**Boğaziçi UniversityVolumetric Analysis & Visualization Group**

Electrical and Electronics Engineering Dept

34342 Bebek / Istanbul

Tel: +90-212-3596465 / 3596414 (Dept.)

Fax: +90-212-2872465

Email: acarbu@boun.edu.tr

Course Code:

EE 373

Course Title:

Signals and Systems

**Credits: 4**

Continuous-time and discrete-time signals and systems, basic system properties. Linear time-invariant systems, convolution. Fourier series representation of periodic signals, Fourier transform of continuous-time and discrete-time signals, Sampling, Laplace transform and z-transform. *DFT and Modulation Theory are covered in EE473 and EE374 respectively.*

**Goals:**

The course is designed to familiarize junior students with the techniques for analyzing and synthesizing continuous-time as well as discrete-time systems. Time domain and frequency domain signal analysis tools are studied, and the subjects of filtering and modulation are introduced as signal processing techniques both in continuous-time and discrete-time. Design concepts are emphasized with respect to filtering and modulation.

**Text Book:**

A. V. Oppenheim and A. V. Willsky with S. H. Nawab, Signals and Systems. Prentice Hall, 1997. Second Edition. (Errata)

**TA:** TBA

**Lecture Hours:**

Monday 15:00-16:00 (PS,TESLA)

Tuesday 11:00-13:00 (TESLA)

Thursday 11:00-13:00 (TESLA)

**Assignments (the course's textbook):**

**A1**: 1.49, 1.54, 1.56, 1.53, 1.55, 1.25, 1.30, 1.27, 1.31, 1.28, 1.32, 1.38, 1.39, 1.42, 1.45, 1.33, 1.36, 1.47, 1.37**A2**: 2.22 ; 2.23; 2.27; 2.36; 2.29; 2.34; 2.41; 2.42; 2.46; 2.49; 2.52; 2.54; 2.60; 2.53; 2.47; 2.44; 2.43; 2.59 ; 2.62; 2.64; 2.65;2.66; 2.67; 2.71**A3**: 3.22; 3.25; 3.26; 3.29; 3.31; 3.36; 3.39; 3.43; 3.44; 3.45; 3.50; 3.52; 3.60; 3.66; 3.70**A4**: 4.22; 4.23; 4.25 ; 4.31; 4.28; 4.37; 4.40; 4.43 ; 4.46; 4.47; 4.44 ; 4.49; 4.48**A5**: 5.21 h,i; 5.23; 5.26; 5,28; 5.30; 5.33; 5.34; 5.41; 5.45; 5.47; 5.48; 5.51; 5.53**A6**: 7.6; 7.9; 7.10; 7.11; 7.16; 7.22; 7.26; 7.28; 7.30; 7.41; 7.44; 7.52; 7.23; 7.27; 7.29; 7.31; 7.34; 7.36; 7.43; 7.48**A7**: 10.22; 10.33; 10.37; 10.45; 10.46; 10.43; 10.55; 10.27; 10.31; 10.34; 10.41; 10.47; 10.48; 10.58; 10.65

**Exams & Grading:**

- Assignments: Not graded
- Pop-quizzes: 15% (Number of quizzes is not pre-determined but the total percentage is fixed.)
- 2 Midterms: 25% each (MT1: 17.10.2019 @ Course Hours ; MT2: 03.12.2019 @ Course Hours)
- Final Exam: 35%
- No make-up exams or quizzes
- You need to have earned minimum 20 pnts (out of 65 pnts) from the midterms and the quizzes to take the final exam.
- Download Formula Sheet

**Resources:**

- Online FSE Demo from JHU
- Online DTFT Demo from JHU
- Online CTFT Demo from JHU
- A note on Up-Samnpling/Down-Sampling: During downsampling a discrete-time signal, x[n], (which can be interpreted as the sampled and discretized version of an underlying BL continuous-time signal, x(t)), we multiply x[n] with an impulse train, p[n], of period N. The corresponding operation in frequency domain is convolution of X(Omega) with P(Omega), which will introduce an amplitude scaling of 1/N. The second step of down-sampling is removal of the zeros, which is contraction in discrete time, n. This will result in expansion in Omega. During upsampling, we insert zeros into a discrete-time signal, x[n]. This is direct expansion in in discrete time, n, and will result in contraction in Omega. The second step of upsampling is a LPF, which will replace the newly inserted zeros with the newly computed samples of the underlying BL continuous-time signal, x(t). If you use a unit amplitude ideal LPF, then the upsampled signal's fourier transform will not have an amplitude change but it will only be contracted. If you use an ideal LPF with amplitude N, then the upsampled signal's fourier transform' magnitude will be multiplied by N and it will also be contracted, preserving the energy. We used unit amplitude LPF, hence said there is no magnitude change in up-sampling. Unless the LPF used or the energy is specified, as long as you specify the LPF you use, and work out the problems accordingly, either way is fine. See the MIT's open-course notes on this topic. Check Figures 19.8 and 19.12.

**Boğaziçi UniversityVolumetric Analysis & Visualization Group**

Electrical and Electronics Engineering Dept

34342 Bebek / Istanbul

Tel: +90-212-3596465 / 3596414 (Dept.)

Fax: +90-212-2872465

Email: acarbu@boun.edu.tr