EHB307E - Lecture 02A - ESD PSD Filters and Transmission

Introduction

• Prepared by: Assoc. Prof. Dr. Ferkan Yilmaz

• Institution: Istanbul Technical University

• Course: EHB 307E / EHB 307 Communications I (2024 Fall)

• All rights reserved; no reproduction without permission.

Course Overview

• Instructor: Assoc. Prof Ferkan Yilmaz

• Department: Electronics and Communication Engineering

• Academic Year: 2022-2023 Fall Semester

Energy Spectral Density

• Definition: Represents the density of signal energy over frequencies.

• Parseval's Theorem: States that the energy of a voltage signal is expressed as:

  • Energy of a signal over a 1 Ohm resistor is crucial in analysis.

  • The real signal property is: X(-f) = X*(f) for real x(t).

Power Spectral Density

• Definition: Represents the density of signal power over frequencies.

Signal Instantaneous Power

• Power Measurement:

  • The bel is derived from Alexander Graham Bell.

  • Decibels (dB) relate to power logarithmically:

    • dBW: 10log10(P) (Power relative to 1 W)

    • dBm: log10(1000*P) = 30 + 10log10(P)

• Decibel applications apply to communications to measure power over varied ranges.

Transmission Through LTI Systems

• Selection of Signals for Transmission: Focus on carrier amplitude, frequency, and phase.

• Distortion Effects:

  • LTI systems can reveal magnitude and phase distortions.

Examples

• Energy of Sinc Signal: Calculation of the energy and spectral density of the x(t) = A sinc(4πf0t).

• Autocorrelation and Fourier Transform: Describes relationships and properties of periodic signals.

Ideal Filters

• Type: Bandpass Filter, Lowpass Filter, Highpass Filter.

• Characteristics: Ideal filters allow for distinct handling of frequency ranges, maintaining constant phase and magnitude.

Bandwidth Considerations

• Signal Bandwidth: Signals cannot be simultaneously time-limited and band-limited. Various bandwidth definitions include:

  • Half-power bandwidth.

  • Null-to-null bandwidth.

  • Fractional power containment bandwidth.

Summary

• Topics include introductions to communication systems, frequency bands, effects of distortion, classification of signals, Fourier series and transform analyses.

• Communication system components, LTI system properties, and ideal filter relationships are all emphasized, including practical implications in the real-world applications of communications.