ztrans

[BobKruse]

Hi,
I'm an octave novice trying to work my way through the examples in Fred Taylor's "Digital Filters: Principles and Applications with MATLAB". And the very first example used a ztrans function that is in MATLAB's Symbolic Math Toolbox but it is not in octaves symbolic package.

It would be nice if someone had the time to add it to the package.

Thanks,
Bob

[cbm755]

I agree that would be nice, but its not (yet) implemented in the upstream sympy project (sympy/sympy#12502). If it were implemented there, it would be easy to support it here.

See also: https://stackoverflow.com/questions/43247480/how-to-do-z-transform-using-python-sympy/43269596

I've added ztrans and iztrans to "nice to have" list in Issue #215.

[BobKruse]

Thank you Colin. Best regards, Bob Kruse Electrical Engineering Manager Control Gaging, Inc. 847 Avis Dr. Ann Arbor MI, 48108 734-669-6584 From: Colin B. Macdonald [mailto:notifications@github.com] Sent: Sunday, December 31, 2017 1:03 AM To: cbm755/octsympy Cc: BobKruse; Author Subject: Re: [cbm755/octsympy] ztrans (#853) I agree that would be nice, but its not (yet) implemented in the upstream sympy project (sympy/sympy#12502 <sympy/sympy#12502> ). If it were implemented there, it would be easy to support it here. See also: https://stackoverflow.com/questions/43247480/how-to-do-z-transform-using-python-sympy/43269596 I've added ztrans and iztrans to "nice to have" list in Issue #215 <#215> . — You are receiving this because you authored the thread. Reply to this email directly, view it on GitHub <#853 (comment)> , or mute the thread <https://github.com/notifications/unsubscribe-auth/AJPC_-3XOSjdthUTqW5KoeHMgVm7FP1yks5tFyOTgaJpZM4RO0YG> . <https://github.com/notifications/beacon/AJPC_7oxeCIcwSTE4_mnRL1RMDPqx3Ypks5tFyOTgaJpZM4RO0YG.gif>

[cbm755]

If you have time, a nice way to move this forward would be to implement it in @sym/ztrans.m just using the mathematical definition. (Based on the upstream comments, it might not be very useful but it would at least get this started).

[Dsantra92]

Has there been any update on this feature-request?

[alexvong243f]

I've been thinking about how to implement iztrans for some time. While ztrans can be implemented using the definition alone, the same cannot be done for iztrans as its definition involves contour integral over some circle centered at the origin with sufficiently large radius such that the function is analytic on and outside the circle. I don't see how to do it in general as sympy can only find isolated singularities of a function, but not non-isolated singularities, branch points, ...

Then I realize we don't actually have to do any integration, all we need is the ability to compute Taylor series coefficients.

Given a sequence (xₙ), its (one-sided) Z-transform is given by the Laurent series

       +∞
      ____
      ╲
       ╲   xₙ
        ╲  ──
x₀ +    ╱   n
       ╱   z
      ╱
      ‾‾‾‾
     n = 1

which is convergent on {z ∈ ℂ | |z| > R} for some R ∈ [0, +∞]

Conversely, given X(z), it can be written as a Laurent series which is convergent on {z ∈ ℂ | |z| > R} for some R ∈ [0, +∞] and hence X(1 / z) is a Taylor series which is convergent on {z ∈ ℂ | |z| < 1 / R}

So basically, to find the inverse (one-sided) Z-transform for X(z), we compute fps(X.subs(z. 1 / z)).subs(z, 1 / z). Unfortunately, this snippet doesn't actually work because subs doesn't work on FormalPowerSeries and AFAIK there is no way to convert a power series into a sequence. As a result, we need to use compute_fps instead.

I haven't work out all the details. If my understanding is correct, this approach should work.

[cbm755]

Interesting! I don't know enough fps and compute_fps to offer much in the way of comments at the moment.

Focusing first ztrans first:

1. How does one represent a sequence x_n (in SymPy and/or Symbolic)?
2. Is SymPy likely to know/figure out what those FormalPowerSeries converge to? I mean, if I put in sin(n), am I likely to get a closed-form solution out?

[alexvong243f]

I have added ztrans in PR #1121.