User`s guide

Unwrap
5-479
Unwrap Method
The Unwrap block unwraps each channel of its input matrix or input vector by
adding to each successive channel element, and updating k at each phase
jump. See the following steps to the unwrap method for details.
Definition of Phase Unwrap
Algorithms that compute the phase of a signal often only output phases
between and . For instance, such algorithms compute the phase of
to be 3, since , and since the actual phase,
, is not between and . Such algorithms compute the phases of
and to be 3 as well.
Phase unwrap or unwrap is a process often used to reconstruct a signal’s
original phase. Unwrap algorithms add appropriate multiples of to each
phase input to restore original phase values, as illustrated in the following
Relevant Unwrap Terms:
•u
i
— ith element of the input channel on which the algorithm operates
• —
Tolerance parameter value
•phase jump or phase discontinuity — difference between phase values of
two adjacent channel entries that exceeds . The diagram in the next
section indicates phase jumps with red arrows.
Steps to the Unwrap Method:
1 Set k to 0 (See “The Two Unwrap Modes” on page 5-475 for more on how
often this step occurs.)
2 Check for a phase jump between adjacent channel elements u
i
and u
i+1
:
- If there is no phase jump between u
i
and u
i+1
, add
to u
i
, and then repeat step 2 to continue checking for phase jumps.
- If there is a phase jump between u
i
and u
i+1
, add
to u
i
, and then go to step 3 to update k.
3 Update k as follows when there is a phase jump between u
i
and u
i+1
. Then
go back to step 2 to add the updated value to u
i+1
and succeeding
channel elements until the next phase jump:
- If (phase jump is negative), increment k.
- If (phase jump is positive), decrement k.
2πk
α
α
u
i 1+
u
i
– α≤()2πk
u
i 1+
u
i
– α>()2πk
2πk
u
i 1+
u
i
<
u
i 1+
u
i
>
π– π
2π 3+()sin
3() 2π 3+()sin=sin
2π 3+
π– π
4– π 3+()sin 16π 3+()sin
2π