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Derivative x(t) (G Dataflow)

Last Modified: March 15, 2017

Performs the discrete differentiation of the sampled signal.

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reset

A Boolean that specifies whether to reset the internal state of the node.

True Resets the internal state of the node.
False Does not reset the internal state of the node.

This input is available only if you wire a double-precision, floating-point number to x(t) or initial condition.

Default: False

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x(t)

Sampled signal from time 0 to n-1, where n is the number of elements in the sampled signal.

This input accepts a double-precision, floating-point number or a 1D array of double-precision, floating-point numbers.

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derivative method

Differentiation method.

This input is available only if you wire a 1D array of double-precision, floating-point number to x(t) or initial condition.

Name Description
2nd Order Central The derivative of the sampled signal is defined by the following equation:
y i = 1 2 d t ( x i + 1 x i 1 )
for i =0, 1, 2, ..., n-1

where

  • n is the number of samples
  • x-1 is the first element in the initial condition
  • xn is the first element in the final condition
4th Order Central The derivative of the sampled signal is defined by the following equation:
y i = 1 12 d t ( x i + 2 + 8 x i + 1 8 x i 1 + x i 2 )
for i =0, 1, 2, ..., n-1

where

  • n is the number of samples
  • x-2 and x-1 are the first and second elements in the initial condition
  • xn and xn+1 are the first and second elements in the final condition
Forward The derivative of the sampled signal is defined by the following equation:
y i = 1 d t ( x i + 1 x i )
for i =0, 1, 2, ..., n-1

where

  • n is the number of samples
  • xn is the first element in the final condition
Backward The derivative of the sampled signal is defined by the following equation:
y i = 1 d t ( x i x i 1 )
for i =0, 1, 2, ..., n-1

where

  • n is the number of samples
  • x-1 is the first element in the initial condition

Default: 2nd Order Central

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initial condition

Initial condition of the sampled signal in the differentiation calculation.

This input accepts a double-precision, floating-point number or a 1D array of double-precision, floating-point numbers.

This node uses the first element of the initial condition if the differentiation method is 2nd Order Central or Forward. This node uses the first two elements in the initial condition if the differentiation method is 4th Order Central.

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final condition

Final condition of the sampled signal in the differentiation calculation.

This input is available only if you wire a 1D array of double-precision, floating-point number to x(t) or initial condition.

This node uses the first element in the final condition if the differentiation method is 2nd Order Central or Forward. This node uses the first two elements if the differentiation method is 4th Order Central.

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error in

Error conditions that occur before this node runs.

The node responds to this input according to standard error behavior.

Standard Error Behavior

Many nodes provide an error in input and an error out output so that the node can respond to and communicate errors that occur while code is running. The value of error in specifies whether an error occurred before the node runs. Most nodes respond to values of error in in a standard, predictable way.

error in does not contain an error error in contains an error
If no error occurred before the node runs, the node begins execution normally.

If no error occurs while the node runs, it returns no error. If an error does occur while the node runs, it returns that error information as error out.

If an error occurred before the node runs, the node does not execute. Instead, it returns the error in value as error out.

Default: No error

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dt

Sampling interval.

Default: 1

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dx(t)/dt

Derivative of the sampled signal.

This output can return a double-precision, floating-point number or a 1D array of double-precision, floating-point numbers.

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error out

Error information.

The node produces this output according to standard error behavior.

Standard Error Behavior

Many nodes provide an error in input and an error out output so that the node can respond to and communicate errors that occur while code is running. The value of error in specifies whether an error occurred before the node runs. Most nodes respond to values of error in in a standard, predictable way.

error in does not contain an error error in contains an error
If no error occurred before the node runs, the node begins execution normally.

If no error occurs while the node runs, it returns no error. If an error does occur while the node runs, it returns that error information as error out.

If an error occurred before the node runs, the node does not execute. Instead, it returns the error in value as error out.

Algorithm for Calculating the Derivative

The differentiation f(t) of a function F(t) is defined by the following equation.

f ( t ) = d d t F ( t )

Let Y represent the sampled output sequence dx(t)/dt.

If derivative method is 2nd Order Central, Y is given by the following equation:

y i = 1 2 dt ( x i + 1 x i 1 )

for i = 0, 1, 2, ..., n - 1

where

  • n is the number of samples in x(t)
  • x-1 is the first element in initial condition
  • xn is the first element in final condition

If derivative method is 4th Order Central, Y is given by the following equation:

y i = 1 12 dt ( x i + 2 + 8 x i + 1 8 x i 1 + x i 2 )

for i = 0, 1, 2, ..., n - 1,

where

  • n is the number of samples in x(t)
  • x-2 and x-1 are the first and second elements in initial condition
  • xn and xn + 1 are the first and second elements in final condition

If derivative method is Forward, Y is given by the following equation:

y i = 1 dt ( x i + 1 x i )

for i = 0, 1, 2, ..., n - 1

where n is the number of samples in x(t) and xn is the first element in final condition.

If derivative method is Backward, Y is given by the following equation:

y i = 1 dt ( x i x i 1 )

for i = 0, 1, 2, ..., n - 1

where n is the number of samples in x(t) and x-1 is the first element in initial condition.

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Note  

If x(t) is a double-precision, floating-point number, Y is given by the above equation and x-1 is the initial condition.

The initial condition and final condition minimize the error at the boundaries.

Where This Node Can Run:

Desktop OS: Windows

FPGA: This product does not support FPGA devices


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