KR20060081848A - Display controller with contrast strech function and method thereof - Google Patents

Abstract

The present invention provides a display controller comprising a contrast enhancement. The display controller of the present invention receives image data from the outside and outputs the image input unit and characteristic curve constants (Cx [n], n = 0, 1, ..., i) and input level values to be output to the contrast enhancement unit. Contains a special register that stores (I [n], n = 0, 1, ..., i). The display apparatus receives a characteristic curve constants Cx [n] and input level values I [n] from the special register and performs a contrast enhancement operation on the image data X from the image input unit. And a contrast enhancement unit for outputting output image data (Y).

Description

Display controller with contrast strech function and method

1 is a block diagram schematically illustrating an application processor according to the present invention.

2 is a block diagram schematically illustrating the display controller of FIG. 1 in accordance with a preferred embodiment of the present invention.

3 is a block diagram schematically illustrating the contrast enhancement of FIG. 2 in accordance with a preferred embodiment of the present invention.

4 is a graph showing a partial nonlinear approximation curve in accordance with a preferred embodiment of the present invention.

5 is a block diagram illustrating in detail the contrast enhancement of FIG. 3 in accordance with a preferred embodiment of the present invention.

6A, 7A, 8A, and 9A show histograms of images input to the display controller of FIG. 1, respectively.

6B, 7B, 8B, and 9B show conversion characteristic curves for enhancing the color contrast of the image histograms shown in FIGS. 6A, 7A, 8A, and 9A, respectively.

6C, 7C, 8C, and 9C illustrate image histograms in which the image histograms shown in FIGS. 6A, 7A, 8A, and 9A are converted according to the conversion characteristic curves of FIGS. 6B, 7B, 8B, and 9B in the display controller and output. Indicates.

* Description of the main parts of the drawings *

240: contrast enhancement unit 214: input level selector

242: shift calculator 243: adder

The present invention relates to a display controller, and more particularly to a display controller for performing a contrast extension function in hardware.

 Contrast Stretch is a method of artificially increasing the color dynamic range of an image so that rich colors can be expressed on display. The purpose of the display controller is to enrich the color of the input image and output it to the display device. However, due to user's carelessness or limitation of camera imaging device (for example, Charge Coupled Device (CCD) or CMOS Image Sensor (CIS) CMOS image, the display device may be distorted. The quality of the image output to the may be reduced. Therefore, new technologies are needed to solve this problem.

It is an object of the present invention to provide a display controller that performs a contrast enhancement operation using a shift operator.

Another object of the present invention is to provide a contrast enhancement method using a shift operation.

In order to achieve the above object, the present invention provides a display controller including a contrast enhancement unit. The display controller includes an image input unit for receiving image data from the outside and outputting the image data to the contrast enhancement unit; Special register to store characteristic curve constants (Cx [n], n = 0, 1, ..., i) and input level values (I [n], n = 0, 1, ..., i) ; The controller receives the characteristic curve constants Cx [n] and input level values I [n] from the special register to perform a contrast enhancement operation on the image data X from the image input unit. And a contrast enhancement unit for outputting output image data (Y).

인 연산을 수행한 결과값을 상기 쉬프트 연산부로부터의 결과값에 합산하여 상기 디스플레이 장치에 출력하는 가산부를 포함한다. 이 경우에, 상기 입력 레벨 선택부 선택된 입력 레벨값은 상기 영상 데이타(X)를 포함하는 입력 레벨 구간의 시작점이다.In one embodiment of the present invention, the contrast enhancement unit determines the value of n by determining the color range of the image data (X), and any one of the input level values from the special register according to the value of n. An input level selector for selecting a; The characteristic curve constants Cx [n], n = 0, 1, ..., i and the input level value I [n], n = 0, 1, ..., i from the special register; A shift calculator which receives the n value and the selected input level value from the input level selector and performs a shift operation to output a result value; And selecting characteristic curve constants corresponding to n-1 values of the characteristic curve constants Cx [n] from the special register according to the value of n;

And an adder configured to add the result value of the phosphorus operation to the result value from the shift calculator and output the sum value to the display device. In this case, the input level selector selected input level value is a starting point of an input level section including the image data (X).

