# trigPoly: Trigonometric Polynomial

### Description

Computes the trigonometric coefficients.

### Usage

 1 trigPoly(x, m) 

### Arguments

 x data from t=0 to t=2*(n-1)*pi/n. m degree of trigonometric regression.

### Details

Compute the coefficients of the trigonometric series of degree m,

a_0 + ∑_k(a_k \cos(k t) + b_k \sin(k t))

by applying orthogonality relations.

### Value

Coefficients as a list with components a0, a, and b.

### Note

For irregular spaced data or data not covering the whole period, use standard regression techniques, see examples.

### References

Fausett, L. V. (2007). Applied Numerical Analysis Using Matlab. Second edition, Prentice Hall.

trigApprox

### Examples

  1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 # Data available only from 0 to pi/2 t <- seq(0, pi, len=7) x <- 0.5 + 0.25*sin(t) + 1/3*cos(t) - 1/3*sin(2*t) - 0.25*cos(2*t) # use standard regression techniques A <- cbind(1, cos(t), sin(t), cos(2*t), sin(2*t)) ab <- qr.solve(A, x) ab # [1] 0.5000000 0.3333333 0.2500000 -0.2500000 -0.3333333 ts <- seq(0, 2*pi, length.out = 100) xs <- ab[1] + ab[2]*cos(ts) + ab[3]*sin(ts) + ab[4]*cos(2*ts) +ab[5]*sin(2*ts) ## Not run: # plot to make sure plot(t, x, col = "red", xlim=c(0, 2*pi), ylim=c(-2,2), main = "Trigonometric Regression") lines(ts, xs, col="blue") grid() ## End(Not run) 

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