I am confused with this sentence:
- ...So, both of the speech signal and envelops were shifted with the same amount
Should I use both or both of and why?
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When you use "both" with two nouns or pronouns joined by "and," you don't say "both of." For example:
Both Mike and I were excited to watch the game.
You use "both of" with a plural noun or pronoun:
Both of us were excited to watch the game.
In your example, since you are using "and," you wouldn't say "both of."