The input level selector may include: an n value selector configured to determine an n value by determining a color range of the image data (X), and output the n value to an input level value selector; The input register receives the input level values I [n], n = 0, 1, ..., i from the special register, and selects one of the input level values according to the n value from the n value selector. And an input level value selector. In this case, the input level value selected by the input level value selector is a starting point of the input level section I [n] -I [n-1] including the image data X.

In one embodiment of the present invention, the shift operation unit may generate the characteristic curve constants Cx [n], n = 0, 1, ..., i and the input level values I [n] from the special register. , n = 0, 1, ..., i), and selecting values corresponding to the n value and the n-1 value among the characteristic curve constants according to the n value from the input level selector. at least one first log operator for performing a log ₂ (Cx [n]-Cx [n-1]) operation and outputting a result value; The input register receives the input level values I [n] from the special register, selects values corresponding to the n value and the n-1 value among the input level values according to the n value from the logarithm operator, and logs ₂ (I [n]-I [n-1]) a second log operator for performing an operation and outputting a result value; At least one first subtractor for outputting a result value by subtracting a result value from the second log operator from a result value from the first log operator; A second subtractor configured to subtract the output value I [n-1] of the input level selector from the input image data X from the video processor and output a result value; And at least one shift calculator for shifting the output value from the first subtractor and the output value from the second subtractor to output a result value.

연산을 수행하여 결과값을 출력하는 제 1 가산기; 상기 쉬프트 연산부로부터의 결과값과 상기 제 1 가산기로부터의 결과값을 합산하여 출력 영상 데이타를 상기 디스플레이 장치로 출력하는 제 2 가산기를 포함한다.In one embodiment of the present invention, the adder receives the characteristic curve constants Cx [n], n = 0, 1, 2, ..., i from the special register and from the shift operator. Select a value corresponding to the n-1 value of the characteristic curve constants according to the n value of,

A first adder for performing an operation and outputting a result value; And a second adder configured to add the result value from the shift calculator and the result value from the first adder to output output image data to the display device.

In one embodiment of the invention, the special register is set by a central processing unit.

In one embodiment of the present invention, the video data is input from a camera device or a digital multimedia broadcasting receiver.

In one embodiment of the present invention, the input level values I [n], n = 0, 1, 2, ..., i are I [n] -I [n-1] = 2 ⁿ , ( satisfies the condition n = 0, 1, 2, ..., i).

In one embodiment of the present invention, the characteristic curve constants Cx [n], n = 0, 1, 2, ..., i are Cx [n] -Cx [n-1] = 2 ⁿ , The condition (n = 0, 1, 2, ..., i) is satisfied.

In order to achieve the above object, the present invention provides a contrast extension method using a shift operation. The contrast expansion method may further include receiving image data X from an external source; Input level values I [n], n = 0, 1, 2, ..., i and characteristic curve constants Cx [n], n = 0, for performing contrast extension operations from a special register. Receiving 1, 2, ..., i); And determining a color range of the image data, and performing a contrast extension operation using a shift operation using the input level values and the characteristic curve constants input from the special register.

In one embodiment of the present invention, the input level values satisfy the condition that I [n] -I [n-1] = 2 ⁿ , (n = 0, 1, 2, ..., i).

In one embodiment of the present invention, the characteristic curve constants satisfy the condition that Cx [n] -Cx [n-1] = 2 ⁿ , (n = 0, 1, 2, ..., i).

Exemplary embodiments of the invention will be described in detail below on the basis of reference drawings.

(Example)

1 is a block diagram schematically illustrating an application processor according to the present invention. Referring to FIG. 1, the application processor 100 includes a camera interface 101, a digital multimedia broadcasting (DMB) decoder 102, a memory controller 103, and a display controller 200.                     

The camera interface 101 receives image data from the camera device 110 such as a digital camera module and transmits the image data to the display controller 200. The DMB decoder 102 receives DMB data from the digital multimedia broadcasting receiver 120, converts the DMB data into a digital signal, and outputs the digital signal to the memory controller 103. The memory controller 103 receives image data from the DMB decoder 102 or the display controller 200 and stores the image data in the memory 130 or outputs the image data stored in the memory 130 to the display controller 200. The display controller 200 is controlled by a central processing unit (CPU) and performs a contrast stretch operation on the image data input from the camera interface 101 or the memory controller. Output to 140. The contrast stretch operation is for converting image data having a narrow color range into image data having a full color range to display a clear image on the display device 140.

