Simbyak.
Do not forget that you have to use the cosine laws over there.
You have the modulating wave ( cos(2*pi*10^5 Hz) ) multiplying a sum of 2 cosine waves over there one with 1500*PI rad/s and 3000*PI rad/s + the DC level.
The DC is gonna give you the carrier component at 10^5 Hz.
The 1500*PI rad/s cosine is going to give you 2 impulses, one at 10^5 + 750 Hz and another at 10^5 - 750 Hz.
The 3000*PI rad/s cosine is going to give you 2 impulses, one at 10^5 + 1500 Hz and another at 10^5 - 1500 Hz.
Haayato,thanks for your contribution. but for me this is where thngs get kind of messy,..well the wave given is amplitude modulated..so to get the frequency spectra..wht i did is multiply each individual sine wave and the Dc level by cos(2*pi*10^5 Hz)..i.e we have 3 product terms now.
So i go on to use the property of modulation for fourier ttransform(attached below)..i am able to get the Dc as the carrier component at 10^5 Hz,however the transform for the 2 sine waves is where it gets me mixed up..
(and for the implses in your answer id expect the freq to be 1500 and 3000 respecctuvely,if u go by the properties attched)
thnx
P.S by saying i gottta use the cosine law..are u referring to this
cos(A-B)=cos A cos B + sin A sin B?...hhmm if you do,doubt it will work coz looks like we gonna end up with a product term of cos which doesnt make lif any easier..
I have looked through my lecture notes and other soursces online and seems like..the spectra is
The DC is gonna give you the carrier component at 10^5 Hz.with a magnitude of 10.
The 1500*PI rad/s cosine is going to give you 2 impulses, with magnitude of 0.5 at 10^5 +1500 Hz and another at 10^5 -1500 Hz.
The 3000*PI rad/s cosine is going to give you 2 impulses .with magnitude of 1, one at 10^5 + 3000 Hz and another at 10^5 -3000 Hz.
Now im stuck at finding the modualtion efficiecny because the modulation is given by (amplitude of modulating wave/amplitude of carrier wave)....so what do we use as the amplitde of the modulating wave given tht our modulating is a sum of 2 waves..