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

# Generate a 5 second 1 kHz signal at 44.1 kHz sampling
	f <- 500			# central frequency
	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
	rg <- 100			# range of random values about zero

# Increment time samples at 44.1 kHz
	t <- seq(rate*time)/rate		# time increments

# Generate a random frequency spectrum
# First value is zero so the mean of the transform is zero
# Second half of the series is an inverted order complex conjugate to insure real values
# The middle value is not duplicated and is real, so [1] and [rate*time/2+1] are not copied
	w1 <- runif(rate*time/2+1, min=-rg, max=rg) + runif(rate*time/2+1, min=-rg, max=rg)*1i
	w1[1] <- 0.0
	w1[rate*time/2+1] <- runif(1, min=-rg, max=rg)
	w2 <- Conj(rev(w1[2:(rate*time/2)]))
	w <- c(w1, w2)	

# Set values for an octave bandpass about the central frequency
	df <- 1/time				# Frequency resolution
	nl <- as.integer(f/sqrt(2)/df)	# Location of low end of pass band
	nh <- as.integer(f*sqrt(2)/df)	# Location of high end of pass band

# Remove the lower frequencies
	w[2:(nl+1)] <- 0
	w[(length(w)-(nl-1)):length(w)] <- 0

# Remove the higher frequencies
	w[(nh+1):(length(w)-(nh-1))] <- 0

# Inverse FFT to generate white noise
	u <- fft( w, inverse=TRUE)

# Rescale the amplitude
	u1 <- as.real(u)
	u2 <- u1*amp/max(abs(u1))
	final <- as.integer( u2 )

# 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] )

# Check the frequencies octave bandwidth
	wl <- f/sqrt(2)
	wh <- f*sqrt(2)
	lines( c(wl,wl), c(0,max(ff)), col=2, lwd=2)
	lines( c(wh,wh), c(0,max(ff)), col=2, lwd=2)

# Fade the signal in and out
	audio <- u2*(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 White500.txt
	write( final, file="White500.txt", ncolumns = 1 )
#	play( final )