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I know how to sketch the spectrum of \$m(t) = \cos(1000)t + \cos (3000)t\$

But I stack with that....when it's multiplied? How to sketch the spectrum \$m(t) = \cos(1000)t \times \cos(3000)t\$?

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Maybe you remember the sine and cosine product formulas from high school?

Replace \$a\$ and \$b\$ with \$1000t\$ and \$3000t\$ and you get a sum of new frequencies. This is also the concept used in superheterodyne radio receivers.

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If you know how to add two cosines, you can use the identity $$\cos(\alpha)\times\cos(\beta) = \frac{1}{2}\left[\cos(\alpha + \beta) + \cos(\alpha − \beta)\right]$$

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