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From the following equation Prove that Fourier transform is Where is a delta function; Use the following representation of the Fourier Transform Write down

From the following equation

\( f(x)=2 \sin (4 x)+8 \cos (2 x) \)

Prove that Fourier transform is

\( i \sqrt{2 \pi} \delta(w-4)+4 \sqrt{2 \pi} \delta(w-2)+4 \sqrt{2 \pi} \delta(w+2) \) \( -i \sqrt{2 \pi} \delta(w+4) \)

Where δis a delta function; Use the following representation of the Fourier Transform


\( F(\omega)=\frac{1}{\sqrt{2 \pi}} \int_{-\infty}^{\infty} f(x) e^{-2 i \pi \omega x} d x \)


Write down all steps and be clean in your writing.

f(x) 2 sin(4x) + 8 cos(2x)

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Step 1 Given that fx 2sin 4x 8cos 2x As we know that pix ix sin x 2i and COS X ... blur-text-image

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