gsignal (version 0.3-1)

shanwavf: Complex Shannon Wavelet

Description

Compute the Complex Shannon wavelet.

Usage

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.

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.

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

# NOT RUN {
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)

# }