Lecture "Advanced Digital Signal Processing"
Basic Information
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Lecture overview | |||
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| Lecturers: | Gerhard Schmidt (lecture) and Owe Wisch (exercise) | |||
| Room: | Online (via zoom) | |||
| 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:
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| 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 |
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News
The lecture will be conducted as a live zoom meeting, sceduled every Monday, 08:15 h. The first lecture starts on November, 2nd. Please register for the lecture via the OLAT platform. After registration you will get a link for accessing the lecture via zoom.
Lecture Slides
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Link | Content | ||
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Slides of the lecture "Introduction" (Contents, literature, analog versus digital signal processing) |
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Slides of the lecture "Digital processing of continuous-time signals" (Sampling, Quantization, AD and DA conversion) |
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Slides of the lecture "Efficient FIR structures" (DFT and signal processing, FFT, DFT of real sequences) |
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Slides of the lecture "DFT/FFT" (DFT and signal processing, FFT, DFT of real sequences) |
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Slides of the lecture "Digital filters" (FIR filters, IIR filters, analysis and design) |
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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.
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Link | Content | ||
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Exercise 1: Sampling | |||
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Exercise 2: Quantization | |||
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Exercise 3: Discrete Fourier Transform (DFT) / Convolution | |||
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Exercise 4: FFT / Radix-2-FFT | |||
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Exercise 5: FFT / FFTs of Real and Complex Signals | |||
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Exercise 6: Signal Flow Graph | |||
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Exercise 7: Round-off Effects in Digital Filters | |||
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Exercise 8: FIR Filter Design |
Evaluation
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Link | Content | Link | Content | ||||
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Current evaluation | |
Completed evaluations |
Matlab demos
Matlab file for the comparison of window sequences (click to expand)
%**************************************************************************
% 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 (click to expand)
%**************************************************************************
% 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)');
Exams
It's an oral exam. Please register for the exam via our exam booking system.
