1. The following state space model is given.
With
a) Calculate the eigenvalues of the matrix A.
b) Graph the impulse and step responses of the system.
2. Calculate the convolution products Place You graphically represent the two signals as well as the results of the convolution products. (Note:
Use the numpy.convolve () function.)
3. A random noise signal should be sampled by a rational factor M / L.
In order to achieve this, an interpolation must first be carried out by means of upward sampling and low pass filtering. You can then scan the target signal down
can be achieved.
a) First create a discrete random noise signal x [n]. The spectrum
of the signal should be band-limited
. Set the signal in
Time and frequency domains graphically. (Note: Use the functions
numpy.random.randomn (), scipy.signal.ellip. (15,0.6,60, Ω / π)
and signal.lfilter ())
b) Now create the interpolation. To do this, first scan the length L = 5 upwards (note: zero padding) and then filter the signal with a low pass (note: use the function
scipy.signal.lfilter ()). Set this intermediate signal v [k] in the time and
Frequency range graphically.
c) Finally, perform a downward scan of length M = 3. Graph this target signal y [m] in the time and frequency domains. (Note: Use
The function scipy.signal.decimate ())
Figure 5.1: Representation of the original, intermediate(zwischen-) and target signal (zeitsignal)in the time(zeit-) and frequency domains