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Given above are the real parts of the signals I to IV. Which of the following statements are correct?

(i): Signal III is the result of the discrete Fourier transform of signal I. The associated imaginary part is 0.

(ii): Signal III is the frequency spectrum of an oscillation with a frequency.

(iii): Signal IV is the frequency spectrum of an oscillation with 2 different frequencies.

(iv): Signal IV is the result of the discrete Fourier transform of Signal III. The associated imaginary part is 0.

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(iii) seems be to correct. Spectrum of two frequencies.

The other choices can be verified,

(i) Fourier transform of $f(t=0)=1$ is 1. So it cannot be graph (iii)

(ii) Signal (iii) is sine wave and there is no spectrum associated with that.

(iv) It's Fourier transform of sine wave (iii) which is

$$f(t)=0.5\cdot \sin(2\pi Ft)$$

and it's transform is

$$\frac{\pi}{i}\left[\delta\left(\omega-2\pi F\right)-\delta\left(\omega+2\pi F\right)\right]$$

Imaginary part is not zero

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