- #1
BriWel
- 3
- 0
I have a practice question, which is to find the Fourier Transform of cos(2^pi^t)
By substitution into the FT formula, and use of eulers formula,I have managed to reduced to:
INTEGRALOF ( (cos(2*pi*t) * ( cos(2*pi*F*t) - j*sin(2*pi*F*t) ) )
By plotting the frequency graph of the original function, I know that the answer I am looking for is: delta(1) + delta(-1)
I have also been told that the integral of two trig functions multiplied together equals 0 if the functions have different frequencies. This indicates that the above formula is only non-zero where F = 1.
My problem is that I don't know how to get from the above formula to delta(1) and delta (-1). Can anybody help?
Also, I'm relatively new to Fourier Transforms, so as much detail as possible in answers will be appreciated!
thanks in advance for any help
By substitution into the FT formula, and use of eulers formula,I have managed to reduced to:
INTEGRALOF ( (cos(2*pi*t) * ( cos(2*pi*F*t) - j*sin(2*pi*F*t) ) )
By plotting the frequency graph of the original function, I know that the answer I am looking for is: delta(1) + delta(-1)
I have also been told that the integral of two trig functions multiplied together equals 0 if the functions have different frequencies. This indicates that the above formula is only non-zero where F = 1.
My problem is that I don't know how to get from the above formula to delta(1) and delta (-1). Can anybody help?
Also, I'm relatively new to Fourier Transforms, so as much detail as possible in answers will be appreciated!
thanks in advance for any help