Digital filters - Signals, Processes, and Systems - page 312

In a physical sense this means that two pieces of information are essential for any
frequency and any sinusoidal signal: i.e. amplitude and phase.

Subsequently the frequencies are “cut out” using the cutout module (i.e. are set at zero)
which are not to be allowed to pass. The same values must be set on both channels (real
and imaginary).

Note:

In the cutout module you will find the values 0 to 8192 preset under “data of
sample”. 8192 gives the largest possible data block length for FFT processing. How
can the desired frequency range be set? Look carefully at Illustration 119, for
example. If you select the sampling frequency equal to the block length (e.g. 1024)
the number range - e.g. from 0 to 40 - gives the conducting state region of the filter
in Hz. In this case the time length of the data block is exactly 1 second and this is
the most straightforward state of affairs. Otherwise you have to be extremely care-
ful. If you select a frequency above the area allowed by the Sampling Principle (in
this example that would be above 512 Hz!) you may find the position of the filter at
a completely different point in the frequency range. Try this out using the circuit in
Illustration 206.

Afterwards you go back into the time domain via an IFFT (inverse FFT). Here “complex
FFT of a complex signal” should be selected from the menu options. In addition, you must
also indicate that you wish to go back into the time domain. Finally, the signal is to be
made up of the frequencies which have been allowed to pass through (sinusoidal oscilla-
tions), that is a FOURIER Synthesis is to be carried out. The filtered signal is only present
in its correct form at each upper output.

Advantages of FFT filters:

• How well an FFT filter of this kind works can be seen from Illustration 120. Individual
frequences are filtered out of a noise signal, the bandwidth is 1 Hz with a date block
length of 1s and represents the absolute physical limit resulting from the Uncertainty
Principle UP . The edge steepness of the filter thus depends on the length of the signal
or the data block.

• A further advantage is the absolute phase linearity , i.e the form or the symmetry of
the signal in the time domain is not changed. Compare in this context the properties
of analog filters in Illustration 141 with those of the FFT filter in Illustration 206

Disadvantages of FFT filters

• The large amount of calculation required for the FFT and IFFT. FFT means “Fast
FOURIER Transformation”. The algorithm was published in 1965 and is much faster
than the ordinary DFT (Digital FOURIER Transformation) by the use of the Symme-
try Principle. FFT and - in addition - IFFT are neverthless still compute-bound in
comparison to other signalling processes.