Recent content by WhiteHaired

Hi Stephen. Thank you for your time again. I am not expert in statistical terminology, so let me try to clarify the subject with the practical problem that I have. We wish to determine the radius ##R## and the length ##L## of a microwave cylindrical resonant cavity from the measurement of...

We are looking for the best (unbiased, efficient, etc.) estimate for a vector-valued quantity of two components [x1, x2], from several measures (see the first previous numerical example). When measurements are independent, the best estimate is the weighted mean of the measurements, where each...

In this case, Google is not my friend, or it is not enough. Indeed there are numerous websites where the data appears, but not with sufficient accuracy or without information on temperature, frequency, reliable reference, etc. For example, values like 1, 10006, 1000589, 10005364, 1000524, etc...

Where can I found values of the relative permittivity of air at different temperatures, frequencies, pressure, humidity, etc. or its dependence? I'm particularly interested in data around 1.4 GHz, 25ºC, 1 atm. 50% hum. Thanks in advance.

Stephen, you described very well my problem. Thank you very much. Yes, we assume than the "large" covariance matrix is known. Actually it is not very large, since each vector has only 2 components and we take 10 measurements.

It has the subscript ##i## since it represents the covariance matrix of ##x_i##, a vector-valued (2 values) quantity. Please, see the numerical example.

##\Sigma_i^{-1}## stands for the inverse of the covariance matrix of the vector-valued quantity ##x_i##.

I'd need to combine several vector-valued estimates of a physical quantity in order to obtain a better estimate with less uncertainty. As in the scalar case, the weighted mean of multiple estimates can provide a maximum likelihood estimate. For independent estimates we simply replace the...

Thank you, not for the moment.

Thank you, not for the moment.

It is always considered that the evolution of the input reflection coefficient, ρ, of a LTI causal passive system with frequency, f, always presents a local clockwise rotation when plotted in cartesian axes (Re(ρ), Im(ρ)), e.g. in a Smith chart, as shown in the attached figure. It must...

It is always considered that the evolution of the input reflection coefficient, ρ, of a LTI causal passive system with frequency, f, always presents a local clockwise rotation when plotted in cartesian axes (Re(ρ), Im(ρ)), e.g. in a Smith chart, as shown in the attached figure. It must...

Thank you Avihai. Very interesting the paper from Dr. Malisuwan et al., but, as you said, it's not a general case. They found a useful modification of the Smith chart representation for microstrip circuits, but no general conclussions about the behaviour of the reflection coefficient in...

Hi Avihai. I looked for it in many fundamental books of physics and electromagnetism, but I couldn't find any proof. Please note that the sign of the inequalities in my last equations is changed. It should read < 0. Any suggestion? Thanks.

It is well known that the evolution of the input reflection coefficient, ρ, of a LTI causal passive system with frequency, f, always presents a local clockwise rotation when plotted in cartesian axes (Re(ρ), Im(ρ)), e.g. in a Smith chart, as shown in the attached figure. It must appointed that...