problem in drawing the frequency spectrum of frequency modulated signal in matlab

here is the coding, the output of the frequency spectrum has no value... the error is

Index exceeds the number of array elements. Index must not exceed 1001.

Error in frequency_modulation (line 39)

plot(f(9500:10500),Vfm_f(9500:10500));

can anyone check? thank you so much.

fs=100000; %sampling frequency

ts = 1/fs ; % time interval between sample point

t = 0 : ts :0.02; % scale of time, maximun=0.02

N= size(t,2);

fm=100;

Vm=2*sin(2*pi*100*t);

fc=10000;

Vc=10*cos(2*pi*10000*t);

Vfm= 10*cos(2*pi*fc*t + 2*sin(2*pi*fm*t)); %modulated signal= Vfm

subplot(4,1,1);

plot(t,Vc);

ylabel('Amplitude (V)');

xlabel('Time(s)');

title('Carrier Signal Time Domain Representation');

grid on;

subplot(4,1,2);

plot(t,Vm);

ylabel('Amplitube (V)');

xlabel('Time (s)');

title('Message signal Time Domain Representation');

grid on;

subplot(4,1,3);

plot(t,Vfm);

ylabel('Amplitube (V)');

xlabel('Time (s)');

title('Frequency Modulated Signal Time Domain Representation');

grid on;

f=fs*(0:N/2)/N;

Vfm_f = (2/N)*abs(fft(Vfm,N));

subplot(4,1,4);

plot(f(9500:10500),Vfm_f(9500:10500));

ylabel('Amplitube (V)');

xlabel('Frequency(Hz)');

title('Frequency Modulated Signal Frequency Representation');

grid on;

Answer 1

[Chunru]

fs=100000;  %sampling frequency
ts = 1/fs  ;  % time interval between sample point
t = 0 : ts :0.02;   % scale of time, maximun=0.02
N= size(t,2);
fm=100;
Vm=2*sin(2*pi*100*t);
fc=10000;
Vc=10*cos(2*pi*10000*t);
Vfm= 10*cos(2*pi*fc*t + 2*sin(2*pi*fm*t)); %modulated signal= Vfm
subplot(4,1,1);  
plot(t,Vc);
ylabel('Amplitude (V)');
xlabel('Time(s)');
title('Carrier Signal Time Domain Representation');
grid on;
subplot(4,1,2);
plot(t,Vm);
ylabel('Amplitube (V)');
xlabel('Time (s)');
title('Message signal Time Domain Representation');
grid on;
subplot(4,1,3);
plot(t,Vfm);
ylabel('Amplitube (V)');
xlabel('Time (s)');
title('Frequency Modulated Signal Time Domain Representation');
grid on;
f=fs*(0:N/2)/N;
Vfm_f = (2/N)*abs(fft(Vfm,N));
Vfm_f=Vfm_f(1:floor(N/2)+1);    % take the half: positive frequency
subplot(4,1,4);
plot(f,Vfm_f);
xlim([5000 15000])
ylabel('Amplitube (V)');
xlabel('Frequency(Hz)');
title('Frequency Modulated Signal Frequency Representation');
grid on;

[NEU JING HUI]

thank you so much