2 is a block diagram schematically illustrating the display controller of FIG. 1 in accordance with a preferred embodiment of the present invention. Referring to FIG. 2, the display controller 200 includes an image input unit 201, a contrast enhancer 240, a special register 250, and a timing controller 260. The image input unit 201 includes a dedicated direct memory access controller (DMA) 210, a first in first out (FIFO) buffer 220, and a video processor 230.

The special register 250 is controlled by a central processing unit (CPU). The special register 250 also stores an input level value I [n] and a characteristic curve constant Cx [n] necessary for the contrast enhancement operation of the contrast enhancement section.

The dedicated DMA controller 210 outputs the image data received from the memory controller 103 or the camera interface 101 to the FIFO buffer 220. The FIFO buffer 220 receives image data from the dedicated DMA controller 210 and temporarily outputs the image data to the video processor 230. The video processor 230 outputs the contrast enhancement unit 240 by performing a predetermined process such as converting the number of data bits per pixel of the image data according to the characteristics of the display device 140.

The contrast enhancer 240 performs a contrast extension operation on the image data having the color scale limited to the predetermined range, and converts the image data into the image data having the color scale of the entire range and outputs the image data to the display device 140.

The timing controller 260 generates a timing control signal suitable for the characteristics of the display apparatus 140 when the display controller 200 outputs image data to the display apparatus 140.

3 is a block diagram schematically illustrating the contrast reinforcement 240 of FIG. 2 in accordance with a preferred embodiment of the present invention. Referring to FIG. 3, the contrast enhancer 240 includes an input level selector 241, a shift calculator 242, and an adder 243.

The input level selector 241 receives input image data (hereinafter referred to as 'X') from the video processor 230 (refer to FIG. 2), classifies a color range of X values, and includes an input level section including X. I [n] -I [n-1]) and the n value required for the selection of the characteristic curve constant (Cx [n]). In addition, the input level values I [n], n = 0, 1, 2, ..., i are input from the special register 250 (FIG. 2), and I [n-1] values are obtained according to n values. Choose.

The shift operator 242 receives n values and I [n-1] values from the input level selector 241, and X values and characteristic curve constants Cx from the video processor 230 (FIG. 2) and the special register 250. Receive each [n]) and calculate constant values Cx [n] -Cx [n-1], I [n] -I [n-1], XI [n-1] for performing the shift operation. do. In addition, the shift operator 242 performs a shift operation on the constant values and outputs the result values Y1 'and Y2' to the adder 243.

The adder 243 receives the characteristic curve constant Cx [n] from the special register 250 (FIG. 2), adds it to the result values Y1 'and Y2' from the shift calculator 242, and outputs the output image data. Outputs a value (hereinafter referred to as 'Y').

Hereinafter, the contrast enhancer 240 uses the conversion characteristic curve (that is, the conversion curve constant Cx [n] received from the special register 250 and the input level value I [n]). ), A method of adjusting the color contrast of the image data will be described in detail.

A partial linear approximation method is used to perform a contrast extension operation using the conversion curve constant Cx [n] and the input level value I [n] representing the conversion characteristic curve. The partial linear approximation method is a method of obtaining an approximation value by using each linear function for a constant input level interval (ie, I [n] -I [n-1]).

4 is a graph showing a partial linear approximation curve according to a preferred embodiment of the present invention. Referring to FIG. 4, the X axis represents an input level I [n] value, and the Y axis represents an output level L [n] value. I [0] -I [i] represent 256 levels divided by 2 ⁿ (n = 0, 1, 2, ..., i), and in FIG. 4, i = 8. L [0] to L [8] are output level L [n] values corresponding to input level I [n]. The input level (I [n]) value is a selectable value, which the designer sets according to the characteristics of the device to be implemented during hardware configuration. As the input level section I [n] -I [n-1] is narrower, an approximation value with less distortion can be obtained.

The output level L [n] value must satisfy the following condition.

L [n] = C1 [n] + C2 [n] + ... + Cx [n]

Where C1 [n] -C1 [n-1] = 2 ⁿ , C2 [n] -C2 [n-1] = 2 ⁿ , and Cx [n] -Cx [n-1] = 2 ⁿ (n = 0, 1, 2, ..., 8).

