Fast Fourier Transform
FFT |
Inverse FFT |
FFT-Object
This object calculates the fast fourier transform of a floating point
vector. On output it returns the real and imaginary part in
two different output vectors as well as
the norm (square root of square sum of imaginary and real part) of
the resulting complex vector. If a scale vector is given it is recalculated
to a frequency scale.
For minimizing of unwanted frequencies the so called
"Apodisation" can be enabled using the property dialog. The default value is
"Subtr. mean". If this is choosen before doing the fourier transform the
mean value of the input vector is calculated and subtracted from the input vector.
The second choice is "Parabel": This means that after subtracting the mean value
the whole input vector is multiplied with a negative parabolic function
which is zero at both ends of the input data vector and 1 in the middle
of the input data vector.
As a fast fourier transformation is used, the input vector normally must have
the length of a power of 2. For the case the input vector doesn't have
the right length, it is extended automatically to the next power of 2. Using the property dialog three methods
can be specified where to get the newly created elements from:
- Median
- The newly created elements are set to the mean value of the input data.
- Left
- The newly created elements are set to the value of the first element
of the input data vector.
- Right
- The newly created elements are set to the value of the last element
of the input data vector.
The frequency spectrum resolution, which is given by the length
of the input vector, can be increased by powers of 2, which can be
done via the property dialog. The increase is done by extending the
input vector appropriately.
Inverse FFT-Object
The inverse FFT performes an inverse fourier transform of the given
real and imaginary data vectors. This can for example be used
together with the forward transform for filtering in the frequency domain.
The lengths of input vectors must be a power of 2, as they are if the output
of the FFT object is used. FFT and following inverse FFT leads to the original
input vector if apodisation is switched of in the FFT object.
The Vimms User Manual