Syllabus             Schedule/Downloads

Schedule/Downloads (25-1)

The schedule is tentative and subject to change. (Last update: 05/19/25)

Chapter # Title Topics Handouts 25-1 week #

　

 25-1 Date and YouTube Link 25-1 CM# and Annotated PDF 25-1 Quiz, Exam, HW Recommended Reading:

Textbook by Oppeheim and Willsky

 - - - -
1 Introduction Syllabus handout01 1 2/18T 01 　 　 　 　 　 　
2 Discrete-Time Signals and Systems 2.1 Mathematical Modeling, Continuous-Time vs. Discrete-Time Signals, Digital Signal, Digital Signal Processing and bits 　 　 　 　 　 　

Overview of the course;
DFT and FFT, how to use DFT;
Cepstrum;
CT signal and continuous-parameter signal;
countable vs. uncountable set, finite set;
being digital and finite number of bits for representation;
discrete-time vs. digital signal;
ADC with 1) a uniform sampler, 2) a scalar quantizer, and 3) a binary encoder;
a function, the graph of a function, and illustration of the graph;
illustration of a DT signal;
meaning of infinity and meaning of 0 in DT time index.

 2/20Th 02 HW02 　 　 　 　 　
unit sample, unit step, real exponential, real exponential signals; complex sinusoidal signals and periodicity; unit sample decomposition of a DT signal; DT periodic signal, existence of fundamental period, uniqueness of period;
2 2/25T 03 HW03 　 　 　 　 　
2.2 identity system; MA system, causal MA, simple MA (SMA), exponentially weighted average (EWA); memoryless system

linearity; time-invariance; causality; stability;

 2/27Th 04 HW04 　 　 　 　 　
2.3  LTI systems; impulse response and convolution sum; properties of convolution and implication to LTI systems;
2.4, 2.5 Def. of a DT causal system; Lemma. A DT LTI system is causal iff ...; Def. A DT signal is causal if ...; Lemma. A DT LTI system is BIBO stable if ...; Def. A DT LTI system is an IIR/FIR system if ... ; Def. Two DT systems are inverse systems to each other if ... ; Lemma. Two DT LTI systems are inverse to each other if ...; Def. An LCCDE is ...; Lemma. A DT system described by an LCCDE is LTI iff ... 3 3/4T 05 HW05 　 　 　 　 　

Not every DT LTI system has the I/O relation describable by an LCCDE.; Even if describable, the uniqueness of the LCCDE is not guaranteed.;

2.6 2.7 Non-uniqueness of LCCDE for a DT LTI system; synthesis equations of DTFS, DTFT; periodicity of DTFT; Def. of frequency response of DT LTI system, eigenfunction and eigenvalue; low vs. high frequency in DTFT		 3/6Th 06 HW06 　 　 　 　 　
handout02 　 　 　 　 　
2.7 NS condition for DTFT to exist; absolute summability; Fourier-Plancherel TF and square summability; the Gibbs phenomenon; 4 3/11T 07 HW07 　 　 　 　 　
2.8 Properties of DTFT 　 　 　 　 　
2.9 DTFT Theorems 　 　 　 　 　
2.10 DT random process and its processing 　 　 　 　 　
3 The z-Transform 3.1 Def. of z-TF of a DT signal and ROC; DTFT/z-TF as a special case of z-TF/DTFT; geometric sequence/progression; summation formula for geometric series; handout03 3/13Th　 08　 Quiz01 　 　 　 　 　
　
no division by zero and ROC; ROC and existence of DTFT; poles and zeros of a rational function of z; pole-zero diagram; an infinite sum into the sum of two infinite sums; common z-TF pairs

