ece4305_L06

# ece4305_L06 - Power Spectral Density ECE4305 Software-Dened...

This preview shows pages 1–5. Sign up to view the full content.

Power Spectral Density ECE4305: Software-Deﬁned Radio Systems and Analysis Professor Alexander M. Wyglinski Department of Electrical and Computer Engineering Worcester Polytechnic Institute Lecture 6 Professor Alexander M. Wyglinski ECE4305: Software-Deﬁned Radio Systems and Analysis

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
Power Spectral Density Theoretical Foundations PSD Characterization Frequency Domain Perspective I It is sometimes more convenient to study a communication system in the frequency domain rather than the time domain I Mathematical analysis is more tractable I Operations such as convolution are transformed into simple multiplications I Physically it makes sense to study wireless transmissions in the frequency domain I Digital communications is the transferral of data based on changes of electromagnetic wave characteristics such as frequency, amplitude, and phase Professor Alexander M. Wyglinski ECE4305: Software-Deﬁned Radio Systems and Analysis
Power Spectral Density Theoretical Foundations PSD Characterization Fourier Transform I Mathematical relationship between a time domain waveform and weighted sum of sinusoidal components that constitute it, i.e., frequency domain representation I Translating between time and frequency domains is achieved using the Fourier transform and inverse Fourier transform: H ( f ) = Z -∞ h ( t ) e - j 2 π ft dt (1) h ( t ) = Z -∞ H ( f ) e j 2 π ft df (2) Professor Alexander M. Wyglinski ECE4305: Software-Deﬁned Radio Systems and Analysis

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
Power Spectral Density Theoretical Foundations PSD Characterization Einstein-Wiener-Khinchin Theorem I In particular, we are interested in the power spectral density (PSD) of a signal, which is related to the autocorrelation function via the Einstein-Wiener-Khintchine (EWK) Relations: S X ( f ) = Z -∞ R X ( τ ) e - j 2 π f τ d τ (3) R X ( τ ) = Z -∞ S X ( f ) e j 2 π f τ df (4) I Relating the PSD between input x ( t
This is the end of the preview. Sign up to access the rest of the document.

## This note was uploaded on 01/13/2011 for the course ECE 4305 taught by Professor Wy during the Spring '10 term at WPI.

### Page1 / 17

ece4305_L06 - Power Spectral Density ECE4305 Software-Dened...

This preview shows document pages 1 - 5. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online