Discrete-time Fourier transform (DTFT) analytic example

Discrete-time pulse of width 2M 

[Graphics:../Images/index_gr_19.gif]

Symmetric discrete-time pulse of width 2M 

[Graphics:../Images/index_gr_20.gif]
[Graphics:../Images/index_gr_21.gif]
[Graphics:../Images/index_gr_22.gif]
[Graphics:../Images/index_gr_23.gif]

Plot results for some sample M

M = 0 
[Graphics:../Images/index_gr_24.gif]

[Graphics:../Images/index_gr_25.gif]

M = 1 
[Graphics:../Images/index_gr_26.gif]

[Graphics:../Images/index_gr_27.gif]

M = 2 
[Graphics:../Images/index_gr_28.gif]

[Graphics:../Images/index_gr_29.gif]

M = 4 
[Graphics:../Images/index_gr_30.gif]

[Graphics:../Images/index_gr_31.gif]

M = 8 
[Graphics:../Images/index_gr_32.gif]

[Graphics:../Images/index_gr_33.gif]

Summary of results 
[Graphics:../Images/index_gr_34.gif]

[Graphics:../Images/index_gr_35.gif]

Comparison to continuous-time Fourier transform (CTFT)

[Graphics:../Images/index_gr_36.gif]

Converted by Mathematica      March 25, 2003