# Calculation Help: Signal modulation

Joined Aug 29, 2011
2
Hi, I'm new here and hoped to find some help to increase my understanding.

I came across a question asking for modulated and demodulated signals whereby the given signal is x(t) = cos(2pi10t),
and the carrier signal is c(t) = cos(2pi100t).

I know that to get the modulated signal I need to multiply m(t) = x(t) * c(t) to get maybe frequencies of 90Hz and 110Hz.

To get demodulated signal I need to multiply d(t) = m(t) * c(t).
I don't understand the way of multiplication this part and maybe anyone can help?

Also, how can we recover the original signal from that d(t) and how do I go about setting the parameters?

Sorry but this kind of questions may seems noob to most you guys, but I'm just started learning these signal processing thingy and got quite a headache in the calculation part. Hope you guys could help =)

#### t_n_k

Joined Mar 6, 2009
5,455
The modulation (multiplication) process creates sum and difference frequency components such as

ω_upper=(ωc+ωm) and ω_lower=(ωc-ωm)

Where

ωc=carrier term
ωm=modulating term

The demodulation of the modulated signal by multiplication with the original carrier frequency also produces sum & difference terms such as

(ω_upper+ωc), (ω_upper-ωc), (ω_lower+ωc) and (ω_lower-ωc)

The second and 4th terms are of interest because they fall out as terms only in ωm [the original modulating signal]. The 1st and 3rd terms have 2*ωc terms which can be rejected by selective filtering or tuned amplification.

Joined Aug 29, 2011
2

So you're saying that from the ω_upper=110, ω_lower=90,

We can get:
(ω_upper+ωc) = 110 + 100 = 210
(ω_upper-ωc) = 110 - 100 = 10
(ω_lower+ωc) = 90 + 100 = 190
(ω_lower-ωc) = 90 - 100 = -10

And we will take 190 and 210 as 2*ωc terms which is the demodulated signal?
Please correct me if I'm wrong.

#### t_n_k

Joined Mar 6, 2009
5,455
And we will take 190 and 210 as 2*ωc terms which is the demodulated signal?
Please correct me if I'm wrong.
Well not quite. I should have better stated it as (2*ωc-ωm) or (2*ωc+ωm).

Demodulation doesn't necessarily occur with a direct multiplication of the incoming modulated signal and a locally generated carrier equivalent to the source carrier frequency. The classic example is the ubiquitous Superheterodyne Radio Receiver which first converts the received modulated RF with variable carrier frequency (say from different AM radio stations) to a constant intermediate frequency (IF) by multiplication in the receiver mixer stage before demodulation takes place. In this case final AM demodulation may simply be accomplished by envelope detection rather than by another multiplication at the IF. It all depends on the type of signal transmission being employed.