## EECS 307 Communications Systems

**CATALOG DESCRIPTION: **Analysis of analog and digital communications systems, including modulation, transmission, and demodulation of AM, FM, and TV systems. Design issues, channel distortion and loss, bandwidth limitations, additive noise.

**REQUIRED TEXT: **R. E. Ziemer and W. H. Tranter, *Principles of Communications *, John Wiley & Sons, Inc., 5 th edition (2002)

**REFERENCE TEXT: **None

**COURSE DIRECTOR: Prof. Michael Honig**

**COURSE GOALS: **To teach the principles underlying modulation and demodulation of analog signals along with associated system design issues. The latter includes power and bandwidth constraints and performance in the presence of additive noise.

**PREREQUISITES BY COURSES: EECS 222** and **EECS 302**

**PREREQUISITES BY TOPIC:**

1: Fourier transforms and linear systems

2: Probability and random variables

**DETAILED COURSE TOPICS:**

**Week 1. **Components of a communications system, benefits of modulation, review of Fourier series and Fourier transform.

( READINGS : Z&T, Chapter 1, 2.1, 2.2, 2.4, 2.5)

**Week 2**. Properties of the Fourier transform, Fourier transform of a periodic signal, linear systems, impulse response, time-invariant systems.

( READINGS : Z&T, 2.5 (cont.), 2.7 (excluding 2.7.13-14))

**Week 3.** Cross-correlation and autocorrelation of deterministic signals, power spectral density, Hilbert transform.

( READINGS : Z&T, 2.6, 2.9.1-2)

**Week 4.** Analytic signals, characterization of bandpass signals, double-sideband and amplitude modulation.

( READINGS : Z&T, 2.9.3-5, 3.1 up to ``Single-Sideband Modulation'')

**Week 5**. Power efficiency of AM, Single- and Vestigial-sideband modulation, mixers.

( READINGS : Z&T, 3.1 from SSB subsection up to ``Frequency Translation and Mixing'')

**Week 6.** Phase and frequency modulation, spectral analysis, FM bandwidth, demodulation of FM.

( READINGS : Z&T, 3.2)

**Week 7. **Superheterodyne receiver, multiplexing, probability review.

( READINGS : Z&T, Sec. 3.1.5, 3.7, Chapter 4)

**Week 8.** Probability review (cont.): densities, random variables, and statistical averages; random processes, first- and second-order statistics, stationarity and ergodicity.

( READINGS : Z&T, Chapter 4, 5.1, 5.2)

**Week 9. **Auto- and cross-correlation, power spectral density of random signals, effect of filtering.

( READINGS : Z&T, 5.3, 5.4)

**Week 10.** Narrowband noise, Signal-to-Noise Ratio analysis of DSB and coherent AM.

( READINGS : Z&T, 5.5.1-2, 6.1)

**HOMEWORK ASSIGNMENTS:**

Homework 1: Problems on using properties of the Fourier transform to evaluate transforms of specific signals.

Homework 2: Problems on characterizing linear, time-invariant filters and input-output relations.

Homework 3: Problems on computing the Hilbert transform, autocorrelation, and power spectral density.

Homework 4: Problems on characterizing bandpass signals and determining properties (e.g., modulation index and transmitted power) of double-sideband and amplitude-modulated signals.

Homework 5: Problems on Amplitude and Single-Sideband modulation and demodulation (e.g., computing power efficiency and determining spectral properties).

Homework 6: Problems on phase and frequency modulation and demodulation (e.g., computing the spectrum for tone modulation and determining bandwidth).

Homework 7: Problems on superheterodyne receivers (e.g., filter specification and determining tuning range), and on random variables.

Homework 8: Problems on statistical averages, second-order statistics, and ergodicity.

Homework 9: Problems on computing power spectral densities, effect of filtering, and characterizing narrowband noise.

**COMPUTER PROJECTS: **none

**LABORATORY PROJECTS:**

1. Uses Hypersignal software on a PC to view signals in the time and frequency domains. The software simulates an oscilloscope and spectrum analyzer. The effects of filtering and modulation are demonstrated.

2. The students build an amplitude modulator based on the Motorola MC1496 modulator chip, along with a noncoherent demodulator. The outputs of the modulator and demodulator are viewed in the time and frequency domains.

3. The students build a frequency modulator and demodulator based on the Exar XR-2207 voltage-controlled oscillator and Exar XR-221 phase-locked loop demodulator. The output of the modulator is viewed in the time and frequency domains, and performance of the demodulator is observed.

**GRADES:**

- Homework: 15%
- Labs: 15%
- Midterms (2): 30%
- Final: 40%

**COURSE OBJECTIVES: **When a student completes this course, s/he should be able to:

1. Evaluate and interpret Fourier transforms of signals by using properties of the Fourier transform.

2. Evaluate the output of a linear, time-invariant system given an input and the impulse response or transfer function.

3. Evaluate the autocorrelation and energy or power spectral density of a deterministic signal.

4. Evaluate the Hilbert transform of elementary signals.

5. Characterize a bandpass signal in terms of in-phase and quadrature components, envelope, and phase.

6. Characterize double-sideband and amplitude modulated waveforms in the time and frequency domains.

7. Characterize double-sideband, amplitude, and single-sideband modulation in terms of bandwidth and power efficiency.

8. Describe phase and frequency modulated signals in the time domain, and tone modulated signals in the frequency domain.

9. Estimate the bandwidth of a phase or frequency modulated waveform.

10. Determine filter specifications and tuning range for a superheterodyne receiver.

11. Determine whether or not a random process is wide-sense stationary and ergodic.

12. Compute the power spectral density of a random process.

13. Compute the autocorrelation and power spectral density of a filtered random process.

14. Specify narrowband noise in terms of low-pass random noise.

15. Compute pre- and post-detection Signal-to-Noise Ratios for linear modulation systems.

**ABET CONTENT CATEGORY: **100% Engineering (Design component).