ABSTRACT
We have seen the theoretical relationship between the DFT coef cien ts and the Fourier series coef cients of a periodic signal x(t) in the previous chapter, and that relation was established by assuming, on the one hand, that x(t) can be represented by a Fourier series x ( t ) = ∑ k = − ∞ ∞ C k e j 2 π k t / T , C k = 1 T ∫ − T / 2 T / 2 f ( t ) e − j 2 π k / T d t ; https://s3-euw1-ap-pe-df-pch-content-public-u.s3.eu-west-1.amazonaws.com/9780429144752/d396f6df-a752-4aea-b000-0783b8bf9d03/content/unequ4_109_1.tif"/> and assuming, on the other hand, that the N discrete-time samples {xℓ } transformed by the DFT were equally spaced over a single period T o f the signal x(t);i.e., we have NΔt = T.
