# Test numerically determined instantaneous frequency against exact instantaneous frequency This function compares the performance of `InstantaneousFrequency` against signals of known instantaneous frequency. The known signal is of the form [REMOVE_ME]$$ x(t) = a\sin(\omega_{1} + \varphi_{1}) + b\sin(\omega_{2} + \varphi_{2}) + ca * \sin(omega_1 + phi_1) + b * sin(omega_2 + phi_2) + c [REMOVE_ME_2]$$ One can create quite complicated signals by choosing the various amplitude, frequency, and phase constants. ## Description This function compares the performance of `InstantaneousFrequency` against signals of known instantaneous frequency. The known signal is of the form $$ x(t) = a\sin(\omega_{1} + \varphi_{1}) + b\sin(\omega_{2} + \varphi_{2}) + ca * \sin(omega_1 + phi_1) + b * sin(omega_2 + phi_2) + c $$ One can create quite complicated signals by choosing the various amplitude, frequency, and phase constants. ```r 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, ...) ``` ## 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. ## Returns - **instfreq$sig**: The time series - **instfreq$analytic**: The exact instantaneous frequency - **instfreq$numeric**: The numerically-derived instantaneous frequency from `InstantaneousFrequency` ## Author(s) Daniel C. Bowman danny.c.bowman@gmail.com ## Examples ```r #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) ``` ## See Also `InstantaneousFrequency`

PrecisionTester function