle α = 22
5 °, the following formula is established, and sin θ is inverted phase angle 4
It can be obtained from the cos table in the ROM by using 5 ° -φ.

[0039]

Sin θ = sin (225 ° + φ) = sin (360 ° -135 ° + φ) = -sin (135 ° -φ) = -cos (135 ° -φ-90 °) = -cos (45 °- φ) (17) In the range of θ = 270 to 315 °, the area phase angle α = 27
It is 0 °, and the following equation is established, and sin θ can be obtained from the cos table in the ROM.

[0040]

(18) sin θ = sin (270 ° + φ) = sin (360 ° -90 ° + φ) = -sin (90 ° -φ) = -cos (90 ° -φ-90 °) = -cosφ 18) In the range of θ = 315 to 360 °, the area phase angle α = 31
It is 5 °, and the following formula is established, and sin θ can be obtained from the sin table in the ROM using the inversion phase angle of 45 ° −φ.

[0041]

Sin θ = sin (315 ° + φ) = sin (360 ° −45 ° + φ) = − sin (45 ° −φ) (19) As described above, the range of θ = 0 to 360 ° Within 4
0 to 360 ° by changing the calculation method in 5 ° units
The sin function for the phase angle of can be obtained. The function value in ROM required at this time is the phase angle φ = 0
Only the sin function value in the range of 45 ° and the cos function value in the range of the phase angle φ = 0 to 45 ° are required.

FIG. 2B shows cos θ with respect to the phase angle θ.
It is a graph showing. The phase angle θ of 0 to 360 ° is divided into units of 45 ° as shown by a broken line in the graph for description. Within each 45 ° range, the same conversion method can be used.

First, the cos function in the range of θ = 0 to 45 ° will be described. In this range, since the region phase angle α = 0 °, the phase angle θ = φ holds. Since the function value in the range of the phase angle of 0 to 45 ° is stored in the ROM as a cos table, cos θ can be obtained as it is by inputting the subdivided phase angle φ = 0 to 45 ° as in the following equation.

[0044]

## EQU20 ## cos θ = cos φ (20) Next, in the range of θ = 45 to 90 °, the sin in the ROM is
By using the table, cos θ can be calculated. The region phase angle α = 45 °, and the reversal phase angle of 45 ° −φ of the subdivision phase angle φ is used from Formula 21, and
sθ can be represented.

[0045]

(21) cos θ = sin (90 ° −θ) (21)

[0046]

Cos θ = sin (90 ° −45 ° −φ) = sin (45 ° −φ) (22) In the range of θ = 90 to 135 °, the area phase angle α = 90 °
And the following equation holds using the subdivided phase angle φ.

[0047]

[Mathematical formula-see original document] cos [theta] = sin (90 [deg.]-90 [deg.]-[Phi]) = sin (-[phi]) Further, it can be expressed by the following formula using Formula 15, and cos [theta] can be obtained from the sin table in the ROM. it can.

[0048]

Cos θ = −sin φ (24) Next, in the range of θ = 135 to 180 °, the area phase angle α
= 135 °, Formula 26 is established from Formula 25,
Using the inversion phase angle of 45 ° -φ, set cos θ to c in the ROM.
It can be obtained from the os table.

[0049]

[Equation 25] −cos θ = cos (180 ° −θ) (25)

[0050]

Cos θ = cos (135 ° + φ) = cos (180 ° −45 ° + φ) = − cos (45 ° −φ) (26) In the range of θ = 180 to 225 °, the area phase angle α = 18
It is 0 °, and can be expressed by the following equation from Equation 25.

[0051]

[Mathematical formula-see original document] cos [theta] = cos (180 [deg.] + [Phi]) =-cos (-[phi]) Further, the following formula is established from the formula 9, and cos [theta] can be obtained from the cos table in the ROM.

[0052]

Cos θ = −cos φ (28) In the range of θ = 225 to 270 °, the area phase angle α = 22
It is 5 °, and the following equation holds, and cos θ can be obtained from the sin table in the ROM using the inversion phase angle of 45 ° −φ.

