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# What is difference between unwrap(angle(X)) and phase(X)?

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Seokseong Jeon on 4 Jan 2017
Commented: Seokseong Jeon on 15 Jan 2018
I am manipulating a CSI (channel state information) a.k.a channel matrix containing complex numbers. And I want to extract phases from them. Hence,:
% X is a channel matrix of size 3 x 30
angle_ = angle(X);
angel_unwrapped_ = unwrap(angle_); % default tolerance is pi. Ref: help unwrap
for i = 1:3
phase_(i, :) = phase(X(i, :)); % always takes only one argument. phase_ is maed to keep it continuous over the pi-borders.. Ref: help phase
end
So, I understood that both functions unwrap() and phase() seem to have the same phase tolerance, pi.
But I've been confused becaseu of a figure below I've got:
I wonder why to functions show different wrapping behavior.
Just in case, I've attached the channel matrix data file.

#### 2 Comments

Walter Roberson on 4 Jan 2017
Please show
which -all phase
I am having difficulty locating a Mathworks phase() routine
Seokseong Jeon on 4 Jan 2017
In my case,
C:\Program Files\MATLAB\R2015b\toolbox\ident\idobsolete\phase.m
C:\Program Files\MATLAB\R2015b\toolbox\ident\ident\@iddata\phase.m % iddata method

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### Accepted Answer

Zhao Wang on 9 Jan 2017
I understand that you want to extract phase angles from channel matrix (which is 'csi' in the data file). However, using the script you provided, I am not able to get the same plot you had.
The difference is that using the "unwrap" function leads to phase angles within a range of [-5 5). This behavior is expected with regards to the documentation page in the following help link.
As described in the above page, the default tolerance of the "unwrap" function is 'pi'. Most of the phase angle jumps (in absolute values) are less than 'pi' in the original phase angle matrix. As a result, the result of using the "unwrap" function includes three sawtooth-shape curves within a range of [-5 5).
The difference you saw might be caused by the tolerance used in the "phase" function. You can inspect the code of this function by executing the following command in the MATLAB Command Window:
>> edit phase
The tolerance used by the "phase" function is '3.5' at line 26. This value is larger than the default tolerance used by the "unwrap" function. If you modify the tolerance in the "phase" function and use it to process the data in 'csi', the result is similar to the curves in the middle plot you had.

#### 1 Comment

Walter Roberson on 9 Jan 2017
This agrees with the analysis that I did. The phase function uses a different tolerance on wrapping.
Also, unwrap() watches out for the possibility of gaps that span multiple 2*pi groups, but phase() does not.

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### More Answers (1)

Rune Dueholm Bådsgård on 15 Jan 2018
Can I ask which app you are using for the phase function?

#### 1 Comment

Seokseong Jeon on 15 Jan 2018
Indoor positioning (AoA, ToA) using IEEE 802.11 CSI (wireless channel).
Is that what you want? I am not sure whether I understood your question correctly.

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