smoothspec=function(y,deltaT)
{

N = length(y)
freqs=2*pi*(1:round((N/2)))/N
plotfreqs=freqs/(2*pi*(deltaT))
nfreq=length(freqs)
a = 1:nfreq
b = 1:nfreq

nlag = N-1
#nlag = 150
c=acf(y,type="covariance",lag.max=nlag)$acf

#lag window width
M = round(N/10)		# M should be even
if(M %% 2 > 0)M=M+1
# try different Window widths and different window types....

#Parzen Window..
lambdas=1:M
lambdas[1:(M/2)]=1-(6*((lambdas[1:(M/2)]/M)^2))+ (6*((lambdas[1:(M/2)]/M)^3))
lambdas[((M/2)+1):M]=2*((1-(lambdas[((M/2)+1):M]/M))^3)
lambda0=1
degf=3.709*N/M

#Tukey window..
#lambdas=1:M
#lambdas[1:M]=0.5*(1+cos(pi*(1:M)/M))
#lambda0=1
#degf=8*N/(3*M)

# number of frequencies possible..
freqs=2*pi*(1:round((N/2)))/N
plotfreqs=freqs/(2*pi*(deltaT))
nfreq=length(freqs)

tordf=1:round((N/2))
tord=1:N

# compute the smoothed periodgram/spectrum.. - Equation 12.3.15 Wei

pgrams=1:nfreq

for(i in 1:nfreq){
pgrams[i]=((lambda0*c[1]) + (2*sum(lambdas*c[2:(M+1)]*cos(freqs[i]*(1:M)))))/pi
}

pgrams
}