somethings wrong with LPF filter?

Hi all, I want to simulate a LPF Filter with parameters: fc=5Khz,Fs=20.5Khz, N =30, Hamming window.

so I initialized a sine wave with fcarrrier = 20Khz, each sine wave was initialized with 200 sample. then it was multiplied by itself! following this code below:

      % code
M=200; % the number of sample of sine periodic
fcarrier=1e4;
T=128/fcarrier; % time to transmit sine wave
P=128; % the number of sine wave initialized!
 t=0: T/M/P: T-T/M/P;
 fs=length(t)/(T-T/M/P);
 df=1/(T-T/M/P);
 f=-fs/2:df:fs/2-df;
 s=sin(2*pi*fcarrier*t);
 s1=s.*s;
 % fc=5Khz,fs= 20.5Khz, N=30,Hamming
 Num=[-0.00142569822564206,0.00104684023675550,0.00257766825164500,-0.00197666192599148,-0.00613453687959036,0.00369061404220200,0.0132498601493775,-0.00590859914987426,-0.0257994044307132,0.00825012956971075,0.0481483043656084,-0.0103040044663240,-0.0961937471263727,0.0117048121269473,0.315044085886135,0.488060675152253,0.315044085886135,0.0117048121269473,-0.0961937471263727,-0.0103040044663240,0.0481483043656084,0.00825012956971075,-0.0257994044307132,-0.00590859914987426,0.0132498601493775,0.00369061404220200,-0.00613453687959036,-0.00197666192599148,0.00257766825164500,0.00104684023675550,-0.00142569822564206];
 s2=filter(Num,1,s1);
 figure(1)
 subplot(2,1,1)
 plot(s)
  title('sine initialized');
 subplot(2,1,2)                                                                                                                                                                              
 plot(f,abs(fftshift(fft(s))))
 figure(2)
 subplot(2,1,1)
 plot(s1)
 title('sine after mul');
 subplot(2,1,2)
 plot(f,abs(fftshift(fft(s1))))
  figure(3)
 subplot(2,1,1)
 plot(s2)
 title('sine after filtering')
 subplot(2,1,2)
 plot(f,abs(fftshift(fft(s2))))

the filter seem does not effect the sine wave, the spectrum of sine wave after filtering seem similar with sine wave after mul! Can anyone help me out! thanks

Answer 1

[Ngoc Lam]

with these picture was specified below: 1. the origin sine wave

2. the signal after multiplying

3. the signal after filtering

Answer 2

[Ngoc Lam]

as you can see, the filter does not effect to the signal after multiplying, anyone can help me? thanks