R: Trigonometric Approximation

trigApprox {pracma} | R Documentation

## Trigonometric Approximation

### Description

Computes the trigonometric series.

### Usage

    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.

### See Also

`trigPoly`

### Examples

    ## 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)

[Package pracma version 2.0.4 Index]