It seems you don't know how to even start. I'll try to guide you a bit.
Matlab will be really useful to you. First, you need to understand the basics. You can find lots of tutorials, for example, this one: http://users.ece.gatech.edu/bonnie/book/TUTORIAL/tutorial.html
Then, once you know how to work with the software, you need to create a script that does the following.
- Generate the two sinusoidal components (x1 and x2) and add them into x=x1+x2.
- Generate the noise in a matrix n of the same length. I assume you are usign White Gaussian Noise, so you can check out this function: http://www.mathworks.es/help/toolbox/comm/ref/wgn.html
- Get the noisy signal xn.
- Compute Xnf and Xf as the spectrums for xn and x. I have always used the following base code, inserting proper values in the "...". Remember Nyquist Sampling Theorem!
Fs = ...; inct = 1/Fs; %Sampling frequency
T = ...; % T*Fs samples
N = Fs*T; % = T/inct;
t = [0:1/Fs:T-1/Fs]; % Time samples for T seconds [0,T)
f = [-Fs/2:Fs/N:Fs/2 – Fs/N]; % Frequency [-Fs/2,Fs/2)
Xf=fftshift(inct*fft(x)) %check fft and fftshift help, as well as FT theory.
Now you can design the filter in the frequency domain. I assume you can go for an ideal filter. You can call it Hf. Now, because of convolution FT property, Y(w)=H(w)X(w). No need for convolution!
Now check the performance. I don't know what "performance" refers to, but I think it has something to do with signal and noise power. If so, keep in mind that you don't need to compute an integral. MATLAB handles discrete signals so you can use the sum function instead.