Calculating Depth of Modulation

depth of modulation

Hi,

My code is as follows:
Fs=100e2;
T=1/Fs;
L=10000;
t=[0:Fs]'/Fs;

fm=10;
fc=48e1;
ka=0.1; %% 0<ka<1

wc=2*pi*fc;
wm=2*pi*fm;

mt=1*sin(wm*t); %% Modulating signal

x=((1+ka*mt).*(cos(wc*t))); %% AM Modulation

y=amdemod(x,fc,Fs); %% AM demodulation
[b,a]=butter(5,fc*2/Fs);
z=filter(b,a,y);

NFFT=2^nextpow2(L);
f=Fs/2*linspace(0,1,NFFT/2);

Y=fft(mt,NFFT)/L;
Z=fft(z,NFFT)/L;

subplot(221)
plot(t,x);axis([0 0.1 -2 2]);grid on

subplot(223)
plot(t,y);axis([0 0.1 -2 2]);grid on

subplot(222)
plot(f,2*abs(Y(1:length(f))));axis([0 100 0 1]);grid on

subplot(224)
plot(f,2*abs(Z(1:length(f))));grid on;axis([0 50 0 0.1]);

when u look at the demodulated signal and its frequency response, u can find that at the starting of the signal there is a spike. The value of spike varies with respect to ka value. lesser the ka value higher the spike level.

But i suppose to not get this in demodulated signal. This affects the computation of 'depth of modulation' from demodulated signal.

depth of modulation = (Amax-Amin)/(Amax+Amin);
where, Amax and Amin are max and min values of envelope signal. (If spike is dominating it results into wrong value of 'depth of modulation').

Can anyone tell me how do i remove the spike. I applied many filtering methods still the problem persists.

Thanks !
Ashwini