[0053]

Cos θ = cos (225 ° + φ) = cos (360 ° -135 ° + φ) = cos (135 ° -φ) = sin (90 ° -135 ° + φ) = -sin (45 ° -φ) (29) In the range of θ = 270 to 315 °, the area phase angle α = 27
It is 0 °, and the following equation holds, and cos θ can be obtained from the sin table in the ROM.

[0054]

Cos θ = cos (270 ° + φ) = cos (360 ° −90 ° + φ) = cos (90 ° −φ) = sin (90 ° −90 ° + φ) = sin φ ... (30) θ = In the range of 315 to 360 °, the area phase angle α = 31
It is 5 °, and the following formula is established, and cos θ can be obtained from the cos table in the ROM by using the inversion phase angle of 45 ° −φ.

[0055]

Cos θ = cos (315 ° + φ) = cos (360 ° −45 ° + φ) = cos (45 ° −φ) (31) As described above, within the range of θ = 0 to 360 ° In 4
By changing the calculation method in units of 5 °, 0-360
The cos function for the phase angle of ° can be obtained.
The function value in ROM required at this time is the phase angle φ = 0.
Sin function value in the range of up to 45 ° and phase angle φ = 0 to 45 °
Only cos function values in the range

FIG. 3 is a table showing a conversion method for obtaining the function values of sin θ and cos θ of the phase angle θ = 0 to 360 ° from the function values of the sin table and the cos table within the range of the phase angle of 0 to 45 °. is there.

The input phase angle θ is represented by an 8-bit digital signal phase [7: 0]. Conversion is performed from the sin table and the cos table at 0 to 45 ° stored in the ROM to the sin function and the cos function at the input phase angle θ.

The processing required for conversion includes phase inversion, sin / cos exchange, and sign inversion as items in the table. Phase inversion, which is the first process, means reversing the direction of change in angle within 45 ° (determining the inversion phase angle). For example, this is a process necessary for conversion within the range of the phase angle θ = 135 to 180 °. Phase angle θ = 1
The sin function in the range of 35 to 180 ° is represented by sin θ = sin (45 ° −φ) as shown in Expression 13. Therefore, using the inversion phase angle φ ′ = 45 ° −φ, si
The sin function is obtained from nφ ′. At this time, the process of obtaining φ ′ = (45 ° −φ) is phase inversion. It can be converted to φ ′ by inverting the phase of the φ digital signal.

For example, from φ = 0 °, φ ′ is obtained by phase inversion.
A case of obtaining = 45 ° will be described. When φ = 0 ° is represented by a digital signal, phase [7: 0] = “00000000”. The signal phase of the lower 5 bits of this signal
Bit invert [4: 0]. Then the signal phase
[7: 0] becomes phase [7: 0] = “00011111”. Then, "1" is added to this bit-inverted signal. As described above, when the lower 5 bits of the signal phase [7: 0] are inverted and “1” is added, phase [7: 0] = “00100000”. The signal after this phase inversion processing represents φ ′ = 45 °.

Thus, when it is necessary to obtain φ '= (45 ° -φ), the phase inversion process is performed. In the range of the phase angle θ where the phase inversion process is required, it is necessary to perform the phase inversion process when obtaining the sin function and also perform the phase inversion process when obtaining the cos function. On the contrary, in the range of the phase angle θ that does not require the phase inversion process, the phase inversion process is not performed when the sin function is obtained, and the phase inversion process does not need to be performed when the cos function is obtained.

Next, the second process, sin / cos exchange, means the exchange of the sin table and the cos table. For example, this is a process necessary for conversion within the range of the phase angle θ = 45 to 90 °. Phase angle θ = 45 to 90 °
In the range of, the sin function is R
The cos function value in the OM is obtained, and the cos function is obtained using the sin function value in the ROM as shown in Expression 22.

