# Ch3 R
# generate time series with 3 cycles

library(ts)

t <- 1:128
x1 <- 2*cos(2*pi*t*6/128) + 3*sin(2*pi*t*6/128)
x2 <- 4*cos(2*pi*t*10/128) + 5*sin(2*pi*t*10/128)
x3 <- 3*cos(2*pi*t*40/128) + 4*sin(2*pi*t*40/128)
x <- x1+x2+x3

min(x)
max(x)

x1 <- ts(x1)

win.graph()
par(mfrow=c(2,2))
ts.plot(x1,gpars=list(main="nu=6/128, amp^2=13", ylim=c(-16,16)))
# in above amp^2=2^2+3^3=13 is the square of the amplitude
ts.plot(x2,gpars=list(main="nu=10/128, amp^2=41", ylim=c(-16,16)))
ts.plot(x3,gpars=list(main="nu=40/128, amp^2=25", ylim=c(-16,16)))
ts.plot(x,gpars=list(main="sum", ylim=c(-16,16)))

# the periodogram of x
win.graph()
par(mfrow=c(1,1))
d <- fft(x)/length(x)
per <- abs(d)^2
freq <- (0:64)/128
per <- per[1:65]
plot(freq,per,type="l")

# try it this way 
win.graph()
spectrum(x, method="pgram", plot=T)
# what is that? 
# ok try this
win.graph()
spec.pgram(x, detrend=F, demean=F, plot=T)
# Note dB=decibel, and the value S in dBs is  10log_10 S