Using the Fourier Analysis
The Fourier Analysis is availabe from the View
menu in the PLECS scope window.
The Fourier analysis window shows the magnitude of the Fourier coefficients for
the given number of harmonics. The analysis range for the Fourier analysis is
determined by the cursors in the scope window. By default it is assumed that the
cursor range covers exactly one period of the base frequency, though this can be
changed in the Fourier parameters. Note that aliasing effects will be visible if
the cursor time range is not an exact integer multiple of the inverse base
frequency.
Calculation Parameters
-
Base Freqency
- The analysis range
is always bound to the cursor range in the
PLECS scope. In general it consists of
periods of the base frequency, i.e.
.
A click on the frequency input field f: in the window title bar opens the Base
Frequency dialog. Two modes are available to set the base frequency: by freely
positioning the cursors in the PLECS scope or by entering the numerical values
directly in the Base Frequency dialog.
The first mode is activated by selecting Calculate from cursor range in
the Base Frequency dialog. In this mode it is assumed that the cursor range
covers a single base period. The two cursors can be positioned independently
from each other and should be set as exactly as possible to the start and end
of a single base period. The corresponding base frequency is displayed in the
window toolbar.
If the base frequency is known beforehand it can be entered directly by
choosing Set base frequency. In this mode the scope cursors are locked to
the number of base periods. Moving the cursors still allows you to select the
analysis range without changing the base frequency.
-
Number of Fourier Coefficients
- The number of Fourier Coefficients which are
calculated can be changed in the input field N: in the window title bar.
Display Parameters ![[Picture]](property-blue.png)
-
Display frequency axis
- The frequency axis is either shown underneath each plot
or underneath the last plot only.
-
Frequency axis label
- The text is shown below the frequency axis.
-
Scaling
- The Fourier analysis window offers three options to scale the Fourier
coefficients: Absolute displays the absolute value of each coefficient. Relative,
linear scales all coefficients such that the coefficient of the base frequency is 1.
When set to Relative, logarithmic (dB) the coefficients are displayed on a
logarithmic scale in Decibels relative to the coefficient of the base frequency.
-
Table data
- The table below the Fourier plots shows the calculated Fourier
coefficients. The values can be displayed without phase (Magnitude only),
with phase values in radians (Magnitude, phase (rad)) or with phase values
in degree (Magnitude, phase (degree)).
The following items can be set for each plot independently:
-
Title
- The name which is displayed above the plot.
-
Axis label
- The axis label is displayed on the left of the y-axis.
-
Y-limits
- The initial lower and upper bound of the y-axis. If set to auto, the
y-axis is automatically scaled such that all data is visible.
Signal Type
As in the scope window the signal type in the Fourier analysis window can be
changed by clicking the small icon next to the signal name in the data view window.
Available types are bars, stems and continuous. By default the signals are displayed
as bars. Changing the signal type for one signal will affect all signals in the same
plot.
Zoom, Export and Print
The Fourier analysis window offers the same zoom, export and print operations as
the PLECS scope. See section Using the PLECS Scope for details.
Calculation of the Fourier coefficients
The following approximation is made to calculate the Fourier coefficients of a signal
with variable sampling intervals
:

where

A piecewise linear approximation is used for continuous signals. Compared to a
fast Fourier transformation (FFT) the above approach also works for signals which
are sampled with a variable sample rate. The accuracy of this approximation highly
depends on the simulation step size,
: A smaller simulation step size yields
more accurate results.