Sin function and co at arbitrary phase angle θ
To obtain the s-function, one of the functions uses the sin function value in ROM, and the other function uses cos in ROM.
Use the function value. In other words, the sin function is si in ROM
The cos function calculated from the n table is cos in the ROM
Calculated from the table, or sin function is in ROM
Either the cos function obtained from the cos table in is obtained from the sin table in the ROM.

Therefore, the sin table in the ROM is used to obtain the sin function, and RO is used to obtain the cos function.
When using the cos table in M, sin / co
The s exchange process may not be performed. On the other hand, when the cos table in the ROM is used to obtain the sin function and the sin table in the ROM is used to obtain the cos function, it is necessary to perform a sin / cos exchange process.

As described above, whether to perform the sin / cos exchange processing is determined depending on which of the sin table and the cos table in the ROM is used to obtain the sin function and the cos function.

The sign reversal, which is the third process, is a process required for conversion within the range of the phase angle θ = 180 to 225 °, for example. Phase angle θ = 180 to 225 °
Within the range, the sin function can be calculated by sin θ = −sin φ as shown in Expression 16. In this way, it is necessary to perform the sign inversion process when the sign of the value in the ROM table and the sign to be obtained are opposite.

Next, the processing required for the conversion of the sin function and the cos function will be described in order from the range of the phase angle θ = 0 to 45 °. The sin function at the phase angle θ = 0 to 45 ° is represented by sin θ = sin φ as shown in Expression 7, and the cos function is represented by cos θ = cos φ as shown in Expression 20. At this phase angle, there is no need for phase inversion processing and no sin / cos exchange processing.

In the range of the phase angle θ = 45 to 90 °, the sin function is sin θ = cos as shown in Expression 8.
(45 ° −φ), and the cos function is represented by cos θ = sin (45 ° −φ) as shown in Expression 22. At this phase angle, the phase inversion process and sin / cos
Exchange processing is required.

In the range of the phase angle θ = 90 to 135 °, the sin function is sin θ = co as shown in Expression 11.
It is represented by sφ, and the cos function is co
It is represented by sθ = −sinφ. At this phase angle,
The phase inversion process is not required, and the sin / cos exchange process and the sign inversion process for cos are required.

In the range of the phase angle θ = 135 to 180 °, the sin function is sin θ = s as shown in Expression 13.
It is represented by in (45 ° −φ), and the cos function is represented by cos θ = −cos (45 ° −φ) as shown in Expression 26. At this phase angle, the phase inversion process and the sign inversion process for cos are required, and the sin / cos exchange process is not required.

In the range of the phase angle θ = 180 to 225 °, the sin function is sin θ = − as shown in Expression 16.
It is expressed by sin φ, and the cos function is expressed by cos θ = −cos φ as shown in Expression 28. At this phase angle, neither the phase inversion process nor the sin / cos exchange process is necessary. Sign inversion processing is performed for both sin and cos.

In the range of the phase angle θ = 225 to 270 °, the sin function is sin θ = − as shown in Expression 17.
It is represented by cos (45 ° −φ), and the cos function is represented by Formula 29.
As shown in, cos θ = −sin (45 ° −φ). At this phase angle, processing for phase inversion is necessary, processing for sin / cos exchange and processing for sign inversion are required.

In the range of the phase angle θ = 270 to 315 °, the sin function is sin θ = − as shown in Expression 18.
It is represented by cos φ, and the cos function is represented by cos θ = sin φ as shown in Expression 30. At this phase angle, the process of phase inversion is not required, but the process of sin / cos exchange and the process of sign inversion for sin are required.

In the range of the phase angle θ = 315 to 360 °, the sin function is sin θ = − as shown in Expression 19.
It is represented by sin (45 ° −φ), and the cos function is represented by Formula 31.
As shown in, cos θ = cos (45 ° −φ). At this phase angle, processing for phase inversion and processing for sign inversion for sin are required, and processing for sin / cos exchange is not required.

As is clear from the graph of FIG. 2, the sign inversion process has a phase angle θ =
The sign reversal process is not required at 0 to 180 °, and the sign reversal process is required at the phase angle θ = 180 to 360 °.

