Signal processing question

[muralicrl]

Hello,

When Z transform will become Fourier Transform? Can you explain.

Regards,

N.Muralidhara

 

[subharpe]

Z transform is related to discrete time functions i.e. samples. Fourier transform, in it's basic form is related to the continuous time signals. But Fourier transform can also be defined in case of discrete time functions. But what I presume is relevant for the discussion is Discrete Time Fourier Transform which works on discrete time signals converts into frequency domain. In Z transform the discrete time signal is converted into a polynomial in Z whereas in DTFT it is a polynomial in exp(jω), ω being the normalized cyclic frequency. Therefore Z transform can be mapped into Dourier transform in the form

Z = exp(jω)

 

[raghuram_msc]

Dear Friend,

To summarise subharpe, the relation of Z-Transform with DFT in discreet domain is much the same as what Laplace is with FT, in continuous time domain.

Sai

 

[pngzhi]

Z transform when is computed on the unit circle is fourier transform MAthematically it's enough to replace z with e^(jω)

 

[avi_e-]

Hi Friend,

Take Inverse Z-Transform and then take the resultant equation and apply Fourier Transform for it. I think it works.


Regards,
Avinash.S.

 

[lgpkarthi]

Hello,

When Z transform will become Fourier Transform? Can you explain.

Regards,

N.Muralidhara

The fourier transform is used to analyse the continuous time periodic and aperiodic signals and systems.But Z-transform is used to analyse the discrete time periodic and aperiodic signals and systems.we can relate the Z-transform with the fourier transform as follows
x(Z)=x(ω);z=exp(jω)