Adams Basic Package > Adams View > View Command Language > panel > panel set twindow_function cosine_fourier_series

panel set twindow_function cosine_fourier_series

The COSINE_FOURIER_SERIES function evaluates a Fourier Cosine series at a user specified value "x". The SHIFT (i.e. x0) and the COEFFICIENTS (i.e. a0, a1,..., a30) parameters are used to define the constants for the Fourier Cosine series. The FREQUENCY (i.e. w) parameter specifies the fundamental frequency of the series. The Fourier Cosine series is defined :
F(x) =\ aj * Tj (x-x0)
where the functions Tj are defined as:
Tj (x-x0) = cos{j * w * (x-x0)}
The index j has a range from zero (0) to n, where n is the number of terms in the series.

Format:

 
panel set twindow_function cosine_fourier_series
x =
run time function
shift =
real
angular_shift =
angle
coefficients =
real
angular_coefficients =
angle
frequency =
angle

Description:

 
Parameter
Value Type
Description
x
Run time function
Specifies a run time function.
shift
Real
Specifies a real variable that is a non-angular shift in a Chebyshev polynomial, Fourier Cosine series, Fourier Sine series, or polynomial function. Or, a phase shift in the independent variable x, for a simple_harmonic_function.
angular_shift
Angle
Specifies a real variable that is a non-angular shift in a Chebyshev polynomial, Fourier Cosine series, Fourier Sine series, or polynomial function. Or, a phase shift in the independent variable x, for a simple_harmonic_function.
coefficients
Real
Specifies the non-angular real variables that define as many as thirty-one coefficients (a0, a1,..., a30) for the series or polynomial.
angular_coefficients
Angle
Specifies the angular real variables that define as many as thirty-one coefficients (a0, a1,..., a30) for the series or polynomial.
Frequency
Angle
Specifies the real variable that is the fundamental FREQUENCY of the series or harmonic function.

Extended Definition:

1. Adams assumes FREQUENCY is in radians per unit of the independent variable unless you use a D after the value.
The FREQUENCY parameter is represented in the following functions as "w".
The SIMPLE_HARMONIC_FUNCTION
SHF = a * sin(w * (x-x0) - phi) + b
The FOURIER_COSINE_SERIES is defined :
F(x) =aj*Tj(x-x0), where the Tj are: Tj(x-x0)=cos{j * w * (x-x0)}
The FOURIER_SINE_SERIES is defined as:
F(x) =aj*Tj(x-x0), where the Tj are: Tj(x-x0)=sin{j * w * (x-x0)}