# observe the effect of convolution (filtering) in the frequency domain
N = 2048
y = runif(N,min=-.5,max=.5) # while noise (flat freq spectrum)
a = c(1,1,1,1,1)/5 # our filter
z = filter(y,a,method="conv",circular=T) # filter (convolve) the y with a
Y = fft(y) # the freq spectrum of filtered data
plot(Mod(Y[1:(N/2)]))
#stopp
Z = fft(z) # the freq spectrum of filtered data
plot(Mod(Z[1:(N/2)])) # plot relevant values
#stopp;
aa = c(a,rep(0,N-length(a))) # pad filter with zeros to get
# same length as y
A = fft(aa) # the transform of the filter
lines(20*Mod(A[1:(N/2)]),col="red") # add plot of filter transform.
# note that FFT(data) x FFT(filter) = FFT(filtered data)