- #1

PainterGuy

- 940

- 70

- TL;DR Summary
- I have been trying to trace an error in my result without any success. I was trying to compare the application of two different forms of Fourier transform formulae.

Hi,

I tried to apply different forms of Fourier transform, exponential and trigonometric forms, to the same function, f(t)=a⋅e^-(bt)⋅u(t). The result reached using exponential form is correct.

Please notice that while appling the trigonometric form of Fourier transform, the factor of 1/π was ignored.

At the very end, the difference lies between "+a²" and "-ia²". I believe that I should have gotten "-ia²" instead of +a²" for A(α)+B(α) result. The error might be somewhere in the calculation for B(α), or the reason might be ignoring the factor of 1/π.

Could you please help me with tracing down that error? Thank you!

I tried to apply different forms of Fourier transform, exponential and trigonometric forms, to the same function, f(t)=a⋅e^-(bt)⋅u(t). The result reached using exponential form is correct.

Please notice that while appling the trigonometric form of Fourier transform, the factor of 1/π was ignored.

At the very end, the difference lies between "+a²" and "-ia²". I believe that I should have gotten "-ia²" instead of +a²" for A(α)+B(α) result. The error might be somewhere in the calculation for B(α), or the reason might be ignoring the factor of 1/π.

Could you please help me with tracing down that error? Thank you!