ece4305_L06

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

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

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

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