gsignal (version 0.3-7)

shanwavf: Complex Shannon Wavelet

Description

Compute the Complex Shannon wavelet.

Usage

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

Value

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.

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.

Author

Sylvain Pelissier, .
Conversion to R by Geert van Boxtel .

Details

The complex Shannon wavelet is defined by a bandwidth parameter fb, a wavelet center frequency fc, and the expression $$\psi(x) = (fb^{0.5} * (sinc(fb * x) * e^{2 * 1i * pi * fc * x}))$$ 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)