Lecture "Digital Signal Processing"

 

Basic Information
Lecturers: Gerhard Schmidt (lecture) and Owe Wisch (exercise)
Room: Building F - SR I (lecture and exercise)
E-mail: This email address is being protected from spambots. You need JavaScript enabled to view it.
Language: German
Target group: Students of Electrical Engineering and Computer Engineering in their
6th semester, also for students of Computer Science or Physics with appropriate knowledge of signals and systems.
Prerequisites: Mathematics for engineers I, II, III, Foundations in electrical engineering I, II
Contents:

Topic overview:

  • Signal digitization
    • analogue-to-digital and digital-to-analogue conversion
    • quantization characteristics, quantization noise
    • sample and hold
    • sampling of functions and sequences with/without phase shift, down- and up-sampling (decimation, interpolation)
  • Spectra (DFT and FFT)
    • convolution via DFT, fast DFT evaluation
    • radix-2/DIT FFT and alternatives
    • transformation of real sequences, "pruning" and "zoom" FFT
    • spectral analysis of infinite sequences (windowing, periodograms of random signals)
  • Digital filters
    • difference and state equations
    • equivalent realisations/transformed structures, diagonal form, transition matrix
    • realisation effects (input, arithmetic, and coefficient errors)
References:     Rabiner, L. R.; Schafer, R. W.: Digital Processing of Speech Signals, Prentice-Hall, 1978
    Kondoz, A. M.: Digital Speech-Coding for Low Bit Rate Communications System, John Wiley & Sons, 1994
    von Grünigen, Daniel: Digitale Signalverarbeitung, Hanser, 2014

 

News

No news available, yet.

 

Lecture slides

Link Content
Slides of the lecture "Introduction"
(Introduction, boundary conditions of the lecture)
Slides of the lecture "Signals"
(Signal types, AD and DA conversion, sample rate conversion)
Slides of the lecture "Spectra"
(DFT, FFT, fast convolution)
Slides of the lecture "Filter"
(Structures, state space desciption, realization)

 

Exercises

Please note that the questionnaires will be uploaded every week before the excercises, if you download them earlier, you won't get the most recent version.

Link Content
main additional  
Exercise 1: Sampling and Quantization
Exercise 2: Reconstruction
  Exercise 3: Sample Rate Conversion / Convolution
  Exercise 4: Discrete Fourier Transform (DFT) / Radix-2-FFT
  Exercise 5: FFTs of real and complex signals
Exercise 6: Windowing effects
  Exercise 7: Signal-flow graph
  Exercise 8: Filter - The effect of coefficient rounding in digital filters (Part 1)
  Exercise 9: Filter - The effect of coefficient rounding in digital filters (Part 2)
  Exercise 10: Signal-flow graph (mixed)

 

Formulary

A formulary can be found below:

Link Content
Formulary

 

 
Current evaluation Completed evaluations

 

Matlab demos

Filter design using linear prediction (click to enlarge and see the code) 

%**************************************************************************
% Parameter
%**************************************************************************
N   =   32;                 % Filterordnung
f_s = 16000;                % Abtastfrequenz

%**************************************************************************
% Stuetzstellen im Frequenz- und dB-Bereich
%**************************************************************************
f_supp        = [0 1000 2000 2900 3000 4000 4100 5000 6000 7000 f_s/2];
H_mag_dB_supp = [0   0     0  -30  -40  -40  -30  -20  -20  -20   -20];

%**************************************************************************
% Interpolation des Stuetzstellenvektors
%**************************************************************************
N_FFT        = 4086;
f_int        = 0:f_s/N_FFT:f_s/2;
H_mag_dB_int = interp1(f_supp, H_mag_dB_supp,f_int,'pchip');

%**************************************************************************
% Bestimmung LDS und AKF
%**************************************************************************
H_mag_int = 10.^(H_mag_dB_int/20);
S_hh      = H_mag_int.^2;
S_hh      = [S_hh, S_hh(end-1:-1:2)];
s_hh      = ifft(S_hh);

%**************************************************************************
% Filterentwurf
%**************************************************************************
[h_iir, pow] = levinson(s_hh,N);
h_fir        = sqrt(pow);

%**************************************************************************
% Analyse
%**************************************************************************
[H_res f_res] = freqz(h_fir, h_iir,N_FFT,f_s);

figure(1)
plot(f_supp, H_mag_dB_supp, 'ro', ...
     f_int, H_mag_dB_int,'b', ...
     f_res, 20*log10(abs(H_res)+eps),'k');
legend('Stuetzstellen','Kubische Interpolation','Entworfenes Filter')
grid on
ylabel('dB')
xlabel('Frequenz in Hz')

 

Current Oral Exams

Below is the list of students with their exam dates. If you do not have a date for the exam yet please use the oral exam booking system on this website. You can find the booking system here. All oral exams take place in the office of Prof. Gerhard Schmidt (Room D-013).

Date Time Students (matriculation numbers) Assessor
xx.xx.xxxx 11:00 h xxxxxxxxx Owe Wisch