In Equation 1, the characteristic curve constants (C1, C2, ..., Cx) are programmable values and can be set by software operation. The x value is set by the designer as well as the input level I [n] value. The larger the x value, the finer the contrast extension can be. The Cx values computed at the central processing unit (not shown) are stored in a special register 250 (see FIG. 2).

Assuming x = 2 (that is, Cx = C1, C2), the equation for calculating the Y value of the output level corresponding to the X value of the input level using the partial linear approximation method is as follows.

Y = [(L [n] -L [n-1]) / (I [n] -I [n-1]) * (X-I [n-1]) + L [n-1]

Here, when Equation 2 is developed using C1 and C2,

Y = [((C1 [n] + C2 [n])-(C1 [n-1] + C2 [n-1])) / (I [n] -I [n-1])] * (XI [n-1]) + L [n-1]

  = [((C1 [n] -C1 [n-1]) + (C2 [n] -C2 [n-1])) / (I [n] -I [n-1])] * (XI [ n-1]) + L [n-1]

 = [(C1 [n] -C1 [n-1]) / (I [n] -I [n-1]) + (C2 [n] -C2 [n-1]) / (I [n]- I [n-1])] * (XI [n-1]) + L [n-1]

Where [(C1 [n] -C1 [n-1]) / (I [n] -I [n-1])] = A, [(C2 [n] -C2 [n-1]) / ( If I [n] -I [n-1])] = B,

Y = (A + B) * (X-I [n-1]) + L [n-1]

  = A * (X-I [n-1]) + B * (X-I [n-1]) + L [n-1]

 to be.

In Equation 4, A and B (ie, [(C1 [n] -C1 [n-1]) / (I [n] -I [n-1])], [(C2 [n] -C2 [ n-1]) / (I [n] -I [n-1])]) become n-squared powers of 2, so the multiply operation for (XI [n-1]) can be processed as a shift operation. have. That is, the contrast extension operation may be performed by a shift operation without using a multiplier and a divider.

Assuming i = 5, the input level intervals I [n] -I [n-1] are all 32 (= 2 ⁸ ). In the case of x = 2, the output level L [n] is obtained from the C1 and C2 values stored in the special register 250, as shown in the following table.

L [n] C1 [n] C2 [n] Value L [0] 0 0 0 L [1] 8 0 8 L [2] 16 0 16 L [3] 32 0 32 L [4] 64 0 64 L [5] 128 32 160 L [6] 192 32 224 L [7] 224 16 240 L [8] 256 0 256

Referring to Table 1 and FIG. 4, assuming that X = 143, the output value Y is obtained from Equation 3 as follows.

Y = [((128 + 32)-(64 + 0)) / (160- (128)] * (X-128) + (64 + 0)

  = [((128-64) + (32-0)) / 32] * (X-128) +64

  = [(64/32)-(32/32)] * (X-128) +64 ------- (1)

= [(2 ¹ )-(2 ⁰ )] * (X-128) +64 ------- (2)

  = [(X-128) << 1]-[(X-128) << 0] + 64 ------- (3)

  = 30-185 + 64

  = 79

Changing the operation of the second ⁿ type of the divide operation (2) in equation (5) (1), it changed the form of 2 ⁿ operations in shift operation of (3).

Hereinafter, the contrast reinforcement unit in which Equation 3 is implemented in hardware will be described in detail.

5 is a block diagram illustrating in detail the contrast enhancement of FIG. 3 in accordance with a preferred embodiment of the present invention. Referring to FIG. 5, the input level selector 241 includes an n value selector 301 and an input level value determiner 302. The n value selector 301 receives an X value from the video processor 230 (FIG. 2), and discriminates the X value from the color range to determine the n value. The input level value selector 302 receives input level values I [n], n = 0, 1, 2, ..., i from the special register 250 (FIG. 2), and selects an n value selector. The value of I [n-1] is determined according to the value n from 301 and output to the shift calculator 242.

The shift operator 242 includes log operators 311, 312, and 313, subtractors 321, 322, and 323, and shift operators 331 and 332. The logarithm operator 311 sends characteristic curve constants C1 [n], n = 0, 1, 2, ..., i and n values from the special register 250 (FIG. 2) and the input level selector 241. Each operation is performed to perform a 'log ₂ (C1 [n] -C1 [n-1])' operation and output the result value a to the subtractor 322. The logarithm operator 312 receives input level values I [n] and n values from the special register 250 (FIG. 2) and the logarithm operator 312, respectively, and log ₂ (I [n] -I [n-). 1]) 'operation to output the result value b to the subtractors 322 and 323. The logarithm operator 313 inputs characteristic curve constants C2 [n], n = 0, 1, 2, ..., i and n values from special register 250 (FIG. 2) and logarithm operator 312, respectively. 'Log2 (C2 [n] -C2 [n-1])' is performed and the result value a 'is output to the subtractor 323.

