1. a)The system is given
Investigate the stability through a simulation. Which system is stable?
b) The system is given
Investigate the stability with the specific input signal
What is your conclusion regarding the stability of the system?
2. Barker Code
Tab6.1 Barker codes bn [k] of length 2 to 13
The transmission of digital data takes place in blocks. Suppose we want 8 bits wide
Transfer words ak as a serial bit stream. To do this, these words are strung together.
The receiver has to reconstruct the words from this bit stream again. To do this must
be known where the word boundaries lie. To solve this task, e.g. a synchronization sequence is sent parallel to the data. Such sequences are e.g. those in
Barker codes bn [k] shown in Table 6.1. n denotes the length of the sequence.
To detect the sequences, a so-called matched filter with the impulse response g [k]
used.
a) Generate a signal that contains 5 Barker codes of length 7 and set
the signal. Generate a second signal that between the barker codes of the
first signal contains 30 randomly selected bits and represent the signal.
b) The matched filter for the Barker codes is defined as:
Plot the impulse response g [k] for n = 7. If the filter is acausal, do
Make it causal by shifting it and present its impulse response.
c) Filter the two generated signals with the causal matched filter. How leave
determine the word boundaries from the filter output? Write a function
the times of the word limits are determined from the data stream of the filter output
and outputs.
3. a) Determine the impulse and step response to the system y [k].
b) Plot the excitation x [k] and the reaction of the system y [k].