EE4206/EE5806 Image Processing : inverse relationship between T and delta-T

EE4206/EE5806 Image Processing : inverse relationship between T and delta-T

excerpted from Digital Image processing by Gonzalez and Woods , ch 4 page 245.

the resolution in frequency ( frequency spacing ), delta-u, of the DFT depends on the duration T over which the continuous function, f(t), is sampled,

and the rnage of frequencies ( ie., the entire frequency range ) spanned by the DFT depends on the sampling interval delta-T.

Observe that both expressions exhibit inverse relationships with respect to T and delta-T.