# Ch3 Splus
# generate time series with 3 cycles

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)

par(mfrow=c(2,2))
tsplot(x1,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
tsplot(x2,main="nu=10/128, amp^2=41", ylim=c(-16,16))
tsplot(x3,main="nu=40/128, amp^2=25", ylim=c(-16,16))
tsplot(x,main="sum", ylim=c(-16,16))

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