How do I convolve delta functions in Fourier transform calculations?

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To find the Fourier transform of Cos(10t)sin(t), it is suggested to simplify the expression using half sum difference identities, resulting in 1/2 (sin(11t) - sin(9t). This approach makes the convolution of delta functions more straightforward, as it involves adding frequency shifts rather than direct convolution. The discussion emphasizes that simplifying the trigonometric expression can significantly ease the calculation process. Overall, this method proves to be an effective strategy for handling such Fourier transform problems.
jackdaniel
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Hi everyone, I need help finding the Fourier transform of Cos(10t)sin(t)

i know that i need to find the transform of cos and sin and then convolve them, but i m not sure how to convolve delta function. I would really appreciate any helps.
 
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No it's better to do it by simplifying the trig expression first using the "half sum difference" identities.

That is, cos(10t)sin(t) = 1/2 ( sin(11t) - sin(9t) )
 
thanks, the way you described made it a lot easier. By using your method I realized that convolving delta functions is simply adding the frequency shifts.

thanks
 
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