Advanced Digital Signal Processing

Basic Information

Lecturers:		Gerhard Schmidt (lecture) and Eric Elzenheimer (exercise)
Room:		KS2/Geb.F - SR-I
Language:		English
Target group:		Students in electrical engineering and computer engineering
Prerequisites:		Basic Knowlegde about signals and systems
Contents:		Students attending this lecture should be able to implement efficient and robust signal processing structures. Knowledge about moving from the analog to the digital domain and vice versa including the involved effects (and trap doors) should be acquired. Also differences (advantages and disadvantages) between time and frequency domain approaches should be learnt. Topic overview: Digital processing of continuous-time signals Efficient FIR structures DFT and FFT Digital filters (FIR filters/IIR filters) Multirate digital signal processing
References:		J. G. Proakis, D. G. Manolakis: Digital Signal Processing: Principles, Algorithms, and Applications, Prentice Hall, S. K. Mitra: Digital Signal Processing: A Computer-Based Approach, McGraw Hill Higher Education, 2000 A. V. Oppenheim, R. W. Schafer: Discrete-time signal processing, Prentice Hall, 1999, 2nd edition M. H. Hayes: Statistical Signal Processing and Modeling, John Wiley and Sons, 1996

News

There will be no lecture and no exercise tomorrow (15.01.2020) due to the bomb defusing!

Exam appointments have to be acquired offline this semester. The following dates are available:

10.02.2020 (morning + afternoon)
19.02.2020 (morning) -> fully booked
27.03.2020 (morning) -> fully booked

Appointments are available in room D-016. You may sit the exam individually or in groups of two.

Lecture Slides

		Slides of the lecture "Introduction" (Contents, literature, analog versus digital signal processing)
		Slides of the lecture "Digital processing of continuous-time signals" (Sampling, Quantization, AD and DA conversion)
		Slides of the lecture "Efficient FIR structures" (DFT and signal processing, FFT, DFT of real sequences)
		Slides of the lecture "DFT/FFT" (DFT and signal processing, FFT, DFT of real sequences)
		Slides of the lecture "Digital filters" (FIR filters, IIR filters, analysis and design)
		Slides of the lecture "Multi-rate digital signal processing" (Upsampling, downsampling, filter banks)

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.

main	additional
		Exercise 1: Sampling
		Exercise 2: Quantization
		Exercise 3: Discrete Fourier Transform (DFT) / Convolution
		Exercise 4: FFT / Radix-2-FFT
		Exercise 5: FFT / FFTs of Real and Complex Signals
		Exercise 6: Signal Flow Graph
		Exercise 7: Round-off Effects in Digital Filters
		Exercise 8: FIR Filter Design

Evaluation

Current evaluation

Completed evaluations

Matlab demos

Matlab file for the comparison of window sequences

%**************************************************************************
% Comparison of "standard" and a bit more "advanced" window functions
%**************************************************************************

%**************************************************************************
% Basis parameters
%**************************************************************************
N_win =   64;
N_dft = 1024*16;

%**************************************************************************
% Basic windows - rectangle window
%**************************************************************************
h_rec     = ones(N_win,1);
h_rec     = h_rec / sum(h_rec);

H_rec     = fft(h_rec,N_dft);
H_rec     = H_rec(1:N_dft/2+1);
H_rec_log = 20*log10(abs(H_rec)+eps);

%**************************************************************************
% Basic windows - Hann window
%**************************************************************************
h_han     = hann(N_win);
h_han     = h_han / sum(h_han);

H_han     = fft(h_han,N_dft);
H_han     = H_han(1:N_dft/2+1);
H_han_log = 20*log10(abs(H_han)+eps);

%**************************************************************************
% Basic windows - Hamming window
%**************************************************************************
h_ham     = hamming(N_win);
h_ham     = h_ham / sum(h_ham);

H_ham     = fft(h_ham,N_dft);
H_ham     = H_ham(1:N_dft/2+1);
H_ham_log = 20*log10(abs(H_ham)+eps);

%**************************************************************************
% Advanced windows - "Chebyshev" window
%**************************************************************************
h_che     = chebwin(N_win,10);
h_che     = h_che / sum(h_che);

H_che     = fft(h_che,N_dft);
H_che     = H_che(1:N_dft/2+1);
H_che_log = 20*log10(abs(H_che)+eps);

%**************************************************************************
% Advanced windows - "Prolate" window
%**************************************************************************
h_pro     = dpss(N_win,1.18);
h_pro     = h_pro / sum(h_pro);

H_pro     = fft(h_pro,N_dft);
H_pro     = H_pro(1:N_dft/2+1);
H_pro_log = 20*log10(abs(H_pro)+eps);

