Integral x(t) (Not in Base Package)

Performs the discrete integration of the sampled signal X. Integral x(t) calculates a definite integral. The value of the output array at any value x is the area under the curve of the input array between 0 and x. Details  Example

	X is the sampled signal.
	initial condition is best described by the equation in the Details section for this VI. The default is 0.0.
	final condition is best described by the equation in the Details section for this VI. The default is 0.0.
	dt is the sampling interval and must be greater than zero. The default is 1.0. If dt is less than or equal to zero, the VI sets Integral X to an empty array and returns an error.
	Integral X is the sampled output sequence.
	error returns any error or warning from the VI. You can wire error to the Error Cluster From Error Code VI to convert the error code or warning into an error cluster.

Integral x(t) Details

The integral F(t) of a function f(t) is defined as

.

Let y represent the sampled output sequence Integral X. The Integral x(t) VI obtains the elements of y using

for i = 0, 1, 2, …, n – 1,

where n is the number of elements in X, x_–1 is specified by initial condition when i = 0, and x_n is specified by final condition when i = n – 1.

The initial condition and final condition minimize the overall error by increasing the accuracy at the boundaries, especially when the number of samples is small. Determining boundary conditions before the fact enhances accuracy.

Example

Refer to the Probability Density VI in the labview\examples\analysis\statxmpl.llb directory for an example of using the Integral x(t) VI.