trigApprox: Trigonometric Approximation In pracma: Practical Numerical Math Functions

Description

Computes the trigonometric series.

Usage

 `1` ```trigApprox(t, x, m) ```

Arguments

 `t` vector of points at which to compute the values of the trigonometric approximation. `x` data from `t=0` to `t=2*(n-1)*pi/n`. `m` degree of trigonometric regression.

Details

Calls `trigPoly` to get the trigonometric coefficients and then sums the finite series.

Value

Vector of values the same length as `t`.

Note

TODO: Return an approximating function instead.

`trigPoly`
 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18``` ```## Not run: ## Example: Gauss' Pallas data (1801) asc <- seq(0, 330, by = 30) dec <- c(408, 89, -66, 10, 338, 807, 1238, 1511, 1583, 1462, 1183, 804) plot(2*pi*asc/360, dec, pch = "+", col = "red", xlim = c(0, 2*pi), ylim = c(-500, 2000), xlab = "Ascension [radians]", ylab = "Declination [minutes]", main = "Gauss' Pallas Data") grid() points(2*pi*asc/360, dec, pch = "o", col = "red") ts <- seq(0, 2*pi, len = 100) xs <- trigApprox(ts ,dec, 1) lines(ts, xs, col = "black") xs <- trigApprox(ts ,dec, 2) lines(ts, xs, col = "blue") legend(3, 0, c("Trig. Regression of degree 1", "Trig. Regression of degree 2", "Astronomical position"), col = c("black", "blue", "red"), lty = c(1,1,0), pch = c("", "", "+")) ## End(Not run) ```