Matlab code for sine wave with varying frequency

How do I generate a sine wave with varying frequency and constant amplitude? I've tried the following code, but it is showing harmonics. How do i eliminate the harmoics?

clc;
fs = 2000; %sampling frequency
dt = 1/fs; %seconds per sample
StopTime = 10; %seconds
t = (0:dt:StopTime);
F = 50.*t; %Sinewave frequency {Hertz)
amp = 1000; 
for i= 1:length(t);
    data(i) = amp*sin(2*pi*F(i)*t(i));
end;
audiowrite('varFsin.wav', data, fs);
sound(data);
figure(1)
clf(1);
plot(t, data)
title('Sine Wave');
figure(2)
spectrogram(data, [80], [40], [256], fs, 'yaxis')
y = fft{data};
n = length(data); %number of samples
f = (0:n-1)*(fs/n); %frequency range
power = abs(y).^2/n; %power of the DFT
figure(3);
plot(f, power)
xlbel('frequency')
ylabel('power')

Answer 1

[Chunru]

clc;
fs = 2000; %sampling frequency
dt = 1/fs; %seconds per sample
StopTime = 10; %seconds
t = (0:dt:StopTime);
F = 50.*t; %Sinewave frequency {Hertz)
amp = 1000; 

The following is equivalent to LFM (linear frequency modulation) signal.

for i= 1:length(t);
    data(i) = amp*sin(2*pi*F(i)*t(i));
end;
%audiowrite('varFsin.wav', data, fs);
sound(data);
figure(1)
clf(1);
plot(t, data)
title('Sine Wave');

figure(2)
spectrogram(data, [80], [40], [256], fs, 'yaxis')

y = fft(data);
n = length(data); %number of samples
f = (0:n-1)*(fs/n); %frequency range
power = abs(y).^2/n; %power of the DFT

figure(3);
powershift = fftshift(power);
fshift = (-n/2:n/2-1)*(fs/n); % zero-centered frequency range
plot(fshift,powershift)

xlabel('frequency')
ylabel('power')

This is not really harmonic. The spectrum has transition region around 0 and +/-fs/2. You have no harmonics to remove.

[Anisia Anil]

Thanks for the help