Here is the sentence.
According to economic signaling theory, consumers may perceive the frequency with which an unfamiliar brand is advertised as a cue that the brand is of high quality.
I have been perplexed by the structure of this sentence and the usage of which.
Here is my thought. The main structure is
Consumers(Subject) perceive(Verb) the frequency(Object) as a cue(Complement).
Here is my question.
What the role of 'which' in the sentence. Is it a relative pronoun?
Why there is a preposition(with) preceding 'which'? What is the role of 'with' in the sentence? Could I change 'with' to other preposition? Also, what is the role of the word that in the sentence 'that the brand is of high quality'.