On the other hand, when the cos function is obtained, the sign inversion processing is not required at the phase angles θ = 0 to 90 ° and θ = 270 to 360 °, and the sign inversion is performed at the phase angle θ = 90 to 270 °. Processing is required.

The phase inversion changes every 45 °, and sin
/ Cos exchange changes in 90 ° increments and sign inversion is 180
It changes in units of °. These changes are the upper 3 bits ph
It can be discriminated using ase [7: 5].

By performing conversion based on the conversion table shown above, the sin function and cos function can be obtained using the sin table and cos table in the ROM. Next, a circuit configuration example of a trigonometric function generating circuit for realizing this conversion will be shown.

FIG. 1 is a block diagram of a trigonometric function generating circuit according to an embodiment of the present invention. The trigonometric function generation circuit inputs sin θ and cos θ with the phase angle θ = 0 to 360 ° as input.
The function value of is output.

The input phase angle θ = 0 to 360 ° is represented by an 8-bit phase angle digital signal phase [7: 0],
The outputs sin θ and cos θ are also represented as 8-bit digital signals.

The input phase angle signal phase [7: 0] is input to the bit division circuit 11, and the upper 3 bits of the signal p
The case [7: 5] is input to the control module 1.

The control module 1 includes a phase inversion circuit 4 for performing a phase inversion process, multiplexers 7 and 8 for performing a sin / cos exchange process, and a code inversion process based on the input signal phase [7: 5]. A control signal is supplied to the sign inversion circuits 9 and 10 which perform the process of.

The signal phase [7: 5] has a phase angle of 4
Since the area phase angle α in units of 5 ° is expressed, si is calculated from the table of FIG.
It is possible to determine the processing required for conversion from nφ and cosφ to sin function and cos function.

The three processes shown in the table of FIG. 3, phase inversion,
A method of generating signals for controlling sin / cos exchange and sign inversion will be described next. First, the signal p1 for controlling the phase inversion process is connected to the line of the bit signal phase5 representing the fifth bit of the input phase angle signal phase [7: 0] in the control module 1. That is,
The input signal phase5 is the control signal p1 as it is.
Is supplied to the phase inversion circuit 4.

In the phase inversion circuit 4, the control signal p1 is "1".
If so, the phase inversion processing is performed, and if the control signal p1 is "0", the phase inversion processing is not performed. That is, the signal phas
If e5 is "1", the phase inversion process is performed and the signal pha
If se5 is “0”, the phase inversion process is not performed.

The phase inversion processing is an input signal phase.
In this processing, bit inversion processing is performed on [4: 0], "1" is added to the inverted signal, and the signal is output. Next, signals m1 and m for controlling the process of sin / cos exchange
2 is generated based on the signal phase5 and the signal phase6.

The signal phase5 and the signal phase6 are
It is input to the EXOR circuit 3 in the control module 1. The EXOR circuit 3 performs an exclusive OR operation on the two input signals and outputs the operation result.

The signal output from EXOR circuit 3 is connected to the lines for control signal m1 and control signal m2. The control signal m1 and the control signal m2 are the same signal and are output signals of the EXOR circuit 3.

The control signal m1 controls the multiplexer 7, and the control signal m2 controls the multiplexer 8. The multiplexers 7 and 8 have a sinφ ROM 5 and a cosφ, respectively.
The respective output signals from the ROM 6 are supplied.
The ROM 5 stores the function value of sin φ at the phase angle φ = 0 to 45 °, and si for the input phase angle.
Output the n-function value. However, the input phase angle is 0
It is in the range of 45 °. ROM 6 has a phase angle φ = 0 to 45
The function value of cos φ at ° is stored, and the cos function value for the input phase angle is output. However, the input phase angle is in the range of 0 to 45 °.

The multiplexer 7 outputs the sin function value supplied from the ROM 5 when the control signal m1 is "1", and outputs the cos function value supplied from the ROM 6 when the control signal m1 is "0". .

