Tools | Integrate

Performs Integration on all (or selected) M#s in a Data Block.

All integration is done in the frequency domain.
Time domain waveforms are transformed to the frequency domain, integrated, and transformed back to the time domain.

Frequency domain measurement are integrated by using the following frequency domain operation,

where:

i = 1 to Block Size

Xi(2pf i) = linear spectrum (FFT FFT is an acronym for Fast Fourier Transform. The FFT algorithm transforms a uniformly sampled time domain signal into its corresponding Digital Fourier Transform (DFT). The Inverse FFT transforms the DFT back into its original time domain signal. The FFT in ME'scope transfroms any number of samples, not just powers of 2.) of the signal for the ith sample.

2pf i = frequency of the ith sample (radians/second).

f i = frequency of the ith sample (Hz).

j - denotes the imaginary operator.

Time domain integration of a signal is equivalent to dividing each sample of its frequency spectrum Xi(2pf i) by its sampled frequency 2pf i.

Integration Errors Due To DC Offset

If a time domain waveform has any DC Offset (or bias) in it, integration of the DC Offset will result in a ramp function.

To minimize errors due to any DC Offset, Tools | Remove DC is automatically executed before integration is performed,

Integration Errors Due To Leakage

The FFT assumes that the signals to be transforming are periodic, or completely contained within their sampling window.  The sampling window is the range of samples in each measurement.

If a time domain waveform is non-periodic, or not completely contained within its sampling window, smearing (called leakage) of its spectrum will occur when it is transformed to the frequency domain.

If a frequency domain waveform is non-periodic, or not completely contained within its sampling window, leakage (called wrap around error) of its time waveform will occur when it is transformed to the time domain.

Removing Lower Frequencies Before Integration

Integration amplifies the lower frequencies in a signal.  To reduce the harmful effects of all non-essential lower frequencies in a signal, they should be removed from its spectrum before integrating it.

• Execute Transform | FFT to transform time domain waveforms to the frequency domain

• Set up the Band cursor to include all non-essential low frequencies

• Execute Transform | Window M#s and apply the Notch window to remove the low frequencies (zero the measurement values)

• Execute Tools| Integrate to integrate the M#s

• Execute Transform | Inverse FFT to transform the integrated signals back to the time domain