# Tag Info

5

As you pointed out in your edit, averaging the values isn't a great fit for this sort of problem. A simple alternative would be to simply fit a line to the four phase measurements using a linear least squares fit. That should perform better than the single-point approach. A possibly even-better solution would be to fit a sinusoid to the four complex samples ...

3

The usual way to approach directional is to move to a (complex) vector approach. For example, if your observations are periodic with period $P$ then the mean of $N$ observations, $\hat\alpha(n)$ can be found as per equation (1) of the above link: $$\hat{\mu}_P = \frac{P}{2\pi} \left[ \arg \left ( \sum_{n=0}^{N-1} e^{j2\pi\hat\alpha(n)/P} \right) \right ]_{... 2 For small \Theta an approximation would be to simply halve the imaginary value. You could also use the ratio of the real and imaginary values as the index to a lookup table that would return the half angle value. You could not store every possible value, of course, so you would have to choose some set of values and then lookup the value that is closest ... 2 Some examples would be the null to null bandwidth(s) as well as the sidelobe levels of the first/second sidelobes. Example vector of 5 numbers: [mainlobe gain, first null location, 1st sidelobe gain, second null, 2nd sidelobe gain] From this you could produce an estimate for the 3 dB points of each lobe using some "reasonable" formula, i.e. halfway ... 2 The covariance matrix is given by$$C_{X,Y}=\begin{bmatrix}E(XX)& E(XY) \\ E(YX )& E(YY) \end{bmatrix}$$This can be written as below:$$C_{X,Y}=\begin{bmatrix}E(R^2cos^2(\Theta) )& E(Rcos(\Theta)Rsin(\Theta)) \\ E(Rsin(\Theta)Rcos(\Theta) )& E(R^2sin^2(\Theta)) \end{bmatrix}$$Since R and \Theta are independent the expectation will ... 2 Both the Laplace and Z transform are generalized versions of their discrete or continuous Fourier counter parts. To get the respective Fourier transform you would evaluate the Z-transform on the unit circle and the Laplace transform on the imaginary axis. Hence it's most practical to represent Z-transform argument in polar coordinates since "frequency" is ... 1 I haven't worked through the algebra, but this page just before that equation: suggests that$$ \operatorname{sinc}\left[2A(\rho-\frac{n}{2A})\right]  might be the correct form of the $\operatorname{sinc}$ term.

1

Mixing is not the correct terminology for what you want to do. Mixing is multiplication and you want additive noise. Convert back to I/Q, add complex noise, then convert back to mag/phase!

1

When you opens the polar plot in the figure editor you can find out that the coordinates around the plot are not from the axis. It are hidden text objects (Press on one you see it). So this means you have to edit them by yourself. a work around for this is this: figure t = 0:.01:2*pi; polar(t,sin(2*t).*cos(2*t),'--r') hHiddenText = findall(gca,'type','text'...

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