The multiplexer 8 outputs the cos function value supplied from the ROM 6 when the control signal m2 is "1", and outputs the sin function value supplied from the ROM 5 when the control signal m2 is "0". .

That is, when the output of the EXOR circuit 3 is "1", the multiplexer 7 outputs the sin function value from the ROM 5, and the multiplexer 8 outputs the cos from the ROM 6.
Output the function value. On the contrary, if the output of the EXOR circuit 3 is "0", the multiplexer 7 outputs c from the ROM 6
The os function value is output, and the multiplexer 8 outputs the sin function value from the ROM 5.

Next, the signals for controlling the sign inversion processing are the control signals s1 and s2. The sign-inverted control signal for the sin function output is the signal s1, and the sign-inverted control signal for the cos function output is the signal s2.

The control signal s1 is connected to the line of the bit signal phase7 representing the input phase in the control module 1. The control signal s2 is generated based on the signal phase6 and the signal phase7.

The signal phase 6 and the signal phase 7 are
It is input to the EXOR circuit 2 in the control module 1. Like the EXOR circuit 3, the EXOR circuit 2 performs an exclusive OR operation on two input signals and outputs the operation result. The signal output from the EXOR circuit 2 is
It is connected to the line of the control signal s2.

The control signal s1 controls the sign inversion circuit 9,
The control signal s2 controls the sign inversion circuit 10. The sign inversion circuits 9 and 10 output a value obtained by inverting the sign of the signal value input according to the control signals s1 and s2.

In the sign inverting circuit 9, the control signal s1 is "1".
In that case, a value obtained by inverting the sign of the input value is output, and if the control signal s1 is "0", the input value is output as it is. If the control signal s2 is "1", the sign inversion circuit 10 outputs a value obtained by inverting the sign of the input value,
If the control signal s2 is "0", the input value is output as it is.

As described above, the input phase angle signal pha
Based on se [7: 5], control signals p1, s1, s2, m1, m2 for controlling each processing circuit are generated. Next, the phase angle signal phase is input to the trigonometric function generation circuit.
[7: 0] is input and the steps until the sin function value and the cos function value for the phase angle are output will be described.

Of the 8-bit phase angle signal phase [7: 0] input to the trigonometric function generation circuit, the upper 3 bits of the signal phase [7: 5] are input to the control module 1 and the control signals p1 and p1. s1, s2, m1, m
2 is output.

On the other hand, the remaining lower 5 bits of the signal p
The phase [4: 0] is input to the phase inverting circuit 4.
The phase inversion circuit 4 receives the signal phas according to the control signal p1.
e [4: 0] is subjected to phase inversion processing and output.

The phase angle signal output from the phase inverting circuit 4 is stored in the ROM 5 and cos 0 to store sin 0 to 45 °.
It is input to the ROM 6 which stores 45 °. ROM5 is
The sin function value corresponding to the input phase angle signal is supplied to the multiplexers 7 and 8. ROM6 is
The cos function value for the input phase angle signal is supplied to the multiplexers 7 and 8.

The multiplexer 7 responds to the control signal m1 by inputting the sin function value from the ROM 5 and the ROM 6
One of the cos function values according to the above is supplied to the sign inversion circuit 9. The multiplexer 8 responds to the control signal m2 by inputting the sin function value by the ROM 5 and the c by the ROM 6
The other of the os function values is supplied to the sign inversion circuit 10.

The sign inverting circuit 9 inverts the positive / negative sign of the input value in response to the control signal s1 and outputs the inverted value. The sign inversion circuit 10 inverts the positive / negative sign of the input value as necessary according to the control signal s2, and outputs it.

The 8-bit signal output from the sign inverting circuit 9 is si with respect to the phase angle signal phase [7: 0].
It is an n-function value. The 8-bit signal output from the sign inverting circuit 10 is the phase angle signal phase [7: 0].
Is the cos function value for.

