shanwavf function

Complex Shannon Wavelet

Compute the Complex Shannon wavelet.

shanwavf(lb = -8, ub = 8, n = 1000, fb = 5, fc = 1)

Arguments

• lb, ub: Lower and upper bounds of the interval to evaluate the waveform on. Default: -8 to 8.
• n: Number of points on the grid between lb and ub (length of the wavelet). Default: 1000.
• fb: Time-decay parameter of the wavelet (bandwidth in the frequency domain). Must be a positive scalar. Default: 5.
• fc: Center frequency of the wavelet. Must be a positive scalar. Default: 1.

Returns

A list containing 2 variables; x, the grid on which the complex Shannon wavelet was evaluated, and psi ($\Psi$), the evaluated wavelet on the grid x.

Details

The complex Shannon wavelet is defined by a bandwidth parameter fb, a wavelet center frequency fc, and the expression

on an n-point regular grid in the interval of lb to ub.

Examples

fb <- 1
fc <- 1.5
lb <- -20
ub <- 20
n <- 1000
sw <- shanwavf(lb, ub, n, fb, fc)
op <- par(mfrow = c(2,1))
plot(sw$x, Re(sw$psi), type="l", main = "Complex Shannon Wavelet",
     xlab = "real part", ylab = "")
plot(sw$x, Im(sw$psi), type="l", xlab = "imaginary part", ylab = "")
par(op)

Author(s)

Sylvain Pelissier, sylvain.pelissier@gmail.com .

Conversion to R by Geert van Boxtel G.J.M.vanBoxtel@gmail.com .