# 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.

CUMTRAPZ

DERIV

FDERIV

FFT

INTEG

ZHPFILT