Description Usage Arguments Details Value Note Author(s) References Examples
The Fourier approximation is determined for any function on domain (0, 2π) and then graphed.
1 |
f |
The function to be approximated by Fourier analysis. |
order |
Integer; the order of the Fourier transformation. |
... |
Optional arguments to be passed to the |
The numerical output consists of a_0/2, a_1, ..., a_n, b_1, ..., b_2. The equation is (constant) + a_1 cos(x) + ... + a_n cos(n x) + b_1 sin(x) + ... + b_n sin(n x).
constant |
The constant term. |
cosine.coefficients |
The coefficients for the cosine terms. |
sine.coefficients |
The coefficients for the sine terms. |
The formulas computed within fourier
are based on the textbook by Larson (2013).
Steven T. Garren, James Madison University, Harrisonburg, Virginia, USA
Larson, R. (2013) Elementary Linear Algebra, 7th edition.
1 2 3 4 5 6 |
$constant
[1] -0.342076
$cosine.coefficients
[1] -0.5009337 -0.2384993 -0.1256040 -0.0754238
$sine.coefficients
[1] -0.3420760 -0.3499125 -0.2814973 -0.2269386
$approximation
[1] "g(x) = -0.342 - 0.501 cos x - 0.342 sin x - 0.238 cos 2x - 0.35 sin 2x - 0.126 cos 3x - 0.281 sin 3x - 0.0754 cos 4x - 0.227 sin 4x"
$constant
[1] 0.1588577
$cosine.coefficients
[1] 0.158857730 0.063543092 0.031771546 0.018689145 0.012219825 0.008586904
[7] 0.006354309
$sine.coefficients
[1] 0.15885773 0.12708618 0.09531464 0.07475658 0.06109913 0.05152143 0.04448016
$approximation
[1] "g(x) = 0.159 + 0.159 cos x + 0.159 sin x + 0.0635 cos 2x + 0.127 sin 2x + 0.0318 cos 3x + 0.0953 sin 3x + 0.0187 cos 4x + 0.0748 sin 4x + 0.0122 cos 5x + 0.0611 sin 5x + 0.00859 cos 6x + 0.0515 sin 6x + 0.00635 cos 7x + 0.0445 sin 7x"
$constant
[1] 0
$cosine.coefficients
[1] 0 0 0 0 0
$sine.coefficients
[1] -2.0000000 -1.0000000 -0.6666667 -0.5000000 -0.4000000
$approximation
[1] "g(x) = - 2 sin x - 1 sin 2x - 0.667 sin 3x - 0.5 sin 4x - 0.4 sin 5x"
$constant
[1] 3.289868
$cosine.coefficients
[1] 4.0000000 1.0000000 0.4444444
$sine.coefficients
[1] 0 0 0
$approximation
[1] "g(x) = 3.29 + 4 cos x + 1 cos 2x + 0.444 cos 3x"
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