thanks very much,but it seems a bit confusing for me,i have left and right singular vectors,so next what i should do?

The left singular vector presents orthonormal basis of the column space of the trajectory matrix. SSA operates on the column space of the trajectory matrix only so you can discard the right singular vector.

but what about my code?how can i fix this error?

from theory point of view i dont need it,i need code just

You did not mentioned any errors in your originl question. If you need just a working code you can take mine implementation and adapt it to Matlab (should be very easy). Or at least read it and take the parts you need. I see from your profile you're mature in math, but I don't see from your question that you don't need a detailed description of SSA algorithm so I provided you with a couple of links, hope this will help.

aa it is old question right,please see this stackoverflow.com/questions/23106669/…

that is what i have tried ,but get error,so please help me to fix this error

@dato, the gist I referred to in my post is derived from the ssa.m and is (I believe) well debugged. Unfortunately, I have troubles running GNU Octave on this machine (and I have no Matlab) so I can't help you to debug Matlab implementation. If you decide to try my code, I can answer your questions on it. Note that 'ssa.m' is not "official", it's just a user-provided content.

please help me with your code,how should i transform it into matlab?i spent whole day without get solution,it is bad

i am here

ok

let say like this

generally i dont know mathematically how they are doing diagonal averaging

somehow i know

but most important for me is reconstruction

because i am working on spectral resolution

I've managed to run GNU Octave on this machine. Will try to adapt the mentioned code to this system... (it's much closer to Matlab than Scilab is).

I think you know that singular spectrum has no relation to frequency spectrum (lets say to PSD). But just in case.

no

it is naother

another think

what i am saying

but

anyway

Do you speak russian?

code itself it important for me

no

Ok.

just english

Give me 10 minutes.

ok

Well, I'm back.

Take a look at this: gist.github.com/werediver/10886388

ok thanks

but one question

1:10

it is

just signal right

Right. Dirty example :)

This is Basic SSA decomposition with L=4 and partial reconstruction from components 1 to 2.

thanks my friend

You can also use ssa_decompose() to analyse decomposition and make a decision how to reconstruct the signal back.

Hope this will help you.

yes

you know

after that

i can take time

to learn code itself

SSA

if we choose window lentg correctly

length

is very great tool

correctly,because it can effectively denoise

Yes, I've played with Basic SSA for some time. Looks good for denoising, but you should carefully choose L and I.

actually yes

i am working on PHD

on this topic

if i have finished everything successfully

i will discuss with you some kind of details ok

?

the point is that

what is difference between

Surely. But I should note that I am "just" a software engineer and far not as mature in math as you seems to be. DSP as applied math is closer to me.

original and reconstructed series

?

less noise or?

no i am not mathematican

i am also supposing programming and mathematics together

in future

so question yes

we have original and reconstructed

they have same values

what is difference

SSA decomposes the original signal in a separable components (if it's possible). They are ranked by the variation contribution. If you'll discard the components with low variance and if you will call such a components a "noise", then yes, the reconstructed time series will have less noise.

?

Ah, you're talking about my example?

but same value right

yes

1:10 --> 1:10?

exactly

That's simple, I reconstruct the time series with first two components and it turns out that it's enough to reconstruct the time series perfectly.

Just a particular case.

i see

in reality it could be

partially reconstructed

Try to generate some "noisy" sinusoids and reconstruct it with a few first components.

The outcome should look like denoising.

for noisy sinusoids

AR model is not prefered right

What we should do with AR model?

i mean

it is not good

to use AR model

with non sttaionary

stationary noise data right

thanks for help

Unfortunately, most of the methods at all works best with stationary time series. SSA claims to handle non stationary somehow.

thanks

see you

please

Bye.

with stackoverflow

upload this answer

Ok, I'll do.

I've updated the code because of a possible bug in adiag() function (introduced while porting from Scilab). Please, grab it once again from the same page ( gist.github.com/werediver/10886388 ).