#### program2

##### Newbie level 1

i have sinwave with 0.1 v amplitude and 1khz frequency mixed with 5v white noise.

i used FFT in Matlab to simulate.

1-(

*Study the use of additional mean value calculation of every data set of FFT spectrum and how it affects the visibility of a present signal*.). so, how can i use additional mean value???????????

2-

*Which window is the best for detecting weak signals in a noisy background?*

i used some of windows but all are not useful!!!!!

Matlab code :

f1=1000; % Signal frequency

fs=5000; % Sampling frequency

N=128; % Number of samples

N1=2048; % Number of FFT points

p=128; % Define Number of samples noise

n=0:N-1; % Index n

f=(0:N1-1)*fs/N1; % Defining the frequency points [axis]

noise=rand(1,p); % Generate Uniformly Random Numbers

x=0.1*sin(2*pi*f1*n/fs)+5*noise; % Generate the signal

XR=abs(fft(x,N1)); % find the magnitude of the FFT using No

% windowing (i.e. Rectangular window)

xh=hamming(N); % Define the hamming samples

xw1=x .* xh'; % Window the signal

XH=abs(fft(xw1,N1)); % find the magnitude of the FFT of the

% windowed signal.

xha=hanning(N); % Define the hanning samples

xw2=x .* xha'; % Window the signal

XHA=abs(fft(xw2,N1)); % find the magnitude of the FFT of the

% windowed signal.

xbl=blackman(N); % Define the blackman samples

xw3=x .* xbl'; % Window the signal

XBL=abs(fft(xw3,N1)); % find the magnitude of the FFT of the

% windowed signal.

xba=bartlett(N); % Define the bartlett samples

xw4=x .* xba'; % Window the signal

XBA=abs(fft(xw4,N1)); % find the magnitude of the FFT of the

% windowed signal.

subplot(3,2,1); % Start plotting the signal

plot(f(1:N1/2),20*log10(XR(1:N1/2)/max(XR)));

title('Spectrum of x(t) using Rectangular Windows');

grid;

xlabel('Frequency, Hz');

ylabel('Normalised Magnitude, [dB]');

subplot(3,2,2);

plot(f(1:N1/2),20*log10(XH(1:N1/2)/max(XH)));

title('Spectrum of x(t) using Hamming Windows');

grid;

xlabel('Frequency, Hz');

ylabel('Normalised Magnitude, [dB]');

subplot(3,2,3);

plot(f(1:N1/2),20*log10(XHA(1:N1/2)/max(XHA)));

title('Spectrum of x(t) using Hanning Windows');

grid;

xlabel('Frequency, Hz');

ylabel('Normalised Magnitude, [dB]');

subplot(3,2,4); % Start plotting the signal

plot(f(1:N1/2),20*log10(XBL(1:N1/2)/max(XBL)));

title('Spectrum of x(t) using Blackman Windows');

grid;

xlabel('Frequency, Hz');

ylabel('Normalised Magnitude, [dB]');

subplot(3,2,5); % Start plotting the signal

plot(f(1:N1/2),20*log10(XBA(1:N1/2)/max(XBA)));

title('Spectrum of x(t) using Bartlett Windows');

grid;

xlabel('Frequency, Hz');

ylabel('Normalised Magnitude, [dB]');

any explain please!!!!