Hello.
Quick question about a F.T. problem that is bugging me. See attached, it's part b) that I am a little unsure of
I know that the Fourier transform of exp(-kt) = 1 / (k + jw)
Then the F.T. of derivative of f(t) - which is (-k)*exp(-kt) will simply be the above multiplied by -k: (-k) / (k + jw)
But now using the derivative property of fourier transforms:
d/dt[f(t)] <==> jw[F(w)]
the transform of the derivative of f(t) should be jw multiplied by the transform of the original function, or in other words: (jw) / (k + jw)
These two answers are supposed to be equal but they're not! I cant re-arrange one into the other, and when I put dummy values in for k and w, I am left with a result of -1/1 when I take one away from the other
Can anyone spot where I went wrong please?
Thanks.
Quick question about a F.T. problem that is bugging me. See attached, it's part b) that I am a little unsure of
I know that the Fourier transform of exp(-kt) = 1 / (k + jw)
Then the F.T. of derivative of f(t) - which is (-k)*exp(-kt) will simply be the above multiplied by -k: (-k) / (k + jw)
But now using the derivative property of fourier transforms:
d/dt[f(t)] <==> jw[F(w)]
the transform of the derivative of f(t) should be jw multiplied by the transform of the original function, or in other words: (jw) / (k + jw)
These two answers are supposed to be equal but they're not! I cant re-arrange one into the other, and when I put dummy values in for k and w, I am left with a result of -1/1 when I take one away from the other
Can anyone spot where I went wrong please?
Thanks.
Attachments
-
81 KB Views: 47