As described above, the signal pha having the desired phase angle is obtained.
By inputting se [7: 0], 8-bit sin function value and cos function value for the phase angle can be obtained at the same time.
At this time, the function value stored in the ROM is 0 to 45 °.
Only the sin function value for the phase angle of and the cos function value for the phase angle of 0 to 45 ° are required.

In FIG. 5, the phase angle θ = 0 to 36 from the function values of the sin table in the range of the phase angle of 0 to 45 ° and the sin table in the range of the phase angle of 45 to 90 °.
9 is a graph showing another example of obtaining the function values of sin θ and cos θ at 0 °.

Compared to the ROM table of the previous embodiment, the 0-45 ° sin table is the same, 0-4
A 45-90 ° sin table is used instead of the 5 ° cos table.

For example, in the above-described embodiment, cosφ is read from the ROM table for the subdivided phase angle φ, whereas in the present embodiment, sin (45 ° + φ) is read from the ROM table to obtain a sin function. Find the cos function.

The input phase angle θ is represented by an 8-bit signal phase [7: 0] as described above, and the subdivided phase angle φ (θ
= [Alpha] + [phi]), when read from the ROM table of 45 to 90 [deg.], The output signal is sin (45 [deg.] + [Phi]).

That is, when the input phase angle θ = 0 ° and θ = 4
At 5 °, the lower 5 bit signals are both phase [4:
0] = “00000”, and the function values read from the ROM table are the same. Comparing the 0-45 ° cos function and the 45-90 ° sin function shown in FIG. 5, it can be seen that the relationship of cosφ = sin (90 ° −φ) = sin (45 ° + 45 ° −φ) holds.

That is, since the lower 5 bits change in synchronization with 45 °, in the above-described embodiment, the subdivision phase angles φ to c.
The function value output using the os table is s for 45 to 90 ° by using the inversion phase angle of 45 ° −φ in the present embodiment.
It can be obtained from the in table. The sin table for 0-45 ° functions as in the previous embodiment. Thus, the sin function and the co
Find the s-function.

FIG. 5A shows sin θ with respect to the phase angle θ.
5B is a graph showing cos θ with respect to the phase angle θ. 0-360 ° phase angle θ
Is divided into 45 ° units as indicated by broken lines in the graph. Within this 45 ° range, the same conversion method can be used.

Using the sin table in the above embodiment, s
The procedure for obtaining the in function or the cos function can be similarly performed in this embodiment using the sin table for 0 to 45 ° as shown in FIGS.

On the other hand, in the above-described embodiment, the procedure for obtaining the sin function or the cos function using the cos table is the reverse phase inversion processing with respect to the subdivided phase angle φ, and then the sin of 45 to 90 °. Read from the table.

Performing the opposite phase inversion process corresponds to inverting the signal controlling the phase inversion process. If the phase inversion processing is necessary in the above-described embodiment, the phase inversion processing is not necessary in this embodiment, and if the phase inversion processing is not necessary in the above embodiment, the phase inversion processing is necessary in this embodiment. is there.

Accordingly, in the above-described embodiment, cos is used when the sin function value is obtained for one input phase angle θ.
Both of them need or do not need the phase inversion processing when obtaining the function, whereas in the present embodiment, only one of them needs to perform the phase inversion processing when obtaining the sin function and the cos function. .

As described above, the sin function and the cos function for the phase angle θ = 0 to 360 ° can be obtained at the same time by using the 0-45 ° sin table and the 45-90 ° sin table.

Similarly, even if the cos table of 0 ° to 45 ° and the cos table of 45 ° to 90 ° are used,
The sin function and the cos function for the phase angle θ = 0 to 360 ° can be obtained at the same time.

FIG. 4 is a block diagram of a trigonometric function generating circuit according to the embodiment of FIG. The trigonometric function generation circuit inputs the phase angle θ = 0 to 360 ° and outputs the function values of sin θ and cos θ.

Input 8-bit phase angle signal phase
[7: 0] is input to the bit division circuit 11, the lower 5 bits of the signal phase [4: 0] are input to the phase inversion circuit 4, and the upper 3 bits of the signal phase [7: 5] are input to the control module 21. Is entered.