The subtractor 321 receives the X value and the I [n-1] value from the video processor 230 (FIG. 2) and the input level value selector 302, respectively, and subtracts the resultant value Y0. The subtractor 322 subtracts the result value b of the log operator 312 from the result value a of the log operator 311 and outputs the result value Y1. The subtractor 323 outputs the result value Y2 by subtracting the result value b of the log operator 312 from the result value a 'by the log operator 313.

The shift operator 331 shifts the result value Y0 of the subtractor 321 and the result value Y1 of the subtractor 322 to output the output value Y1 ′. The shift operator 331 shifts the result value Y0 of the subtractor 321 and the result value Y2 of the shift operator 331, and outputs an output value Y2 ′.

인 연산을 수행하고 결과값(Y4)를 출력한다. 가산기(342)는 쉬프트 연산기(331)의 출력값(Y1') 및 쉬프트 연산기(332)의 출력값(Y2')을 가산하여 결과값(Y3)을 출력한다. 가산기(343)는 가산기(341)의 출력값(Y4) 및 가산기(342)의 출력값(Y3)을 가산하여 결과값(Y)을 출력한다. 즉, 출력 영상 데이타(Y)값이 디스플레이 장치(140, 도 2참조)로 출력된다. The adder 243 includes adders 341, 342, and 343. The adder 341 receives characteristic curve constants C1 [0] to C1 [n] and n values from the special register 250 (FIG. 2) and the logarithm operator 313, respectively.

Performs the in operation and outputs the result value (Y4). The adder 342 adds the output value Y1 'of the shift operator 331 and the output value Y2' of the shift operator 332 to output the result value Y3. The adder 343 adds the output value Y4 of the adder 341 and the output value Y3 of the adder 342 to output the result value Y. That is, the output image data Y value is output to the display device 140 (see FIG. 2).

6A, 7A, 8A, and 9A show histograms of images input to the display controller of FIG. 1, respectively. 6B, 7B, 8B, and 9B show conversion characteristic curves for enhancing the color contrast of the image histograms shown in FIGS. 6A, 7A, 8A, and 9A, respectively. 6C, 7C, 8C, and 9C show image histograms in which the image histograms shown in FIGS. 6A, 7A, 8A, and 9A are converted according to the conversion characteristic curves of FIGS. 6B, 7B, 8B, and 9B in the display controller and output. Indicates.

6A, 6B, and 6C, the input image histogram of FIG. 6A does not have a high level and a low level color scale, and only a middle level color scale. In order to extend the color scale of the input image shown in FIG. 4A to the full range, the characteristic curve constant Cx [n] and the input level value I [n] of the Transformation Characteristic Curve shown in FIG. 4B. Use As described above with reference to FIG. 5, the contrast enhancement unit 240 receives the characteristic curve constant Cx [n] and the input level value I [n] to convert the input image histogram of FIG. 4A. Then, an output image histogram with the full range of color scale of FIG. 4C is created.

Referring to FIGS. 7A, 7B, 7C, 8A, 8B, 8C, 9A, 9B, and 9, an intermediate level color scale is hardly present in the input image histogram of FIG. 7A, and the input image histogram of FIG. 8A is not present. Low level color scales are hardly present, and high level color scales are hardly present in the input image histogram of FIG. 9A. Similarly, in this case, the characteristic curve constant Cx [n] and the input level value I [n] are input from the contrast enhancing unit 240 (see FIG. 5), and the inputs of FIGS. 7A, 8A, and 9A are input. Converting the image histogram produces an output image histogram with a full range of color scales.

In addition, a contrast extension operation can be performed on the input image data using various conversion characteristic curves according to the user's setting.

Although the configuration and operation of the circuit according to the present invention are illustrated in accordance with the above description and the drawings, this is merely an example and various changes and modifications are possible without departing from the technical matters of the present invention.

