Digital Signal Processing Reference
In-Depth Information
FFT
Cut out
IFFT
Sawtooth
T ime domain
Sampling
2,0
Time domain
1,5
Sample frequency = 32 Hz
See the plot of the sum
of the first 16 frequencys
1,0
0,5
0,0
-0,5
A sinusoidal signal of 16 Hz
changes in rythm of a sample
frequency of 32 Hz!
-1,0
-1,5
-2,0
0.25
0.50
0.75
1.0
s
Illustration 191:
Block length, sampling frequency and bandwidth of the spectrum displayed
Using a rather ingenious circuit it will be indicated why in Illustration 190 with a sampling frequency of
32 Hz the highest frequency of the spectrum displayed is 16 Hz. For this purpose the sawtooth is connected
with an almost ideal lowpass filter of 16 Hz in the circuit diagram at the top. The highest frequency 16 Hz
- as in the spectrum - is at the output of the lowpass.
The sum of the first 16 frequencies has the input signal superimposed (sawtooth 1 Hz) and the 32 sampling
values of this sawtooth. It can be clearly seen that the sawtooth signal of 16 Hz is able to model the shor-
test time change in the sampled signal of 1/32 s. To put it another way, because a sine changes twice per
period, a sine of 16 Hz changes its polarity 32 times per second.
This immediately suggests the following questions:
• Can the original real signal be reconstituted retrospectively from the bits and pieces
of the digital signal?
• Is it contained exactly in the digital signal or is the information only partly present?
