## 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
;
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and assuming, on the other hand, that the N discrete-time samples {x_{ℓ}
} transformed by the DFT were equally spaced over a single period T o f the signal x(t);i.e., we have NΔt = T.