diric {gsignal}

Dirichlet function

Description

Compute the Dirichlet or periodic sinc function.

Usage

diric(x, n)

Arguments

x

Input array, specified as a real scalar, vector, matrix, or multidimensional array. When x is non-scalar, diric is an element-wise operation.

n

Function degree, specified as a positive integer scalar.

Details

y <- diric(x, n) returns the Dirichlet Function of degree n evaluated at the elements of the input array x.

The Dirichlet function, or periodic sinc function, has period 2 \pi for odd N and period 4 \pi for even N. Its maximum value is 1 for all N, and its minimum value is -1 for even N. The magnitude of the function is 1 / N times the magnitude of the discrete-time Fourier transform of the N-point rectangular window.

Value

Output array, returned as a real-valued scalar, vector, matrix, or multidimensional array of the same size as x.

Author(s)

Sylvain Pelissier, [e-mail].
Conversion to R by Geert van Boxtel [e-mail].

Examples

## Compute and plot the Dirichlet function between -2pi and 2pi for N = 7
## and N = 8. The function has a period of 2pi for odd N and 4pi for even N.
x <- seq(-2*pi, 2*pi, len = 301)
d7 <- diric(x, 7)
d8 <- diric(x, 8)
op <- par(mfrow = c(2,1))
plot(x/pi, d7, type="l", main = "Dirichlet function",
     xlab = "", ylab = "N = 7")
plot(x/pi, d8, type="l", ylab = "N = 8", xlab = expression(x / pi))
par(op)