Discrete Fourier transform, sine function as spectrum

Question

Consider the following (real part) of some signal $x$:

Can we say $x$ represents the frequency spectrum of an oscillation with a frequency?

I know that the signal represents a sine wave, but can sin be a spectrum? Any help would be much appreciated.

Answer 1

The answer is evidently "yes", using the inverse Fourier Transform.

Here is the result for the function at hand that I have assumed to be a cosine function over one period : it is clearly a double dirac, as one could await.

with the following Matlab script :

a=40;ic=ifft(cos((-a:a)*pi/a));
plot(abs(fftshift(ic)));