task7.1.txt

7.1: A short introduction to Digital Signal Processing

Question 1: What is the defining property of Gaussian noise?

The Gaussion noise is noise that follows a normal distribution and was named after German mathematician Karl Friedrich Gauss. 
This is why the normal distribution can also be referred to the Gaussian distribution. The Gaussian noise has a probability density function (pdf), 
the graph of which reflects a bell curve. Therefore the tails go much faster towards the value zero compared to other functions (e.g. decaying exponentials and 1/x). 

Question 2: What does a low-pass filter do in general?

A low-pass filter is used to pass or block frequencies. When frequencies are blocked or passed by the low-pass filter depends on the cutoff frequency. 
The low-pass filter allows signals with frequencies below the cut-off frequency to pass while signals with frequencies are blocked above the cut-off frequency. 

Ouestion 3: Is a moving average filter a low-pass or a high-pass filter? Why?

We've come to the assumption that a moving average filter is a low-pass filter. Steven W. Smith describes "the moving average is an exceptionally good smoothing filter (the action in the time domain), 
but an exceptionally bad low-pass filter (the action in the frequency domain)" (Smith, 1997, p. 280). 
Steven W. Smith cites the "slow roll-off and poor stopband attenuation" (Smith, 1997, p. 280) as reasons 
why the moving average is a bad low-pass filter.


Sources: 

Smith, S. W. (1997). The Scientist and Engineer’s Guide to Digital Signal Processing. California Technical Pub.
Wikipedia contributors. (2021, 17. Januar). Gaussian noise. Wikipedia. https://en.wikipedia.org/wiki/Gaussian_noise