# Clear the Workspace
	rm (list=ls())

# Generate a 5 second 1 kHz signal at 44.1 kHz sampling
	f <- 500			# central frequency
	omega <- 2*pi*f		# central angular frequencey
	amp <- 26213		# amplitude of the wave
	tau <- 0.015		# fade in and out time constant
	time <- 5			# time duration in seconds
	rate <- 44100		# audio file sample rate
	len <- time *rate		# length of the file
	wf <- 4			# warble rate in times per second
	womega <- 2*pi*wf		# warble angular frequency
	wa <- 37.5			# amplitude of phase shift

# Increment time samples at 44.1 kHz
	t <- seq(rate*time)/rate		# time increments
	ph <- wa*sin(womega*t)			# shift the phase
	poffset <- 2*pi*wa			# offset on the phase to prevent a negative angle
	theta <- poffset + omega*t - ph	# time dependent angle

	audio <- amp*sin(theta)			# generate warble for analysis
	final <- as.integer(audio)

# Analyze the results
#	plot( final, pch="." )
#	lines( c(1, length(final)), c(0,0) )
	lwin <- 1
	hwin <- 10000
	ff <- Mod( fft( final )[1:(length(final)/2)] )
	feq <- (seq(length(ff))-1)*rate/length(final)
	plot( feq[lwin:hwin], ff[lwin:hwin] )

# Most of the frequency content falls +- wa*wf from the central frequency
	lines( c(f-wa*wf,f-wa*wf), c(0,max(ff)), col=2, lwd=2)
	lines( c(f+wa*wf,f+wa*wf), c(0,max(ff)), col=2, lwd=2)

# Fade the signal in and out
	audio <- amp*sin(theta)*(1-exp(-t/tau))*(1-exp(-(time-t)/tau))

# Append zero a 1/2 second before and 1/2 second after
	t1 <- seq(rate/2)*0
	final <- as.integer(c(t1, audio, t1))

# Save the file to Warble500.txt
	write( final, file="Warble500.txt", ncolumns = 1 )
	play( final )