The control module 21 includes phase inversion circuits 4a and 4b for performing phase inversion processing based on the input signal phase [7: 5], multiplexers 7 and 8 for performing sin / cos exchange processing, A control signal is supplied to the sign inversion circuits 9 and 10 that perform the sign inversion process.

Of the signals generated by the control module 21, the signal p21 controls the phase inversion circuits 4a and 4b, the signal m21 controls the multiplexer 7, and the signal m2.
2 controls the multiplexer 8, the signal s21 controls the sign inverting circuit 9, and the signal s22 controls the sign inverting circuit 10.

Phase angle signal phase of lower 5 bits
[4: 0] is input to the phase inversion circuits 4a and 4b, the phase inversion circuit 4a performs the phase inversion process only when the control signal p21 is "1", and the phase inversion circuit 4b outputs the control signal p.
Only when 21 is “0”, the phase inversion process is performed.

The phase angle signal output from the phase inverting circuit 4a is the ROM 2 which stores a sin table of 0 to 45 °.
The phase angle signal supplied from the phase inversion circuit 4b to the signal RO is stored in the RO table storing the sin table of 45 to 90 °.
It is supplied to M26.

The sin function value read from the ROM 25 and the sin function value read from the ROM 26 are supplied to the multiplexer 7 and the multiplexer 8, respectively.
The signal output from the multiplexer 7 is the sign inversion circuit 9
And the signal output from the multiplexer 8 is supplied to the sign inverting circuit 10.

The 8-bit signal output from the sign inverting circuit 9 is si with respect to the phase angle signal phase [7: 0].
It is an n-function value. The 8-bit signal output from the sign inverting circuit 10 is the phase angle signal phase [7: 0].
Is the cos function value for.

As described above, the signal pha of the desired phase angle is
By inputting se [7: 0], 8-bit sin function value and cos function value for the phase angle can be obtained at the same time.
At this time, the function value stored in the ROM is 0 to 45 °.
Only the sin function value for the phase angle of and the sin function value for the phase angle of 45 to 90 ° are required.

As an example of the method of obtaining φ ′ = 45 ° −φ in the conversion equation, the example of performing the phase inversion processing by the phase inversion circuit has been described, but the method is not limited to this. For example, if the sin function value is sequentially stored in the ROM address with respect to the phase angle, and the address is calculated and read from the beginning of the address, sin φ is obtained, and the address is calculated and read from the end of the address. For example, sin (45 °
-Φ) can be obtained.

In the processing of the sign inverting circuit, the example of inverting the positive and negative signs has been described, but the present invention is not limited to this, and a positive sign or a negative sign may be given to the absolute value of the input value. In this embodiment, sin for a phase angle of 0 to 45 °
When using two ROMs of a function and a cos function for a phase angle of 0 to 45 °, and two ROMs of a sin function for a phase angle of 0 to 45 ° and a sin function for a phase angle of 45 to 90 °. Although the case has been described, the present invention is not limited to these combinations and can be realized by using a trigonometric function value in the range of the phase angle of another 45 °.

Further, it is not always necessary to have two ROMs. For example, if a dual port memory is used, one ROM can store the function values in two ranges. In the trigonometric function generating circuit according to the present embodiment, the capacity of the ROM for storing the trigonometric function value can be small, so that a compact circuit with a small amount of hardware can be realized and the power consumption of the circuit can be reduced.

Further, by reading the trigonometric function value from each of the two ROMs only once, it is possible to generate both the sin function value and the cos function value at the same time. Although the present invention has been described above with reference to the embodiments, the present invention is not limited thereto. For example, it will be apparent to those skilled in the art that various changes, improvements, combinations, and the like can be made.

[0131]

Since the capacity for storing the trigonometric function value can be reduced, a compact circuit with less hardware can be realized and the power consumption of the circuit can be reduced.

[Brief description of drawings]

FIG. 1 is a block diagram of a trigonometric function generating circuit according to an embodiment of the present invention.

