ECEN 5254 Remote Sensing Signals and Systems Professor Albin J. Gasiewski Lecture #3 – January 24, 2012 EECCOOTT 224466 303-492-9688 (O) [email protected] Classes: ECCS 1B14 TR 9:30-10:45 AM 1 ECEN 5254 Remote Sensing Signals & Systems Spring 2012 University of Colorado at Boulder Administration • Reading: – RSSS, chapters 1,3 – UFM,, chappter 1 Material posted on CULearn* * UUssee ooff ppoosstteedd UUFFMM mmaatteerriiaall iiss rreessttrriicctteedd ttoo tthhee purposes of this course. 2 ECEN 5254 Remote Sensing Signals & Systems Spring 2012 University of Colorado at Boulder Last Lecture • Energy & Power Signals •• FFoouurriieerr ttrraannssffoorrmmss • Correlation • WWiiener-KKhhiinchhiine thheorem • QM signal analysis 3 ECEN 5254 Remote Sensing Signals & Systems Spring 2012 University of Colorado at Boulder Today’s Lecture • Coherence • Transmission line radiation •• RRaayylleeiigghh-JJeeaannss aapppprrooxxiimmaattiioonn • Johnson thermal noise • 1-D radiative transfer • Planck ((3-D)) sppectrum • Wien’s law •• SStteeffaann-BBoollttzzmmaannnn llaaww 4 ECEN 5254 Remote Sensing Signals & Systems Spring 2012 University of Colorado at Boulder Quasi-Monochromatic Signals Slowly time-varying phasor Auto- or cross-correlation requires time-averaging, e.g. : 5 Coherence of QM Signals Note Coherency function: CCan shhow: ((trivial)) Im Degree of coherence: V(t) RRee Provides measure of how closely W(t) ttwwoo ssiiggnnaallss oosscciillllaattee ((nnoott hhooww similar their voltages or powers are) 6 Example of Coherence Covariance: ((zero correlation)) Coherence: 7 Example of Coherence (cont’d) Covariance function: CCovariiance peakks ffor ttiime llags off ±±9900oo, ±±227700oo, ettc… 8 Thermal Noise 9 Thermal Noise • Fundamental limit to sensitivity of any receiver for either remote sensing or communications • OOnnllyy ffuunnddaammeennttaall nnooiissee mmeecchhaanniissmm iinn mmiiccrroowwaavvee ppoorrttiioonn of the spectrum for terrestrial temperatures – all others are anthropogenic or sporadic •• GGeenneerraatteedd bbyy aannyy ddiissssiippaattiivvee eelleemmeenntt oorr lloossssyy transducer at non-zero temperature Examples of thermal noise generators: Z o ~ T (K) Terminated Transmission Line 10