How to add noise to sine signal and filter it?

Hi. I have two questions. 1) How to add noise with specific frequency (for example 2kHz-4kHz) to sine signal? 2) How to filter that signal (for example by using a bandpass filter) Please help me!

Answer 1

[matico]

Here I didn't use bandpass filters, but I just remove some harmonics from a signal using FFT and IFFT. The signal has got high 5th harmonics, which I want to include. Higher than that I want to remove. You can play with this in line: yFFT(7:end-7) = 0;

If you write:

 yFFT(2:end-2) = 0;

Then you include only 0th harmonics -> this is offset (1.5 in my case).

 yFFT(3:end-3) = 0;

You include offset + 1st harmonics. ...

 yFFT(7:end-7) = 0;

Here are included offset and first 5 harmonics.

%%Create signal
clear; clc;

fSampling = 5000;            % Hz
tSample = 1/fSampling;
T = 0:tSample:1-tSample;     % 1s  

Offset = 1.5;
F1 = 5; A1 = 3;
NoiseAmp = 0.5;

Sig = Offset + A1*sin(2*pi*F1*T) + NoiseAmp*(rand(1,length(T))-0.5);

 %%FFT -> choose harmonics -> IFFT

yFFT = fft(Sig);
yFFT(7:end-7) = 0;  % Play with numbers. Both must be the same
yFiltFFT = real(ifft(yFFT));

plot(T,Sig, T, yFiltFFT); grid;

Edit: Upps, now I see that you have specified frequency for a noise.