## Laplace to Z transform for second order lag.

Started by in comp.dsp7 years ago 12 replies

I have a problem with verifying the results for the conversion of a Laplace transform to a z transform. The Laplace transform is in a table and...

I have a problem with verifying the results for the conversion of a Laplace transform to a z transform. The Laplace transform is in a table and is: (b-a)/((s+a)*(s+b)) The z transform for this transfer function is: ( z*(exp(-a*T)-exp(-b*T))/((z-exp(-a*T)*(z-exp(-b*T)) Now let: a=1 b=2 T=.001 Where a and b are the poles and T is the sample interval. When s-> 0 the Laplace transfer

## equivalence between Z-transform and Laplace-Transform

Started by in comp.dsp17 years ago 2 replies

Hi all, I am studying a digital phase locked loop. The closed loop filter of this loop has the following Z-Transform : H(z) =...

Hi all, I am studying a digital phase locked loop. The closed loop filter of this loop has the following Z-Transform : H(z) = ((K1+K2)*z^-1 - K1*z^-2) / (1 + (K1+K2-2)*z^-1 + (1-K1)*z^-2) I would like to know the damping factor and the natural pulse of the equivalent time continuous filter H(p). by equivalent, I mean a filter H(p) that would give in the time domain, the same resp...

## Re: equivalence between Z-transform and Laplace-Transform

Started by in comp.dsp17 years ago

AG wrote: > Hi Tim, -- snip -- > > > The term "damping ratio" is much more slippery when you're talking > > about discrete-time...

AG wrote: > Hi Tim, -- snip -- > > > The term "damping ratio" is much more slippery when you're talking > > about discrete-time systems. Assuming that I'm not messing up the > > math, if you find the pole locations of your transfer function, z_0 = > > e^{jw + q) then the "damping ratio" is > > > > zeta = q / sqrt(w^2 + q^2). > > What I finally discovered in reading books, is that

## Who Invented the Z Transform

Started by in comp.dsp16 years ago 34 replies

It's pretty easy to figure out who was responsible for the Fourier transform, ditto for the Laplace. Does anybody out there know who dreamed...

It's pretty easy to figure out who was responsible for the Fourier transform, ditto for the Laplace. Does anybody out there know who dreamed up the z transform (Please tell me it wasn't someone named 'Z')? ------------------------------------------- Tim Wescott Wescott Design Services http://www.wescottdesign.com

## Laplace vs. Fourier Transform

Started by in comp.dsp16 years ago 7 replies

I understand the mathematical differences between the two - e.g. - a) LT is more general b/c it is a function of a complex variable...

I understand the mathematical differences between the two - e.g. - a) LT is more general b/c it is a function of a complex variable 's', whereas FT is a function of an imaginary variable (real part = 0) b) LT converges for a larger range of functions But when to use which? I have used LT for solving differential eqns and thus for anything that is derived from diff eqs, and FT for frequ...

## can this be a proper Laplace transform?

Started by in comp.dsp16 years ago 15 replies

sin(s)/(s^2+4), can it be a proper Laplace transform? why? ----------------- I honestly claim this is not a HW problem. Thanks a lot!

sin(s)/(s^2+4), can it be a proper Laplace transform? why? ----------------- I honestly claim this is not a HW problem. Thanks a lot!

## What is the Laplace transform of an ideal low pass filter?

Started by in comp.dsp16 years ago 5 replies

I failed to integrate the exponential kernel against the sinc function... Does anybody know what is the Laplace transform of an ideal low...

I failed to integrate the exponential kernel against the sinc function... Does anybody know what is the Laplace transform of an ideal low pass filter? thanks

## inverse laplace transform

Started by in comp.dsp16 years ago 8 replies

Hi all I'm working on trying to model a non-linear system (described by a second order differential eqn) into a discrete IIR filter. I guess...

Hi all I'm working on trying to model a non-linear system (described by a second order differential eqn) into a discrete IIR filter. I guess I'm trying to follow the impulse invariance IIR filter design method. In the laplace domain, the transfer function looks like this H(s) = a^2/(s+a)^2 I tried looking up laplace transform tables to find the time domain form for this and the closes...

## does anybody know how to find laplace transform of a gaussian function?

Started by in comp.dsp16 years ago 1 reply

I did the following in Matlab and got bounced back with no meaningful results... What's wrong? > > syms t s real > > ...

I did the following in Matlab and got bounced back with no meaningful results... What's wrong? > > syms t s real > > laplace(1/sqrt(2*pi)/s*exp(-t^2/2/pi/s^2)) ans = 7186705221432913/18014398509481984/s*laplace(exp(-1/2*t^2/pi/s^2),t,s)

## does anybody know how to get the inverse laplace transform of this wierd thing?

Started by in comp.dsp16 years ago 6 replies

Want to find the inverse Laplace transform of the following term: H(s)=1/s^2*exp(s^2*a^2/2)*integrate(exp(-u^2/2), u from s*a to...

Want to find the inverse Laplace transform of the following term: H(s)=1/s^2*exp(s^2*a^2/2)*integrate(exp(-u^2/2), u from s*a to +infinity) How to do that? ------------------------------ Making relaxation to the problem, if I have to find only certain sampled values of the inverse Laplace transform of H(s), let's denote it as h(t), I just need to find h(1), h(2), h(3), etc. Is ...

