- #1
dmorr
- 5
- 0
Hey everyone,
I am trying to understand the phenomena behind the technique of using amplitude modulation in sound synthesis. When you have two frequencies, for example, w1=200hz and w2=300hz, and you use the amplitude of one (w1) to modulate the amplitude of the other (w2), it creates 3 signals, one of which is the original carrier frequency, plus 2 others which are called the "sum" and "difference".
you can read more about it here:
http://www.soundonsound.com/sos/mar00/articles/synthsecrets.htm
Anyways, to get the point here... the equation to explain this looks like this:
A1= a1cos(w1t)) + 1/2 [a2cos(w1+w2)t] + 1/2[a2cos(w1-w2)t]
so "1" is the carrier and "2" is the modulator frequency
A= instantaneous amplitude
a= maximum amplitude possible (just using an arbitrary unit here)
w= frequency
t= time
It's probably a basic trigonometry equation, but I haven't done trig since high school, and it's all a blur. What my goal is is to compare two sets of outcomes of data going through this equation. I just don't know how to do the math, so if someone could help me plug in these pairs of data into the equation, that would be awesome.
I want to compare the outcome of this carrier and modulator pair with another.
1. FIRST PAIR>> carrier: a1 = 100, w1= 100hz, t=3 seconds (also arbitrary)
modulator: a2 = 50, w2= 1hz, t =3
2. SECOND PAIR>> carrier: a1 = 100, w1= 100hz, t=3 seconds (also arbitrary)
modulator: a2 = 50, w2= 80hz, t =3
I would like to see what the instantaneous amplitude of the carriers would be in each cases, ideally it would be better if someone could just explain to me how to do the math, and then I could do a bunch of calculation myself.
Thank you so much if someone is able to help me.
dylan
I am trying to understand the phenomena behind the technique of using amplitude modulation in sound synthesis. When you have two frequencies, for example, w1=200hz and w2=300hz, and you use the amplitude of one (w1) to modulate the amplitude of the other (w2), it creates 3 signals, one of which is the original carrier frequency, plus 2 others which are called the "sum" and "difference".
you can read more about it here:
http://www.soundonsound.com/sos/mar00/articles/synthsecrets.htm
Anyways, to get the point here... the equation to explain this looks like this:
A1= a1cos(w1t)) + 1/2 [a2cos(w1+w2)t] + 1/2[a2cos(w1-w2)t]
so "1" is the carrier and "2" is the modulator frequency
A= instantaneous amplitude
a= maximum amplitude possible (just using an arbitrary unit here)
w= frequency
t= time
It's probably a basic trigonometry equation, but I haven't done trig since high school, and it's all a blur. What my goal is is to compare two sets of outcomes of data going through this equation. I just don't know how to do the math, so if someone could help me plug in these pairs of data into the equation, that would be awesome.
I want to compare the outcome of this carrier and modulator pair with another.
1. FIRST PAIR>> carrier: a1 = 100, w1= 100hz, t=3 seconds (also arbitrary)
modulator: a2 = 50, w2= 1hz, t =3
2. SECOND PAIR>> carrier: a1 = 100, w1= 100hz, t=3 seconds (also arbitrary)
modulator: a2 = 50, w2= 80hz, t =3
I would like to see what the instantaneous amplitude of the carriers would be in each cases, ideally it would be better if someone could just explain to me how to do the math, and then I could do a bunch of calculation myself.
Thank you so much if someone is able to help me.
dylan