Amplitude Modulation Concepts

Question

I am currently learning about telecommunications but I have some concept issues.

Firstly, does it matter if I am using cosine or sine in the equation? I understand that they are basically the same thing but there is a phase shift difference between them. Should I account for that phase shift?

For instance if I am making a computer program (matlab) that is going to generate an amplitude modulated signal, should I use cosine or sine?

My equation for the program is as follows:

output = amplitude * (1 + depth * cos(2 * pi * modu * (i / exp_rate)));

Where:

• modu is the modulating frequency
• exp_rate is the carrier frequency
• i is the i^th pulse
• depth is the depth I want in the modulated frequency

Is it correct?

Note: I am trying to apply amplitude modulation to a train of biphasic pulses. So in the end it should be a train of biphasic pulses going up and down periodically. The amplitude of the ith pulse will follow the modulation waveform and there is no carrier term.

Answer 1

I don't understand I in your formula.

Normally (traditionally) AM is: -

y(t) = [A + M cos(ωm t + φ)] . sin(ωc t)

where

• y(t) is the final modulated signal
• M is the amplitude of the modulating cosine (or sine to answer your question)
• A is the amplitude of the carrier sine (or cosine to reinforce the answer!!)
• φ is the phase displacement of the modulating sinewave but is irrelevant all but mathematically
• ωm and ωc are the frequencies of modulation and carrier.

Maybe I just don't recognize your formula but the answer is, like Jim Dearden implies swap them up or use the same because carrier and modulator are not going to be the same frequency when dealing with AM.

Answer 2

You have to notice that a phase offset always exist betweent the transmitter and the receiver in practice which is varies very slowly in time and using can be eliminated by some circuts such as PLL...

In your simulation you have to consider same phase for the transmitter and receiver oscillator if you are not going to assess the effect of phase offset.

$$x_{Am}(t) = A(1+\mu x(t))\cos \omega_c t$$ Note that multiplying to \$\cos\$ just translates signal form base band to pass band and a \$\sin\$ waveform does it too...