ASN4 -Fourier Transform property: Difference between revisions
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Find the Fourier transform of <math> cos(2\pi f_0t)g(t)= \!</math> | Find the Fourier transform of <math> cos(2\pi f_0t)g(t)= \!</math> | ||
<math> \mathcal{F}[cos(2\pi f_0t)g(t)] \!</math> | |||
<math> | Applying the forward Fourier transform | ||
<math> =\int_{-\infty}^{\infty}cos(2\pi f_0t)g(t)e^{-j2\pi ft}dt \!</math> | |||
Applying Euler's cosine identity | |||
<math> = \int_{-\infty}^{\infty} [\frac{1}{2}e^{j2\pi f_0t}+\frac{1}{2}e^{-j2\pi f_0t}]g(t)e^{-j2\pi ft}dt\!</math> | <math> = \int_{-\infty}^{\infty} [\frac{1}{2}e^{j2\pi f_0t}+\frac{1}{2}e^{-j2\pi f_0t}]g(t)e^{-j2\pi ft}dt\!</math> |
Revision as of 11:13, 19 December 2009
Find the Fourier transform of
Applying the forward Fourier transform
Applying Euler's cosine identity
Identifying that the above equation contains Fourier Transforms the solution is