# FINTEG

## Purpose:

Performs frequency domain integration.

## Syntax:

FINTEG(series, n,
fc)

series |
- |
A series or table, the data to integrate. |

n |
- |
Optional. An integer, the integration order.
Defaults to 1, first order integration. |

fc |
- |
Optional. A real, the high pass cutoff frequency.
Defaults to -1.0, no high
pass filtering. |

## Returns:

A series or array.

## Example:

W1: gnorm(1000, 1)

W2: integ(w1)

W3: finteg(w1)

W2 contains a standard time domain integration
of W1. W3 contains the integration as performed in the frequency domain.

## Example:

W1: gnorm(10000, 1/1000);setvunits("G")

W2: finteg(W1, 2, 5)

W1 contains data sampled at 1000 Hz. W2
high pass filters the data with a
cutoff frequency of 5 Hz and double integrates the result.

## Example:

n = 1000;

x = extract(linspace(0, 2*pi, n), 1, n-1);

W1: -sin(x + 2*cos(3*x)) * (1-6*sin(3*x))

W2: cos(x + 2*cos(3*x))

W3: finteg(W1)

W4: abs(W2 - W3)

W1 contains 999 samples of the periodic function:

W2 contains the analytic integral of W1

W3 computes the frequency domain integration and W4 displays the difference
between the analytic and calculated. In this case, the
difference is negligible.

## Remarks:

FINTEG performs integration in the frequency
domain using the following Fourier transform relation:

where X(f) is the Fourier transfrom of
the time domain series and f is the frequency range
of the transform.

X[1]
is set to 0 to de-mean the result. The integration calculation is transformed
back into the time domain.

This method performs a de-meaned integration
where the DC offsets of the input and output series are removed.

To view the result in the frequency domain,
try:

spectrum(finteg(s))

finteg(s, n) computes the nth order
integration with:

X(f) / (i 2πf )^{n}

If **fc**
>= 0, the input data is high passed filtered. The filter is implemented
by zeroing out the frequency domain components of the **series**
<= **fc**. See ZHPFILT
for more details.

See INTEG
for a time-domain implementation of integration using Simpson’s rule.

See FDERIV for
an implementation of a frequency domain derivative.

## See Also:

CUMTRAPZ

DERIV

FDERIV

FFT

INTEG

ZHPFILT