pracma (version 1.9.9)

trigApprox: 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.

Value

Vector of values the same length as t.

Details

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

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)