Visible to Intel only — GUID: GUID-8C164739-D8CE-4964-B9B2-7024B561261D
Visible to Intel only — GUID: GUID-8C164739-D8CE-4964-B9B2-7024B561261D
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 * cth(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 * [cth(2π* rFreq*n + phase) + j * sth(2π* rFreq*n + phase)], n = 0, 1, 2,...
The cth () function is determined as follows:
H = π + h
cth (α + k* 2π) = cth (α), k = 0, ±1, ±2, ...
When H = π , asymmetry h = 0, and function cth() is symmetric and a triangular analog of the cos() function. Note the following equations:
cth (H/2 + k*π) = 0, k = 0, ±1, ±2, ...
cth (k* 2π) = 1, k = 0, ±1, ±2, ...
cth (H + k* 2π) = -1, k = 0, ±1, ±2, ...
The sth () function is determined as follows:
sth (α + k* 2π) = sth (α), k = 0, ±1, ±2, ...
When H = π , asymmetry h = 0, and function sth() is symmetric and a triangular analog of the sine function. Note the following equations:
sth (α) = cth (α + (3π + h)/2) , k = 0, ±1, ±2, ...
sth (k* π) = 0, k = 0, ±1, ±2, ...
sth ((π -h)/2 + k* 2π) = 1, k = 0, ±1, ±2, ...
sth ((3π +h)/2 + k* 2π) = -1, k = 0, ±1, ±2, ...
- Triangle
Generates a triangle with a given frequency, phase, and magnitude.