Digital Signal Processing Reference
In-Depth Information
FFT00
1
input
… 1
output
Uncomplete FOURIER-Transformation
Time
domain
Frequency
domain
Input
: Real signal in time domain
Output
: Amplitude- or Phasespectrum
FFT00
1
input
… 2
outputs
Complete FOURIER-Transformation
Time
domain
Frequency
domain
Input
: Real signal in time domain
Output 0
: Real part of frequency vector
Output 1
: Imaginary part of frequency
vector … in the Gaussian plane
FFT00
1
input
… 2
outputs
Complete Invers FFT (IFFT)
Frequency
domain
Time
domain
Input 0
: Real part of frequency vector
Input 1
: Imaginary part of frequency vector
Output 0
: Real signal in time domain
Illustration 94:
Selection of FFT functions
The FFT module allows various different variants. This is most strikingly apparent in the number of inputs
and outputs of this module (see top left). Up to now we have only made use of the "real FFT...". In this
case, too, there are various different alternatives (see centre).
As we shall see, the Symmetry Principle
SP
is exploited in the two forms of the "complex FFT..." in order
to achieve the "back and forwards" between the time and frequency domains (see bottom). For the path
from the time to the frequency domain (FT) we require the module with one input and two outputs and for
the reverse path (IFT) the module with two inputs and outputs. It is very important to select the setting
"FOURIER synthesis" because you want to put together the time signal from the sinusoidal oscillations of
the spectra.
