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Signals and Systems by Smarajit Ghosh

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11.2 PROPERTIES OF FOURIER TRANSFORM

Let us take x(n) as a real sequence.

From Eq. (11.1), we can write

 

image

 

Therefore, X(ω) has real and imaginary parts.

 

image

 

and image

 

where XR(ω) and X1(ω) are the real and imaginary parts of X(ω).

Table 11.1 gives the symmetry properties of Fourier transform and Table 11.2 gives the properties of Fourier transform.

 

Table 11.1 Symmetry Properties of Fourier Transform

 

Table 11.2 Properties of Fourier Transform ...

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