Trigonometric function and complex exponential

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Homework Help Overview

The discussion revolves around the multiplication of a trigonometric function, specifically Akcos(ωt), with a complex exponential, e-jωt. Participants are exploring the implications of this multiplication in the context of further operations, such as convolution with a real function.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants attempt to express the product of the trigonometric function and complex exponential using the identity for cosine. There is a question about the validity of taking the real part of the resulting expression when considering convolution with a real function.

Discussion Status

Some guidance has been provided regarding the expression of the product, and there is an ongoing exploration of the implications of ignoring the imaginary part in the context of convolution. Multiple interpretations of the mathematical expressions are being discussed.

Contextual Notes

Participants are considering the assumptions involved in manipulating complex expressions and the potential impact of these assumptions on the results of convolution with real functions.

asifadio
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1. Homework Statement
- multiplication of trigonometric function and complex exponential




2. Homework Equations
the question is, Akcos(ωt) × e-jωt




3. The Attempt at a Solution
it is, Ak/2 + (Ak/2)e-j2ωt ?
by using cos(ωt) = 1/2ejωt + 1/2e-jωt
 
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asifadio said:
1. Homework Statement
- multiplication of trigonometric function and complex exponential




2. Homework Equations
the question is, Akcos(ωt) × e-jωt




3. The Attempt at a Solution
it is, Ak/2 + (Ak/2)e-j2ωt ?
by using cos(ωt) = 1/2ejωt + 1/2e-jωt

Looks ok to me.
 
thanks!
but if i want to convolute with some real function, f(x),
can i just take a real part of
Ak/2 + (Ak/2)e-j2ωt

which is Ak/2 + (Ak/2)(2cos(ωt))?
 
asifadio said:
thanks!
but if i want to convolute with some real function, f(x),
can i just take a real part of
Ak/2 + (Ak/2)e-j2ωt

which is Ak/2 + (Ak/2)(2cos(ωt))?

I hope you mean Ak/2 + (Ak/2)(cos(2ωt)). But what makes you think you can ignore the imaginary part?
 

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