PrecisionTester: Test numerically determined instantaneous frequency against exact instantaneous frequency

Description

This function compares the performance of InstantaneousFrequency against signals of known instantaneous frequency. The known signal is of the form $$ x(t) = a\sin(\omega_{1} + \varphi_{1}) + b\sin(\omega_{2} + \varphi_{2}) + c$$ One can create quite complicated signals by choosing the various amplitude, frequency, and phase constants.

Usage

PrecisionTester(tt = seq(0, 10, by = 0.01), method = "arctan", lag = 1, 
    a = 1, b = 1, c = 1, omega.1 = 2 * pi, omega.2 = 4 * pi, 
    phi.1 = 0, phi.2 = pi/6, plot.signal = TRUE, 
    plot.instfreq = TRUE, plot.error = TRUE, new.device = TRUE, ...)

Value

instfreq$sig: The time series
instfreq$analytic: The exact instantaneous frequency
instfreq$numeric: The numerically-derived instantaneous frequency from InstantaneousFrequency

Arguments

tt: Sample times.
method: How the numeric instantaneous frequency is calculated, see InstantaneousFrequency
lag: Differentiation lag, see the diff function in the base package.
a: Amplitude coefficient for the first sinusoid.
b: Amplitude coefficient for the second sinusoid.
c: DC shift
omega.1: Frequency of the first sinusoid.
omega.2: Frequency of the second sinusoid.
phi.1: Phase shift of the first sinusoid.
phi.2: Phase shift of the second sinusoid.
plot.signal: Whether to show the time series.
plot.instfreq: Whether to show the instantaneous frequencies, comparing the numerical and analytical result.
plot.error: Whether to show the difference between the numerical and analytical result.
new.device: Whether to open each plot as a new plot window (defaults to TRUE). However, Sweave doesn't like dev.new(). If you want to use PrecisionTester in Sweave, be sure that new.device = FALSE
...: Plotting parameters.

Author

Daniel C. Bowman danny.c.bowman@gmail.com

Examples

Run this code


#Simple signal
tt <- seq(0, 10, by = 0.01)
a <- 1
b <- 0
c <- 0
omega.1 <- 30 * pi
omega.2 <- 0
phi.1 <- 0
phi.2 <- 0
PrecisionTester(tt, method = "arctan", lag = 1, a, b, c, 
    omega.1, omega.2, phi.1, phi.2)

#That was nice - what happens if we use the "chain" method...?

PrecisionTester(tt, method = "chain", lag = 1, a, b, c, 
    omega.1, omega.2, phi.1, phi.2)

#Big problems!  Let's increase the sample rate

tt <- seq(0, 10, by = 0.0005)
PrecisionTester(tt, method = "chain", lag = 1, a, b, c, 
omega.1, omega.2, phi.1, phi.2)

#That's better

#Frequency modulations caused by signal that is not symmetric about 0

tt <- seq(0, 10, by = 0.01)
a <- 1
b <- 0
c <- 0.25
omega.1 <- 2 * pi
omega.2 <- 0
phi.1 <- 0
phi.2 <- 0

PrecisionTester(tt, method = "arctan", lag = 1, a, b, c, 
omega.1, omega.2, phi.1, phi.2)

#Non-uniform sample rate
set.seed(628)
tt <- sort(runif(500, 0, 10))
a <- 1
b <- 0
c <- 0
omega.1 <- 2 * pi
omega.2 <- 0
phi.1 <- 0
phi.2 <- 0

PrecisionTester(tt, method = "arctan", lag = 1, a, b, c, 
omega.1, omega.2, phi.1, phi.2)