Digital filters - Signals, Processes, and Systems - page 313

Pulse Complex FFT LP filter R eal/Imagin. C om plex IFFT

T ime domain

Time domain

Frequency domain

0, 5
0, 4
0, 3
0, 2
0, 1
0, 0
-0,1
-0,2
-0,3
-0,4
-0,5
0, 3
0, 2
0, 1
0, 0
-0,1
-0,2
-0,3
0, 3
0, 2
0, 1
0, 0
-0,1
-0,2
-0,3
0, 3
0, 2
0, 1
0, 0
-0,1
-0,2
-0,3

0,004
0,003
0,002
0,001
0,000
-0,001
-0,002
-0,003
-0,004
0,100
0,050
0,000
-0,050
-0,100
-0,150
0,004
0,003
0,002
0,001
0,000
-0,001
-0,002
-0,003
-0,004
0,100
0,050
0,000
-0,050
-0,100
-0,150
0,004
0,003
0,002
0,001
0,000
-0,001
-0,002
-0,003
-0,004
0,100
0,050
0,000
-0,050
-0,100
-0,150
0,004
0,003
0,002
0,001
0,000
-0,001
-0,002
-0,003
-0,004
0,100
0,050
0,000
-0,050
-0,100
-0,150

Real part

Imaginary part

Sawtooth of 1 Hz

Real part

LP filter 10 Hz
10 frequencies

Imaginary part

Real part

LP filter 18 Hz
18 frequencies

Imaginary part

Real part

LP filter 24 Hz
24 frequencies

Imaginary part

0 50 150 250 350 450 550 650 750 850 950 5 10 15 20 25 30 35 40 45 50 55 60

ms

Hz

Illustration 207: FFT-filtering of a sawtooth signal

This shows clearly how simply FFT filters work in principle: the frequency range which is of interest is
literally cut out using the “cutout” module. After re-transformation into the time domain by means of an
IFFT the filtered signal appears.

• It is unsuitable for long lasting signals. As shown in Chapter 3 under the heading
“Frequency measurements in the case of non-periodic signals” and in Chapter 4
“Language as an information carrier” these would have to be cut up into segments
using an appropriate window, then arranged with overlapping and filtered. This
would be too error-prone and compute-bound for nothing more than filtering.

An (apparent) inconsistency of the FFT filter should be explained. In Illustration 206 the
filter appears as “non-causal” as a result of the representation. The output signal is present
on the screen before the input signal arrives at the input!