Sascha Spors, Professorship Signal Theory and Digital Signal Processing, Institute of Communications Engineering (INT), Faculty of Computer Science and Electrical Engineering (IEF), University of Rostock, Germany
Winter Semester 2022/23 (Master Course #24505)
Feel free to contact lecturer frank.schultz@uni-rostock.de
What we should learn in the exercise 1 and 2 is
The detailed DFT Tutorial is worth to comprehend. It contains useful information and very detailed calculus on the items above. Furthermore, five exercise tasks including their solutions are given in the tutorial, that might serve as first insight into DFT used for spectral analysis. These exercises are also covered in the dedicated Exercises of DFT Tutorial notebook.
DFT as matrix operation is again covered in DFT Fundamentals, we should not miss this viewpoint! It is also programmed in the DFT / DTFT of Complex Exponential notebook.
Then, there are more Jupyter notebooks that cover stuff from the DFT Tutorial in a more playground matter with some reference Python code. So if we need a break from all the equations in the pdf file, we might play around with these:
After studying we should be able to answer
-the matrix versions of it with an idea what the Fourier matrix is and how it is set up
At this stage it is also worth to think about two fundamental applications heavily used in DSP
The discussion on the characteristics of the frequency response of either $H(\Omega)$ or $W(\Omega)$ and how these act on the DTFT spectrum of the input signal $x[k]$ is a vital part on DSP. So, when considering finite length signals for $h[k]$ and $w[k]$, we can use the same concepts and principles for designing such signals only using different design goals. A FIR filter application probably needs a different spectrum than an optimized window application.
So, what role plays the DFT here? We should recall that for finite length signals all spectrum information is stored in the DFT coefficients. The DTFT can then be interpolated from the DFT coefficients, see DFT Interpolation to DTFT. So, by knowing the DFT of an FIR filter, we basically know the whole frequency response of this FIR system and we can tell which frequencies in the input signal are gained/attenuated in the convolution process $y[k] = x[k] \ast h[k]$. And, by knowing the DFT of a window, we know the frequency response of the window and are able to estimate the smoothing effect that happens in the convolution $Y(\Omega) = \frac{1}{2\pi} X(\Omega) \circledast_{2\pi} W(\Omega)$. That's why we should learn about DFT in very detail. We could check Pole/Zero Plot and Frequency Response of Windows.
We should get an idea on
We discuss how LTI systems act on random input signals.
We should get familiar with the following aspects
In this exercise we will have a detailed look to the concept of amplitude quantization.
We should get familiar with
We should listen to the audio examples for the dithering exercise. Especially the case when the sine amplitude is below the quantization step is interesting, as one would assume that this sine signal cannot be perceived at all. Please, DO NOT HARM YOUR EARS! Start with low playback level.
In this exercise we deal with FIR filters, more precisely with non-recursive LTI systems.
We should get familiar with
In this exercise we deal with recursive systems, more precise with recursive systems that exhibit an infinite impulse response, which we call IIR filter (most textbooks do this as well).
We should get familiar with
The following list contains established and often cited textbooks on DSP:
A.V. Oppenheim, R.W. Schafer (2010): "Discrete-Time Signal Processing.", Pearson, 3rd ed. Also available in German.
L.R. Rabiner, B. Gold (1975): "Theory And Application Of Digital Signal Processing.", Pearson.
S.D. Stearns, D.R. Hush (1990): "Digital Signal Analysis.", Prentice Hall. Also available in German.
J.G. Proakis, D.G. Manolakis (1996): "Digital Signal Processing.", Prentice Hall, 3rd ed.
R.G. Lyons (2011): "Understanding Digital Signal Processing.", Prentice Hall, 3rd ed.
L.R. Rabiner, R.W. Schafer (1978): "Digital Processing of Speech Signals.", Prentice Hall.
E.C. Ifeachor, B. W. Jervis (2002): "Digital Signal Processing.", Prentice Hall, 2nd ed.
Y. Stein (2000): "Digital Signal Processing.", Wiley.
S. J. Orfanidis (2010): "Introduction to Signal Processing.", Pearson.
B. Girod, R. Rabenstein, A. Stenger (2001): "Signals and Systems." Wiley. Also available as a 4th ed. in German.
Besides direct translations of English textbooks, there exist several established German textbooks by:
If one looks for more practical approaches, the books in German language by
might be considered.
The following video/html resources might be helpful as well:
Finally, although not traditionally related to DSP, it is recommended to have a look at
since discrete signals can be interpreted as vectors, and multiple signals as vector spaces, that might form a vector base... So, a lot of concepts of linear algebra appear to be very useful in DSP.
The notebooks are provided as Open Educational Resources. Feel free to use the notebooks for your own purposes. The text is licensed under Creative Commons Attribution 4.0, the code of the IPython examples under the MIT license. Please attribute the work as follows: Frank Schultz, Digital Signal Processing - A Tutorial Featuring Computational Examples with the URL https://github.com/spatialaudio/digital-signal-processing-exercises