3.2 Properties of ROC; ROC and z-TF may not exist; ROC must be specified

 5 3/18T 09 　
　 　 　 　 　
3.3 inverse z-TF, PFE, power series 3/20Th 10 HW10 　 　 　 　 　
3.4 z-TF properties and ROCs, pole-zero cancellation 　 　 　 　 　
3.5 LCCDE and z-TF 　 　 　 　 　
The limit of a linear combination of convergent sequences is the linear combination of the limits; The z-TF converts an LCCDE to an algebratic equation; DT LTI system whose I/O relation describable by an LCCDE; the system function of a DT LTI system; the system function of a DT LTI system whose I/O relation describable by an LCCDE; LCCDE vs. causality of the impulse response; stability and system function; filter and Fourier transform and z-TF 6 3/25T 11 　
Filter property and DTFT, filter design using z-TF, evaluation of z-TF on unit circle; notch filter and z-TF, all-pass filter and z-TF, conjugate reciprocal; Not every DT signal is obtained by sampling a CT signal 3/27Th 12 HW12
4 Sampling of Continuous-Time Signals 4.1 periodic/uniform sampling and scalar quantization; DT LTI system built using delay components, adders and scalar multipliers; ADC with uniform sampler, scalar quantizer, and binary encoder; digital signal defined in the textbook vs. by circuit engineers; uniform sampling in TD and FD; two-stage representation of C/D converter, sampling function,

4.2 C/D and Fourier transforms of the input and output signals;  aliasing, perfect reconstruction, bandlimitedness and no aliasing

 handout04 7 4/1T 13 　 　 　 　 　 　
sampled signal in TD and FD, relation between CTFT of the input and DTFT of the output of C/D converter; 4/2 19:00-22:00 at LG 104 Midterm Exam 　 　 　 　 　
    

4.3  D/C converter, DT to modulated Impulse train and ideal LPF, uniform Interpolation, interpolation function; reconstruction using sinc pulse, sample and hold, correction/compensation filter

 4/3Th 14 HW14 　 　 　 　 　
two-stage representations of C/D and D/C; sampling vs. conversion rates; interpolation function/pulse; Convergence of a sequence of functions, (1) everywhere (2) almost everywhere (3) mean-square (4) in measure; Nyquist's sampling theorem and mean-square convergence 8 4/8T 15 　 　 　 　 　 　
4.4 DT processing of CT signals 　 　 　 　 　
4.5 CT processing of DT signals;
  • resampling at non-harmonically related rate
  • surface acoustic wave (SAW) filter: exploiting the slow propagation speed of ・.
  • laser-optics
  • nonlinear, neuromorphic circuit 
  • etc
 　 　 　 　 　
4.6 Sampling of a DT signal to obtain a DT signal
  • downsampling as a special case of decimation; downsampling in TD and FD; filter-bank implementation of decimation;
  • upsampling as a special case of DT interpolation; upsampling in TD and FD; filter-bank implementation of interpolation
 4/10Th 16 HW16 　 　 　 　 　
upsampling using filterbank; polyphase filter and delay;
9 4/15T 17 　 　 　 　 　 　
4.7 combining decimator and interpolator = multi-rate signal processing; multi-stage interpretation of upsampling;

4.8 AAF; sample and hold; quantizer and its asymmetry, round, floor, ceil

 　 　 　 　 　

multistage decimation, multistage interpolation; two-channel filter and subband coding; ADC and DAC symbols; uniform quantizer vs. non-uniform quantizer; clipping, nulling, sawtooth mapping in scalar quantizers; a justification of additive quantization noise, histogram and power spectrum; SQNR; ZOH and compenstation filter;

4/17Th 18 HW18

harmonica.wav

 　 　 　 　 　
　 　 　 　 　
　 　 　 　 　
8 The Discrete-Fourier Transform 8.0 DTFT vs. DFT; DFT vs. FFT; OFDM and FFT, IFFT; DTFT and inner product; DTFS and DFT; sampling of DTFT and DFT; DFT and DFTF of finite-support DT signal; linear convolution of finite-support signals and DFT; handout05 　 　 　 　 　
Def. of DFT as a linear transform of a vector into a vector; N-DFT matrix as a row of column vectors;
  • 1st interpretation of DFT
  • So, the DFT of x is a linear combination of these column vectors with combining weight given by the input vector x.
  • The IDFT matrix is 1/N times the Hermitian transposition of W.
    • The IDT matrix consists of rows of rotationg-phase vectors with different number of counter-clockwise rotations on the unit circle divided into N sections. 
    • In unitary DFT, both the DFT and IDFT matrices have the scaling factor of 1/sqrt(N).
  • Relation b/w DTFT of a finite-suppot DT signal
    • If the DT signal is time limited to 0 to N-1, then the DFT of the vector [x[0], ・x[N-1]] is the sampling of DTFT with omega = 2pi/N times the index from 0 to N-1.
 10 4/22T 19 　 　 　 　 　 　
  • 2nd interpretation of DFT
  • The DFT matrix W consists of rows (a column vector of row vectors) which are the Hermitian transposed column vectors of rotating-phase vectors with different number of counter-clockwise rotations on the unit circle divided into N sections. 
  • So, the DFT of x is a projection of the input vector to the direction of these column vectors times sqrt(N).
  • The IDFT matrix is 1/N times the Hermitian transposition of W.
  • The IDT matrix consists of columns of rotationg-phase vectors with different number of counter-clockwise rotations on the unit circle divided into N sections. 
  • So, the IDFT of X is a linear combination of these columns with combining weight given by X.
  • Relation b/w DTFS of a periodic signal with period N and DFT of a single-period vector

