EECS 451 W04 Outline - Jeff Fessler This list is based on what I covered in F98. With luck, this list will be updated regularly over the course of the semester. Course Text: Proakis and Manolakis, 3rd edition Lecture# (x.x indicate sections from text) 1 Course Policies 1.1 terms analog vs digital 1.2 classification of signals 1.3 frequency 1.4 a/d, sampling, quantization, d/a (brief) 2.1 discrete-time signals representations energy, power, periodicity, symmetry 2.6 cross-correlation, auto-correlation. skip: time-delay estimation 2 2.2 discrete-time systems input-ouput relationship, block diagram time properties: causality, memory, time invariance amplitude properties: BIBO stability, invertibility, linearity 2.3 analysis convolution 3 convolution properties LTI properties in terms of impulse response causality, invertibility, memory, stability FIR vs IIR 4 2.4 difference equations motivation for IIR recursive implementation 2.5 implementation applications (not in notes): image edge detection, time-delay estimation 5 3.1 Z Transform examples ROC properties 6 3.2 Z transform properties convolution, correlation, examples 7 more properties 3.3 rational z-transforms pole zero plots signal properties for real poles 8 signal properties for complex pole pair system function for LTI by const. coef. diff. eq. all zero, all pole, pole-zero 9 3.4 inversion of z transform only mention contour integration series expansion example PFE 10 PFE example (impulse response) 4.5.7 digital sine-wave generator (2nd-order block diagram) 3.6.1 characterizing response of rational LTI systems natural response, forced response 3.6.3 transient and steady-state response 11 3.6.4 stability 3.6.6 poles on unit circle 3.6.5 pole-zero cancellations 12 3.6.7 schur-cohn stability test (mention only) Ch 4. Frequency Analysis complex exponentials are eigenfunctions family of Fourier transforms Fourier series / power spectral density 13 4.2.1 DTFS, properties 4.4.3 periodic signals through LTI 14 DTFT Inverse DTFT 2pi periodicity DTFT vs Z Convergence of DTFT Gibbs phenomenon 4.2.5 energy density spectrum Parseval's relation for DTFT 4.2.8 DTFT for periodic signals 15 exam1 16 4.3 DTFT properties symmetry properties DTFT properties continued convolution property 4.2.12 dualities (Read!) 17 4.4 Frequency-domain char. of LTI systems 4.5 LTI systems as filters 4.5.x ideal filters simple "treble boost" example skip: 60Hz notch filter example (done in 206) 4.4.6 computing freq. response from pole-zero plot 18 (Yendiki) 4.2.9 sampling theorem relations between DTFT and FT etc. aliasing bandlimited signals sinc reconstruction 19 (Yendiki) interpolation and applications 20 phase response from pole-zero plot steady state, transient response (no, done already) linear phase, group delay 4.5.2 simple lowpass filters highpass from lowpass digital resonators (bandpass) (brief) 21 4.5.6 all pass filters 4.6 inverse filters, deconvolution minimum phase 4.5.7 generating sinusoids (no, done earlier) 22 linear phase summary of DTFS, Z, frequency response, etc. mid-term evaluations 23 A/D D/A upsampling, down-sampling example. 24 8.1 Digital filter design causality and Paley-Wiener theorem 25 8.2 FIR linear phase causal filter design delays / taps 26 8.2 FIR design using windows 8.2.2 FIR design by using windows time-delay, sidelobes, transition band 27 8.2.3 FIR design by frequency sampling 8.2.4 FIR equiripple design 28 remez algorithm usage and tradeoffs 8.3 IIR filter design from analog filters causal stable IIR filters cannot have linear phase 8.3.3 bilinear transformation 29 cheby1 use of practical filters before downsampling bandpass 30 5. DFT overview DFT introduction, examples 31 exam 2 32 Inverse DFT by coefficient matching DFT of sinusoids DTFT sampling 33 DTFT sampling example periodic superposition, circular extension time-limited signals DFT, IDFT - computational perspective (skip) 5.2 DFT properties linearity circularly even sequence circularly odd sequence symmetry properties 34 review of transient response 35 5.2.2 convolution property circular convolution linear convolution via zero-padded DFT 36 5.2.3 other properties of DFT shift properties correlation 5.3.1 filtering with DFT's 5.3.2 filtering long sequences 37 DFT-based filtering by sampling H(omega) 5.4 freq. analysis of signals via DFT (fftshift) 38 upsampling/interpolation via DFT (interpft) brief overview of discrete wavelet transform. 5.5 summary 39 (blatt) 6.1 FFT radix 2 40 (blatt) 6.2 FFT methods 41 wavelets (for review of up/down sampling) course evaluations 42 wavelets in freq. domain (more review) over-sampled A/D and transition band ----------------- stuff i didn't have enough time to cover ---- 2D DTFT 2D frequency response 2D filtering examples 2D DFT Dolby application? D/A zero-order hold / filter