## Re: laplace tranform convert to code

Started by in comp.dsp15 years ago

Tim Wescott wrote: ... > Check his original URL: The author has a clever way of building the > prewarping into the bilinear...

Tim Wescott wrote: ... > Check his original URL: The author has a clever way of building the > prewarping into the bilinear transform. Dunno if I'd want to make a > habit of using it, but it's cute. If w0 is half way between the edges of a bandpass filter in the s domain, it won't be after bilinear transformation. The simplest way I know is too specify the band edges separate

## Re: laplace tranform convert to code

Started by in comp.dsp15 years ago

Jerry Avins wrote: > Tim Wescott wrote: > > ... > > > Check his original URL: The author has a clever way of building the > > ...

Jerry Avins wrote: > Tim Wescott wrote: > > ... > > > Check his original URL: The author has a clever way of building the > > prewarping into the bilinear transform. Dunno if I'd want to make a > > habit of using it, but it's cute. > > > If w0 is half way between the edges of a bandpass filter in the s > domain, it won't be after bilinear transformation. The simplest way I > k

## Inverse Fourier/Laplace transform of a periodic function?

Started by in comp.dsp15 years ago 46 replies

HI, If a function F(u) is known to be a Fourier transform of some function f(t), and F(u) is periodic in u, which can be deemed as...

HI, If a function F(u) is known to be a Fourier transform of some function f(t), and F(u) is periodic in u, which can be deemed as frequency variable, with a period 2*pi. If I want to find its inverse Fourier transform, I know I should try either DTFT/IDTFT, or Fourier series, for such a periodic function, and the target function f(t) in the time-domain should be a discrete comb-like fu...

## how to compute the laplace and fourier transform of this function?

Started by in comp.dsp15 years ago 4 replies

Hi there, Suppose I have a function f(t) which I knew its laplace and fourier transform. What is the laplace and fourier transform of the...

Hi there, Suppose I have a function f(t) which I knew its laplace and fourier transform. What is the laplace and fourier transform of the following: exp(a*f(t)) ??? ---------------------------- Is there a way to evaluate the laplace transform of heaviside((exp(x)-a)), where the heaviside function is also called step function, heaviside(x) = 1, when x> 0, and =0, when x ...

## transfer function

Started by in comp.dsp15 years ago

hi all, is the tranfer function H(s)=Output(s)/Input(s) only when the initial state of the system is zero? If the initial state of the system...

hi all, is the tranfer function H(s)=Output(s)/Input(s) only when the initial state of the system is zero? If the initial state of the system is non-zero then the Output(s)=Something*x(0)+H(s)*Input(s). where x(0) is the initial state of the system, ..(s) is the Laplace transform. Is it correct? Thanks

## numerical inverse Laplace-Stieltjes transform

Started by in comp.dsp15 years ago 6 replies

Hello, I am working on a CDO pricing problem as outlined in a paper . For the computation of the tranch margins one needs several steps of...

Hello, I am working on a CDO pricing problem as outlined in a paper . For the computation of the tranch margins one needs several steps of numerical integration, but before that also has to compute the distribution function of a discrete or mixed random variable from it's characteristic or moment generating function, that is, from the Fourier-Stieltjes or Laplace-Stieltjes transfo...

## z transform of a digital filter

Started by in comp.dsp15 years ago 5 replies

hello!! I hope you can help me out. I need to find the Z tansform from a Laplace expresi?n: 5(1-e^-sT)/s(s+1)(s+2) Now, I...

hello!! I hope you can help me out. I need to find the Z tansform from a Laplace expresi?n: 5(1-e^-sT)/s(s+1)(s+2) Now, I know that there is a table to calculate this but I can't find anything on the web, maybe you have one, or you'd know someway to solve this, I really need it, I hope you can help me, thanks!

## Differentiating impulse response

Started by in comp.dsp14 years ago 10 replies

As differentiation in the time domain corresponds to multiplication by s in the Laplace domain, it seems reasonable (to me) in terms of the...

As differentiation in the time domain corresponds to multiplication by s in the Laplace domain, it seems reasonable (to me) in terms of the Bilinear transform that multiplying the same digitized transfer function by 1-z^?? ------ 1+z^?? should give the same desired effect in discrete case. But why doesn't this work? (If I, however, just multiply by 1-z?? it ofcourse corresponds to a finit...

## Please comment on my solution of this equation using Laplace transform

Started by in comp.dsp14 years ago 17 replies

Hi all, Sorry for my rustiness on Laplace transforms. I used the Laplace transform to solve the following equation, and got some results....

Hi all, Sorry for my rustiness on Laplace transforms. I used the Laplace transform to solve the following equation, and got some results. Could you please comment on the correctness of my solution? The equation is: f(t)=a+b*Integrate( exp(-c*(t-s)) * f(s), ds, s from 0 to t) Here f(t) is a function that only takes values on [0, +inf). Here "*" denotes the multiplication. a, b, an...

## Laplace transform and poles and region of convergence...

Started by in comp.dsp14 years ago 7 replies

Hi all, I have a function f(x) and I take its unilateral Laplace transform to obtain F(z) where z is on the complex plane. However it is...

Hi all, I have a function f(x) and I take its unilateral Laplace transform to obtain F(z) where z is on the complex plane. However it is complicated and it is possible only to obtain the F(z) numerically. That's to say: f(x) -- (numerical) Laplace Transform -- > F(z) However, I want to find (hopefully theoretically) the poles and hence the region of convergence of F(z), because t