8.1 Representation of Periodic Sequences: DTFS

8.3  DTFT of periodic signals; periodic extension; windowing

8.4 Sampling the DTFT; time-domain aliasing,

4/24Th 20 HW20 　 　 　 　 　
8.5 Fourier Representation of Finite Duration Sequences; windowing function, Dirichlet kernel;

8.6 Properties of DFT; circular shift; circular convolution;

11 4/29T 21 　 　 　 　 　 　
　 　 　 　 　
　 5/1Th 22  Quiz 2 　 　 　 　 　
8.7 Computing Linear Convolution Using DFT HW22 　 　 　 　 　
　 　 　 　 　
9 Computation of the Discrete-Fourier Transform 9.1 Direct Computation and Complexity; The Goertzel algorithm and complexity handout06 for chapter 9 12 5/13T 23 HW24 　 　 　 　 　
      Goertzel's algorithm for computing DTFT at a non-DFT frequency

9.2 Decimation in Time FFT Algorithm

  • butterfly computation

9.3 Decimation in Frequency FFT Algorithm

 5/15Th 24 　 　 　 　 　
　 　 　 　 　 　
9.4 Practical Considerations
9.5 Complexity comparison
9.6 Implementation of the DFT using convolution
】 the chirp transform algorithm (CTA)
】 the chirp z-transform (CZT) algorithm		 　 13 5/20T 25 HW26 　 　 　 　 　
10 Fourier Analysis of Signals Using DFT 10.1 relation between the sampling rate, CTFT, and DTFT; effect of window function on DTFT; effect of window length on DTFT; effect of number of DFT points on resolution; short-time Fourier transform

10.2 example with sinusoidal signals

10.3 Short-Time Fourier Transform

 handout06.5 for chapter 10 5/22Th 26 　 　 　 　 　
STFT and spectrogram
　

PSD estimation
     parametric vs. non-parametric
     non-parametric
         10. 4 periodogram
         10. 5 auto-covariance

 14 5/27T 27 　 　 　 　 　 　
11 Parametric Signal Modeling All-pole modeling of signals

Model order

The Levinson–Durbin Recursion

 handout06.6 for chapter 11 　 5/29Th 28 　 　 　 　 　 　
　 　 　 　 　 6/4W 19:00-23:00, LG 102 Final Exam 　 　 　 　 　
　 　 　 　 　 　 　 　 　 　 　 　 　
　 　 　 　 　 　 　 　 　 　 　 　 　
　 　 　 　 　 　 　 　 　 　 　 　 　
　 　 　 　 　 　 　 　 　 　 　 　 　
　 　 　 　 　 　 　 　 　 　 　 　 　
5 Transform Analysis of LTI Systems 5.1 handout07 　 　 　 　 　 　 　 　 　
5.2 　 　 　 　 　 　 　 　 　
5.3 　 　 　 　 　 　 　 　 　
5.4 　 　 　 　 　 　 　 　 　
5.5 　 　 　 　 　 　 　 　 　
5.6 　 　 　 　 　 　 　 　 　
5.7 　 　 　 　 　 　 　 　 　
6 Structure of DT Systems 6.1 handout08 　 　 　 　 　 　 　 　 　
6.2 　 　 　 　 　 　 　 　 　
6.3 　 　 　 　 　 　 　 　 　
6.4 　 　 　 　 　 　 　 　 　
6.5 　 　 　 　 　 　 　 　 　
6.6 　 　 　 　 　 　 　 　 　
7 Filter Design Techniques 7.1 handout09 　 　 　 　 　 　 　 　 　
7.2 　 　 　 　 　 　 　 　 　
7.3 　 　 　 　 　 　 　 　 　
7.4 　 　 　 　 　 　 　 　 　
7.5