Hi there! I have searched extensively online and in text books in attempts to learn how to derive the fourier transform of Exp(jwot), that is fourier transformer of e to the power of 'j times omega-subscript nought times t', where 'j' is the imaginary number symbol (otherwise known as 'i'), and wo is 2*pi*fo.
According to fourier transform 'tables', the fourier transform of e^jwot is 2.pi.delta(w-wo), where w is the angular frequency variable, and delta is the 'impulse' function). So the answer is saying that the fourier transform of e^jwot is an impulse in the frequency domain, and the impulse is at frequency of wo.
I know that the equation to start off with for the fourier transform for e^jwot is integral (from -infinity to +infinity) of e^-j(w-wo)t. dt
But from there on, the text books all typically then go straight to the 'answer' - namely 2.pi.delta(w-wo). But I'm very keen to try understand how they reach the answer with the delta function. I'm thinking that I'm missing some maths theory to get there, so thought I'd like to ask the experts for advice to point me in the right direction to understanding the derivation (without using the fourier transform look-up tables).
Thanks in advance!