EEG DWT : How to get desired frequency spectrum after DWT

Hi, I am working on EEG signal. At first i applied the Butterworth Low Pass Filter to extract 0-64 Hz frequency. Then i applied DWT to extract BETA (16-32Hz) and ALPHA(8-16Hz) wave . So, according to theory , 2nd and 3rd level coefficient of DWT should provide the beta and alpha wave. But when i performed the fft of D3 wave i did not get the desired spectrum. I cant understand the problem. Please help.......

Following is my code. I used the EEG DATASET-1 of the following link....... https://sites.google.com/site/projectbci/

MATLAB CODE:

clc

clear all

load('C:\Users\COOL\Documents\MATLAB\Subject1_1D.mat');

fs=500;

T=1/fs; %T=.002

tmax=3;

Nsamps = tmax*fs;

t = 0:1/fs:tmax-1/fs;

s = right(6,1:1500);

l_s = length(s);

%Plot in Time Domain Original EEG

figure(1)

plot(t,s)

xlabel('Time (s)')

ylabel('Amplitude (V)')

title('Original Signal')

ylim([-100 100])

grid

%Spectrum of origonal EEG

N = fs;

S=fft(s,N);

CS=[S(1:N/2+1)];

freq=[0:N/2]/(N*T);

mag=abs(CS);

figure(2);

plot(freq,mag);

title('Spectrum of Original Signal')

xlabel('Frequency (Hz)');

ylabel('Amplitude');

ylim([0 1000])

grid

%Apply butterworth Low Pass Filter

N=6;

Wn_t = 64/fs;

[c,d] = butter(N,Wn_t);

s1 = filtfilt(c, d, s);

%Spectrum of filtered EEG N = fs;

S=fft(s1,N);

CS=[S(1:N/2+1)];

freq=[0:N/2]/(N*T);

mag=abs(CS);

figure(3);

plot(freq,mag);

title('Spectrum of filtered Signal')

xlabel('Frequency (Hz)');

ylabel('Amplitude');

ylim([0 1000])

grid %Perform DWT

[C,L] = wavedec(s1,3,'db4');

cA5 = appcoef(C,L,'db4',3);

cD3 = detcoef(C,L,3);

cD2 = detcoef(C,L,2);

cD1 = detcoef(C,L,1);

A3 = wrcoef('a', C, L,'db4',3);

D3 = wrcoef('d',C,L,'db4',3);

D2 = wrcoef('d',C,L,'db4',2);

D1 = wrcoef('d',C,L,'db4',1);

%Spectrum of filtered D3(Level 3 coefficient reconstructed)

N = fs;

S=fft(D3,N);

CS=[S(1:N/2+1)];

freq=[0:N/2]/(N*T);

mag=abs(CS);

figure(4);

plot(freq,mag);

title('Spectrum of D3')

xlabel('Frequency (Hz)');

ylabel('Amplitude');

ylim([0 500])

xlim([0 100])

grid