how to do discrete laplace transform (like fft) in matlab ?

To be more specific, suppose we have a function like f(t)=exp(-a*t) and we would like to transform this function to the 'a' domain (F(a)) by using some transform (just like we transform f(t)=exp(-i*w*t) from time domain to 'w'(frequency) domain). so i thought laplace transform would be useful then i read somewhere that discrete laplace transform is called z transform. but when i am applying it in matlab it is showing some error saying 'laplace/z-transform is not defined for the type double'. please help anyone. thanks in advance.

[sarah gebai]

w0=2*pi/Np;
X=zeros(size(x));
for n=0:Np-1
    for k=0:Np-1
        Xi=x(k+1)*exp(-1j*w0*n*k);
        X(n+1,1)=X(n+1,1)+Xi;
    end
end

plot(w,2*abs(X(1:length(w)))/Np,'g')
title('DFT freq');xlabel('w (rd/s)');ylabel('|X(jw)|')

Answer 1

[Azzi Abdelmalek]

The z-transform is not the discrete Laplace transform, also the z transform of a discrete signal is a continuous function. The ztrans function of symbolic math toolbox calculate the symbolic z-transform of your signal.

[ankur gupta]

thanks for your reply. but the question remains - is there a way to do laplace transform of a function for a discrete set of values just like fft(fast fourier transform). moreover i searched the internet and found that there is a method called fast laplace transform developed by P.F.Bertholet.

[Azzi Abdelmalek]

Ok, I never heard about it, but looking in the internet I found an article about it. I think before doing this, you should, first, define what is the laplace transform of a discrete signal, and how are you going to use it.

[ankur gupta]

thanks for your interest in my question. i am a chemistry student and not a mathematics student, so i don't know much about various transforms.but i would like to have a discrete function or discrete set of values after applying laplace transform to a discrete signal. i have already explained in the question what i would like to do with a given function for a discrete set of values. in wiki it is given that "In mathematics and signal processing, the Z-transform converts a time-domain signal, which is a sequence of real or complex numbers, into a complex frequency-domain representation.It can be considered as a discrete-time equivalent of the Laplace transform." so i thought it is analogous to fft, in dealing with discrete quantities. also i would like to plot the transformed function.