Python Blackbox Exercise

LTIs & Impulse Responses

Impulse responses (IR) can fully describe any LTI system. This relation can be used to decipher unknown systems, or black boxes. An LTI will respond to an impulse with the impulse response. We can thus send an impulse to a system, and measure the IR at the output. In the following exercise, three LTI systems will be analyzed in this way.

Get the Impulse Responses

1. Activate the DSP venv

   • This ensures all modules are available.

2. Download the module systems.py and place it in your python working directory.

   • https://ringbuffer.org/download/ringbuffer_data/DSP/LTI/systems.py

3. Load the module

import systems

• The module has three functions, that can be accessed with the dot-syntax:

systems.system1()
systems.system2()
systems.system3()

- Each function represents an LTI system with an individual impulse response and takes one single argument.

4. Create in Impulse x[n]

   • The impulse needs to be a list of integers or a numpy array (even if it is only one element).

   • The amplitude of the impulse is 1.

5. Create an impulse response for each of the three systems.

Evaluate the Results

1. Plot the impulse responses with matplotlib.

2. Describe each system in your own words.