%**************************************************************************
% Show results
%**************************************************************************
fig = figure(1);
f = (0:N_dft/2)/N_dft*2;

plot(f,H_rec_log,'b', ...
     f,H_han_log,'r', ...
     f,H_ham_log,'k', ...
     f,H_che_log,'m', ...
     f,H_pro_log,'c', ...
     'LineWidth',2);
legend('Rectangle window', ...
       'Hann window', ...
       'Hamming window', ...
       'Chebyshev window', ...
       'Prolate spheroidal window')
grid on;
xlabel('Normalized frequency \(\Omega/\pi\)','interpreter','latex');
ylabel('dB')
ylim([-90 10])

Matlab file for the effects of quantization on filter design

%**************************************************************************
% Design parameters
%**************************************************************************
N   =  8;     % Filter order
f_c =  0.1;   % Normalized cut-off frequency (0 ... 1)
R_p =  0.5;   % Ripple in dB in passband
R_s = 80;     % Stopband attenuation in dB

%**************************************************************************
% Design of an elliptic lowpass filter
%**************************************************************************
[b,a] = ellip(N, R_p, R_s, f_c);

%**************************************************************************
% Show frequency response
%**************************************************************************
fig = figure(1);
set(fig,'Units','Normalized');
set(fig,'Position',[0.1 0.1 0.8 0.8]);
[H,Omega] = freqz(b,a,2048*4,'whole',2);
plot(Omega,20*log10(abs(H)+eps),'b','LineWidth',2);
grid on
axis([0 2 (-R_s -20) 20])
xlabel('Normalized frequency \Omega/\pi')
ylabel('dB')


%**************************************************************************
% Quantization
%**************************************************************************
B = 32; % Number of bits

a_max = max(abs(a));
b_max = max(abs(b));

a_q = round(a / a_max * 2^B) / 2^B * a_max;
b_q = round(b / b_max * 2^B) / 2^B * b_max;

%**************************************************************************
% Show frequency response of quantized filter
%**************************************************************************
[H_q,Omega] = freqz(b_q,a_q,2048*4,'whole',2);
hold on;
plot(Omega,20*log10(abs(H_q)+eps),'r','LineWidth',2);
hold off;
legend('Non-quantized',['Quantized with ',num2str(B),' bits'])

%**************************************************************************
% Show coefficients
%**************************************************************************
format long;
a
a_q
b
b_q

%**************************************************************************
% Transform to cascade of biquad filters
%**************************************************************************
[sos,g] = tf2sos(b,a);

[L,L_tmp] = size(sos);

sos_q = round(sos / max(max(abs(sos))) * 2^B) / 2^B * max(max(abs(sos)));
g_q   = round(g^(1/L) * 2^B) / 2^B;

H_bq_q = freqz(g_q*sos_q(1,1:3),sos_q(1,4:6),2048*4,'whole',2);
for k = 2:L
    H_bq_q = H_bq_q .* freqz(g_q*sos_q(k,1:3),sos_q(k,4:6),2048*4,'whole',2);
end;

%**************************************************************************
% Show frequency response of quantized biquad filters
%**************************************************************************
[H_q,Omega] = freqz(b_q,a_q,2048*4,'whole',2);
hold on;
plot(Omega,20*log10(abs(H_bq_q)+eps),'k','LineWidth',2);
hold off;
legend('Non-quantized',['Quantized with ',num2str(B),' bits'],...
       'Biquad structure (also qunatized)');

Previous Exams

		Exam of the summer term 2018				Corresponding solution
		Exam of the winter term 2017/2018				Corresponding solution
		Exam of the summer term 2017				Corresponding solution
		Exam of the winter term 2016/2017				Corresponding solution
		Exam of the summer term 2016				Corresponding solution
		Exam of the winter term 2015/2016				Corresponding solution
		Exam of the summer term 2015				Corresponding solution
		Exam of the winter term 2014/2015				Corresponding solution

Website News

27.01.2020: Contributions on nerve signal modeling and magnetic muscle measurement by OPMs availaible on IEEE (early access).

27.01.2020: Talk about magnetic shielding by Allard Schnabel (PTB, Berlin) takes place on Feb 13, 2020, 17 h, Room: C-SR 1.

26.01.2020: Some reflections on the year 2019 are online now.

17.12.2019: Journal paper on signal processing for breathing protection masks published.

23.11.2019: GaS price 2019 for Jannek Winter for an excellent bachelor topic on underwater communication systems.

15.11.2019: Our new MIMO-SONAR system (sponsored by DFG) is now ready for "take off".

20.10.2019: We had a very good retreat on the island of Sylt.

07.08.2019: Talk from Juan Rafael Orozco-Arroyave added.

11.07.2019: First free KiRAT version released - a game for Parkinson patients

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Lecture "Advanced Digital Signal Processing"