As described above, according to the present invention, the contrast extension operation may be performed by hardware, so that a high quality image may be displayed in a portable device.

In addition, the hardware can be implemented as a simple circuit using a shift operator without using a multiplier or divider to reduce costs and reduce power consumption.

Claims (12)

An image input unit which receives image data from the outside and outputs the image data to a contrast enhancement unit; Special register to store characteristic curve constants (Cx [n], n = 0, 1, ..., i) and input level values (I [n], n = 0, 1, ..., i) ; And Receives characteristic curve constants Cx [n] and input level values I [n] from the special register, and performs a contrast enhancement operation on the image data X from the image input unit. A display controller comprising a contrast enhancement unit for outputting output image data (Y). The method of claim 1, The contrast reinforcement An input level selector which determines a value of n by determining a color range of the image data (X), and selects one of the input level values from the special register according to the value of n; The characteristic curve constants Cx [n], n = 0, 1, ..., i and the input level value I [n], n = 0, 1, ..., i from the special register; A shift calculator which receives the n value and the selected input level value from the input level selector and performs a shift operation to output a result value; And According to the value of n, characteristic curve constants corresponding to n-1 values of the characteristic curve constants Cx [n] are selected from the special register.

And an adder configured to add the result value of the in operation to the result value from the shift calculator and output the sum value to the display device. The input level selector The selected input level value is a start point of an input level section (I [n] -I [n-1]) including the image data (X). The method of claim 2, The input level selector An n value selector that determines an n value by determining a color range of the input image data X, and outputs the n value to an input level value selector; And Receiving the input level values I [n], n = 0, 1, ..., i from the special register, and selecting one of the input level values according to the n value from the n value selector; An input level value selector, And an input level value selected by the input level value selector is a starting point of an input level section (I [n] -I [n-1]) including the image data (X). The method of claim 2, The shift calculator The characteristic curve constants Cx [n], n = 0, 1, ..., i and the input level values I [n], n = 0, 1, ..., i from the special register; Is inputted, and selects values corresponding to the n value and the n-1 value among the characteristic curve constants according to the n value from the input level selector, and log ₂ (Cx [n]-Cx [n−). 1]) at least one first log operator for performing an operation and outputting a result value; The input register receives the input level values I [n] from the special register, selects values corresponding to the n value and the n-1 value among the input level values according to the n value from the logarithm operator, and logs ₂ A second log operator configured to perform a (I [n]-I [n-1]) operation and output a result value; At least one first subtractor for outputting a result value by subtracting a result value from the second log operator from a result value from the first log operator; A second subtractor configured to subtract the output value I [n-1] of the input level selector from the input image data X from the video processor and output a result value; And And at least one shift calculator configured to shift the output value from the first subtractor and the output value from the second subtractor to output a result value. In claim 2, The addition unit The characteristic curve constants Cx [n], n = 0, 1, 2,..., I) are input from the special register, and among the characteristic curve constants according to n values from the shift operator. select the value corresponding to n-1,

A first adder for performing an operation and outputting a result value; And a second adder configured to add a result value from the shift calculator and a result value from the first adder to output output image data to the display device. The method of claim 1, Wherein said special register is set by a central processing unit. The method of claim 6, And the image data is input from a camera device or a digital multimedia broadcasting receiver. The method of claim 2, The input level values I [n], n = 0, 1, 2, ..., i are I [n] -I [n-1] = 2 ⁿ , (n = 0, 1, 2,. Display controller that satisfies the condition The method of claim 8, The characteristic curve constants Cx [n], n = 0, 1, 2, ..., i are Cx [n] -Cx [n-1] = 2 ⁿ , (n = 0, 1, 2, Display controller that satisfies the condition ..., i). Receiving image data (X) from the outside; Input level values I [n], n = 0, 1, 2, ..., i and characteristic curve constants Cx [n], n = 0, for performing contrast extension operations from a special register. Receiving 1, 2, ..., i); And And determining a color range of the image data, and performing a contrast extension operation including a shift operation using the input level values and the characteristic curve constants input from the special register. The method of claim 10, And the input level values satisfy a condition that I [n] -I [n-1] = 2 ⁿ , (n = 0, 1, 2, ..., i). The method of claim 11, And the characteristic curve constants satisfy the condition that Cx [n] -Cx [n-1] = ²ⁿ , (n = 0, 1, 2, ..., i).

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