FIG. 2 shows the phase angle θ = 0 to 3 from the function values of the sin table and the cos table in the range of the phase angle of 0 to 45 °.
It is a graph which shows the procedure which calculates | requires the function value of 60 degree sin (theta) and cos (theta). FIG. 2A shows sin with respect to the phase angle θ.
FIG. 2B is a graph showing θ, and FIG. 2B is a graph showing cos θ with respect to the phase angle θ.

FIG. 3 shows phase angles θ = 0 to 3 from the function values of the sin table and the cos table in the range of the phase angle of 0 to 45 °.
6 is a table summarizing conversion methods for obtaining function values of sin θ and cos θ of 60 °.

FIG. 4 is a block diagram of a trigonometric function generating circuit according to another embodiment of the present invention.

FIG. 5 is a sin table in a phase angle range of 0 to 45 ° and a sin table in a phase angle range of 45 to 90 °.
From the function value in the table, sin of phase angle θ = 0 to 360 °
6 is a graph for explaining a procedure for obtaining a function value of θ and cos θ. 5A is a graph showing sin θ with respect to the phase angle θ, and FIG. 5B is co with respect to the phase angle θ.
It is a graph showing sθ.

[Explanation of symbols]

 1, 21 Control module 2, 3 EXOR circuit 4 Phase inversion circuit 5, 6, 25, 26 ROM 7, 8 Multiplexer 9, 10 Sign inversion circuit 11 Bit division circuit

─────────────────────────────────────────────────── ───

[Procedure amendment]

[Submission date] June 23, 1994

[Procedure Amendment 1]

[Document name to be amended] Statement

[Name of item to be corrected] Figure 3

[Correction method] Change

[Correction content]

FIG. 3 shows phase angles θ = 0 to 3 from the function values of the sin table and the cos table in the range of the phase angle of 0 to 45 °.
6 is a chart summarizing conversion methods for obtaining function values of sin θ and cos θ of 60 °.

Claims (4)

[Claims] 1. An input terminal for receiving an input signal representing an arbitrary phase angle θ of 0 to 360 degrees, a sin output terminal for outputting a signal representing sin θ, a cos output terminal for outputting a signal representing cos θ, and a phase A region phase angle signal α in units of 45 degrees from the input signal representing the angle θ and a subdivided phase angle signal φ representing an angle of 0 to 45 degrees.
And a division signal forming means (11) for forming and so that θ = α + φ, and an inversion phase angle signal (45 ° −
phase inversion means (4) for outputting φ), and stores the sin function value and the cos function value for 0 to 45 degrees, or the sin function value for 0 to 90 degrees or c
A memory (5, 6) for storing the os function value and simultaneously generating two outputs, and a subdivided phase angle signal φ or an inverted phase angle signal (45 ° −φ) in the memory based on the area phase angle signal α. And a memory input means (1) for inputting, and selectively inverting the sign of the two outputs from the memory based on the area phase angle signal α, one output to the sin output terminal, the other output to the cos output Means for supplying to terminals (1,
7, 8, 9, 10) and a digital trigonometric function generating circuit. 2. The memory is sin for 0-45 degrees
2. A function and a cos function are stored, and the memory input means selectively inputs the subdivided phase angle signal φ or the inverted phase angle signal (45 ° −φ) to the memory based on the area phase angle signal α. Digital trigonometric function generator. 3. The memory has a sin related to 0 to 90 degrees.
A function value or a cos function value is stored, and a signal representing an angle of 0 to 45 degrees is input to 0 to 45 degrees and 45 to 90 degrees.
The sine function value or the cos function value for the degree is output, and the memory input means outputs the subdivided phase angle signal φ and the inverted phase angle signal (45 ° −φ) based on the area phase angle signal α.
3. The digital trigonometric function generating circuit according to claim 1, wherein is input to the memory. 4. The digital trigonometric function according to claim 1, wherein the input signal is a binary signal, and the divided signal forming means is means for dividing the input signal into a high-order bit signal and a low-order bit signal. Generator circuit.