Developer Reference

  • 2020
  • 07/15/2020
  • Public Content
Contents

Triangle-Generating Functions

This section describes the functions that generate a periodic signal with a triangular wave form (referred to as “triangle”) of a given frequency, phase, magnitude, and asymmetry.
A real periodic signal with triangular wave form
x
[
n
] (referred to as a real triangle) of a given frequency
rFreq
, phase value
phase
, magnitude
magn
, and asymmetry
h
is defined as follows:
x
[
n
] =
magn
*
ct
h
(2π*
rFreq
*
n
+
phase
)
,
n
= 0, 1, 2,...
A complexl periodic signal with triangular wave form
x
[
n
] (referred to as a complex triangle) of a given frequency
rFreq
, phase value
phase
, magnitude
magn
, and asymmetry
h
is defined as follows:
x
[
n
] = magn * [
ct
h
(2π*
rFreq
*
n
+
phase
) + j *
st
h
(2π*
rFreq
*
n
+
phase
)]
,
n
= 0, 1, 2,...
The
ct
h
() function is determined as follows:
H
= π +
h
ct
h
(α +
k
* 2π) =
ct
h
(α)
,
k
= 0, ±1, ±2, ...
When
H
= π , asymmetry
h
= 0, and function
ct
h
() is symmetric and a triangular analog of the
cos
() function. Note the following equations:
ct
h
(
H
/2 +
k
*π) = 0
,
k
= 0, ±1, ±2, ...
ct
h
(
k
* 2π) = 1
,
k
= 0, ±1, ±2, ...
ct
h
(
H
+
k
* 2π) = -1
,
k
= 0, ±1, ±2, ...
The
st
h
() function is determined as follows:
st
h
(α +
k
* 2π) =
st
h
(α)
,
k
= 0, ±1, ±2, ...
When
H
= π , asymmetry
h
= 0, and function
st
h
() is symmetric and a triangular analog of the sine function. Note the following equations:
st
h
(α) =
ct
h
(α + (3π +
h
)/2)
,
k
= 0, ±1, ±2, ...
st
h
(
k
* π) = 0
,
k
= 0, ±1, ±2, ...
st
h
((π -
h
)/2 +
k
* 2π) = 1
,
k
= 0, ±1, ±2, ...
st
h
((3π +
h
)/2 +
k
* 2π) = -1
,
k
= 0, ±1, ±2, ...

Product and Performance Information

1

Intel's compilers may or may not optimize to the same degree for non-Intel microprocessors for optimizations that are not unique to Intel microprocessors. These optimizations include SSE2, SSE3, and SSSE3 instruction sets and other optimizations. Intel does not guarantee the availability, functionality, or effectiveness of any optimization on microprocessors not manufactured by Intel. Microprocessor-dependent optimizations in this product are intended for use with Intel microprocessors. Certain optimizations not specific to Intel microarchitecture are reserved for Intel microprocessors. Please refer to the applicable product User and Reference Guides for more information regarding the specific instruction sets covered by this notice.

Notice revision #20110804