dq.algorithm: Calculates instantaneous frequency of freqeuncy carriers using the DQ method

Description

Calculates instantaneous frequency of frequency carriers using the direct quadrature method from Huang et al., 2009.

Usage

dq.algorithm(fc, dt)

Arguments

a matrix of amplitude between -1 and 1, making up the frequency carrier

a vector of depth or time values

Value

a list of the depth/time (dt), frequency (f), and identity tuning (idt), i.e. depths adapted to transform the frequency carrier into a cosine of period 1.

References

Huang, Norden E., Zhaohua Wu, Steven R. Long, Kenneth C. Arnold, Xianyao Chen, and Karin Blank. 2009. "On Instantaneous Frequency". Advances in Adaptive Data Analysis 01 (02): 177<U+2013>229. https://doi.org/10.1142/S1793536909000096.

Examples

Run this code

# NOT RUN {
n <- 600

t <- seq_len(n)

p1 <- 30

xy <- sin(t*2*pi/p1 + 50)

int <- c(rep(1, 99 + 100), seq(1,3,2/100), seq(3,1,-2/100), rep(1,100 + 99))

dt <- cumsum(int)

cond <- dt < 75

xy <- xy[!cond]
dt <- dt[!cond]/1.2 - 62.5

res <- dq.algorithm(xy, dt)

opar <- par("mfrow")

par(mfrow = c(3,1))

plot(dt, xy, type = "o", pch = 19, main = "Frequency carrier")

plot(dt, 1/res$f, pch = 19, type = "l", log = "y", lwd = 2, ylim = c(25,80),
     main = "Period (Direct Quadrature method)", ylab = "Period")

plot(res$idt[,1], xy, type = "o", pch = 19,
     main = "Identity tuning", axes = FALSE, ylab = "xy", xlab = "dt")

ap <- approx(x = dt, y = res$idt[,1], xout = seq(0,600, by = 20))

axis(1, at = ap$y, labels = ap$x)
axis(2)
box()

par(mfrow = opar)

# }