Complex angle calculation with no reset of argument: continuous unbounded angle

Question

Consider the following example Simulink (Download example) system:

Input is a magnitude and an ever increasing angle, which will return two sine, the real and imaginary part as expected:

Calculating the Magntitude from real and imaginary part is no issue. Getting the angle in the domain between -pi and pi neither:

But I'm really struggling in calculating the original angle from the imaginary and real part. Do you have any ideas how to get rid of the discontinuity (yellow line, last picture)?

score 2 · Answer 1 · edited May 23 '17 at 11:59

Daniel's Solution was exact what I was looking for, but in case the DSP System Toolbox is not available, like in case of my project partners, I came up with the following solution:

with

function [y, corr]  = phase_unwrap(zz,z,v)
%#codegen

d = diff([v,z,zz]);
if abs(d(1)) > pi
    y = sign(d(1));
    corr = -3/2*d(2);
else
    y = 0;
    corr = -3/2*d(1);
end

end

The discrete time integrator has the same sampling time as the zero-order-hold and a gain of 2*pi.

The example output is satisfying, but I still need to test it for the real case.

score 2 · Accepted Answer · edited Dec 22 '15 at 10:19

2

How about this example?

function [ub_ang,ang] = phase_unwrap(re, im, theta)
%#codegen

ang = atan2(im,re);

tmp = [theta ang];

uang = unwrap(tmp);

ub_ang = uang(2);

Scope1 plot is below

Scope plot is below.

edited Dec 22 '15 at 10:19

Robert Seifert

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answered Dec 22 '15 at 08:21

KKS

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Apart from that you need to swap imaginary and real part in the `atan` calculation and you shouldn't use `real` and `imag` as variable names, as they are in-built functions - it works great! – Robert Seifert Dec 22 '15 at 10:20
Tjank you for your comment~ – KKS Dec 22 '15 at 11:38

Daniel · Answer 3 · 2015-12-22T13:27:10.393

1

Use the block called unwrap. In case the toolbox is not available, this discrete implementation in simulink could be used:

edited Dec 22 '15 at 13:27

answered Dec 21 '15 at 09:38

Daniel

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Exactly what I was looking for! Unfortunately it's for discrete time, but I'd guess there are no continous solutions anyway. – Robert Seifert Dec 21 '15 at 09:42
Though I have the toolbox, my project partners don't. I wonder how I could utilize the `unwrap` of the main matlab, which does the same, for Simulink. – Robert Seifert Dec 21 '15 at 09:47
I will take a closer look on tuesday, when I have access to simulink. – Daniel Dec 21 '15 at 10:05
Therer is a matlab function block on User-defined functions group in simulink. – KKS Dec 21 '15 at 11:08
@김갑수 I'm aware of that, but it can't be used out opf the box. – Robert Seifert Dec 21 '15 at 11:40

Complex angle calculation with no reset of argument: continuous unbounded angle

3 Answers3