The basic confusion

[Abhy]

What is the difference between multipling and adding a signal. if i have two signal f1 and f2.

is f1 + f2 is same as f1 . f2?

I am confused with terminology used at many places..
multiply or add a signal.

if f1 = sin 10 wt and f2 sin 100 wt.
The time domain representation would look same for both f1 + f2 and f1 . f2?

I do not remember the site but while reading it seems
out f1 + f2 the call superposition (each point add) and
f1 . f2 multiplication (each point multiply) but the time
domain the resultant signal looked exactly same.



When one uses addition and when mutliplication.

TIA,
Abhy.

[Ram]

Hi Abhy, regd the sum and product of the sinusoids, the first operation gives
sin10t+sin100t
whereas the product gives
sin10t*sin100t i.e, cos 90t-cos100t
these two are never the same.
one is a DSB-SC and other is a combination of two tones.

[Abhy]

thanks for addressing the Q. Few more..

is it going to be cos90t - cos100t or cos90t - cos 110t?

Also - do not we see sin10t * sin100t
is also combination of two tones?
which is cos 90t and cos 110t?

Ok, One more..
If i play two key in a piano together ...
it is sum or multiply?

Sum means -- superposition?

[Reese]

Acutally sin(10t)sin(100t)=1/2[cos(90t)-cos(110t)]
"Product to sum" formula for sin(u)*sin(v)

when 2 tones are heard together - it is a addition.