Can anybody please help me read the properties of Discrete Fourier Transformation from the given figure. Here is the image link
Thank you guys, appreciate you help.
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What you are seeing are the amplitudes for the various complex sines that - when combined linearly - approximate the original function. Because the sines are complex, there are two graphs; one for the imaginary and one for the real part. – Bobson Dugnutt Jan 24 '16 at 16:56
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So, which property of DFT does the image shows? – MessitÖzil Jan 24 '16 at 17:20
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The amplitudes. – Bobson Dugnutt Jan 24 '16 at 20:05
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Note that the real part $X_R[k]$ satisfies
$$X_R[k]=X_R[N-k]\tag{1}$$
where $N$ is the DFT length. The imaginary part satisfies
$$X_I[k]=-X_I[N-k]\tag{2}$$
Combining $(1)$ and $(2)$ gives the following condition for the complex DFT $X[k]=X_R[k]+iX_I[k]$:
$$X[k]=X^*[N-k]\tag{3}$$
where $*$ denotes complex conjugation. Equation $(3)$ means that the original sequence $x[n]$ (the DFT of which is $X[k]$) is real-valued.
Matt L.
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