changing frequency and divide 2 section

hi everyone,

i have created a sinusoidal signal having frequency 100Hz in MATLAB. In below you see the code, i want to ask 2 thing.

1. Firstly, i want to divide 2 sections. 1st half 100hz and 2nd half 500hz.
2. Secondly, frequency starting 100hz and increasing to 1000hz. 100 to 1000.

fSampling = 10000;          %Sampling Frequency
tSampling = 1/fSampling;    %Sampling Time
L = 10000;                  %Length of Signal
t = (0:L-1)*tSampling;      %Time Vector
F = 100;                    %Frequency of Signal

%%Signal Without Noise
xsig = sin(2*pi*F*t);
subplot(2,1,1)
plot(t,xsig);
grid on;
axis([0 0.1 -1.2 +1.2])
xlabel('\itTime Axis \rightarrow');
ylabel('\itAmplitude \rightarrow');
title('\itxsig(t) of Frequency = 100Hz');
pause(2);

%%Frequency Transform of above Signal
subplot(2,1,2)
NFFT = 2^nextpow2(L);
Xsig = fft(xsig,NFFT)/L;
f1 = fSampling/2*(linspace(0,1,NFFT/2+1));
semilogy(f1,2*abs(Xsig(1:NFFT/2+1)),'r');
grid on;
axis([-50 500 1.0000e-005 1])
title('\itSignle-Sided Amplitude Sepectrum of xsig(t)');
xlabel('\itFrequency(Hz) \rightarrow');
ylabel('|Xsig(f)| \rightarrow');
pause(2);

%%Addition of Noise in Signal when Signal is Transmitted over some
% transmission medium
xnoise = xsig +0.25*randn(size(t));
figure;
subplot(2,1,1)
plot(t,xnoise,'r');
grid on;
xlabel('\itTime Axis \rightarrow');
ylabel('\itAmplitude \rightarrow');
title('\itxnoise(t) of Frequency = 100Hz (Noise Addition)');
pause(2);

%%Frequency Transform of the Noisy Signal
subplot(2,1,2)
NFFT = 2^nextpow2(L);
XNoise = fft(xnoise,NFFT)/L;
f1 = fSampling/2*(linspace(0,1,NFFT/2+1));
semilogy(f1,2*abs(XNoise(1:NFFT/2+1)),'r');
grid on;
axis([-50 500 1.0000e-005 1])
title('\itSingle-Sided Amplitude Spectrum of xnoise(t)');
xlabel('\itFrequency(Hz) \rightarrow');
ylabel('|XNoise(f)| \rightarrow');
pause(2);

%%Comparision of both Spectrums
figure;
subplot(2,1,1)
semilogy(f1,2*abs(Xsig(1:NFFT/2+1)));
grid on;
axis([-50 500 1.0000e-005 1])
title('\itSingle-Sided Amplitude Spectrum of xsig(t)');
xlabel('\itFrequency(Hz) \rightarrow');
ylabel('|Xsig(f)| \rightarrow');

subplot(2,1,2)
semilogy(f1,2*abs(XNoise(1:NFFT/2+1)),'r');
grid on;
axis([-50 500 1.0000e-005 1])
title('\itSingle-Sided Amplitude Spectrum of xnoise(t)');
xlabel('\itFrequency(Hz) \rightarrow');
ylabel('|XNoise(f)| \rightarrow');

Answer 1

[Geoff Hayes]

Deniz - if I understand your question correctly, for the part one you want the first section (the first 5000 samples) to be generated from a sinusoidal signal at 100 Hz and the second section (the remaining 5000 samples) to be generated from a sinusoidal signal at 500 Hz. Look at how your are generating your signal

 xsig = sin(2*pi*F*t);

where F is 100 Hz. This would be equivalent to

 a = ones(1,L);
 xsig = sin(2*pi*F*a.*t);

where we F*a is just an array with all elements equal to 100 Hz. Then, F*a.*t is just he pairwise multiplication of each element of F*a with t. This doesn't change what you have already - we are still generating a 100 Hz sinusoidal signal. But to get the second half at 500 Hz, we just set the second half of a to 5 so that F*a is an array of 100s (the first half) and 500s (the second half)

 a = ones(1,L); % or a = ones(size(t));
 a(L/2+1:end) = 5;
 xsig = sin(2*pi*F*a.*t);

Now, for your second part, you want the frequency to run from 100 Hz to 1000 Hz. Does this mean you want a linear transition from 100 Hz to 1000 Hz, or every one hundred samples to be at a multiple of 100 Hz or something else? Do you expect to analyze this data using the same code from above or with something else?