# Digital Signal Processing

• Instructor:  Prof. Dr.-Ing. Werner Henkel

The course is actually a combination of standard DSP contents and applications in digital communications. The standard DSP contents are linear transforms, Sampling theorem, quantization, networks with delay elements difference equations, filter structures (implementations in C/Matlab), z-transform, frequency-domain characterization (Parseval), DFT, window functions, frequency response of frequency-selective filters, fast convolution (overlap save, overlap add), power spectral density, periodogram, design of poles and zeros, least squares identification and prediction (LPC, Toeplitz algorithms), design of digital filters (short introduction to wave digital filters), sampling rate conversion, subband coding, FFT algorithms, quadrature mirror filters, filter banks, two-dimensional transforms, discrete cosine transform, (wavelets) and an introduction to video coding. The communications part is essentially an introduction to digital communications with channel properties, passband and complex baseband description, PAM, QAM, matched filter, whitened matched filter, equalizer structures and its adaptation with LMS and ZF. An introduction to multicarrier transmission (OFDM, DMT) and the relation to filter banks will be given, too. OFDM and DMT are the transmission methods used in every current wireless and wireline system (LTE, WLAN, DSL, DVB-t,…). Overall, the course provides a complete coverage of digital signal processing and the essential basics of digital communications. The course is hence mandatory for ECE and a must for other students with a focus towards signal processing, video and audio, and communications.

• Overview over linear transforms
• Sampling theorem
• Quantization
• Networks with delay elements
• Difference equations
• Filter structures I, Implementations in C/Matlab
• Z-transforms in some more detail
• Frequency-domain characterization (Parseval’s relation)
• DFT, window functions
• Frequency response of frequency-selective filters
• DFT methods (overlap save, overlap add)
• Power density spectrum, periodogram
• Design of poles and zeros
• Least squares identification and prediction (LPC, Toeplitz algorithms)
• Filter structures II
• Design of digital filters
• Short introduction to wave digital filters
• Sampling rate conversion
• FFT algorithms
• Filter banks
• Adaptive filters under equalization in the communications part
• Two-dimensional transforms, discrete cosine transform
• Some aspects of audio and video coding
• Wavelets

Digital Signal Processing in Communications

• Channel properties
• Passband and equivalent baseband description
• PAM
• QAM
• Equalizer structures, adaptation with zero forcing and least mean squares
• Multicarrier transmission, wavelets, filter banks

[Detailed syllabus]