**Factor 2 error in Inverse Laplace Transform #2**There was a discussion of a curious LaplaceTransform glitch a while
ago in this group ( http://forums.wolfram.com/mathgroup/archive/2004/Oct/msg00248.html
). Here is a similar example in version 5.1:
In[1]:=
InverseLaplaceTransform[p*(PolyGamma[p + 2] - PolyGamma[p]), p, t]
Out[1]=
2 - 1/(2*E^t)
Since PolyGamma[p + 2] - PolyGamma[p] == 1/p + 1/(p + 1), the correct
answer is 2*DiracDelta[t] - E^(-t). It is interesting to trace where
the error comes from. Let
f(t) = 1 + E^(-t), F(p) = L[f] = 1/p + 1/(p + 1).
Mathematica evaluates the inverse transform of p*F(p) by using the
...

**laplace transforms #2**HI there.
I have done out this differential equation below using laplace
transforms.
d^2i/dt^2+a(di/dt)+bi(t)=detla(t-5)
given i(0)=0 and i"(0)=c
But i would like to check using matlab.
Any help on how to start this would be great.
thank you for your attention.
dominick
...

**Laplace transform #2 980756**Hi there,
I am trying to have a sine wave laplace transformed with an decaying cosine wave, and these both have double values. Cannot figure out how im going to integrate them, as int uses sym. Would i need to use quad and make a seperate function.
Thanks alot
Ana
"Ana " <filter_world@yahoo.com> wrote in message
news:hcq3bf$ntc$1@fred.mathworks.com...
> Hi there,
>
> I am trying to have a sine wave laplace transformed with an decaying
> cosine wave, and these both have double values. Cannot figure out how im
> going to integrate them, as int uses sym. Wou...

**Numerical Laplace transform #2**Hi all!
I have a problem about computing numerically laplace transform from a vector.
I don't have the analytic form of the function that I would like to transform, because my data are a vector of values of concentration acquired at different time samples.
Ex:
time = [7.5;22.50262;37.50008;52.50036;67.50043;82.50053;97.50076;112.5008;127.501005;142.501;165.0011;195.0016;225.0018;255.002;285.0021;334.1693;394.1695;454.1707;514.171015;574.1711;685.1639;835.1641;1065.2923;1370.788;1675.5025;1980.81945;2285.738]./60;
Conc = [3.8;87.1;76.5;108.0;120.5;99.5;106.1;94.8;111.5;115.3;100....

**Inverse Laplace Transform #2**Hello!!
I could really need some help on a problem where I need the inverse
laplace transform of a function. I have tried solving it
analytically, but I have doubts whether the solution is correct..
Maybe I could check it numerically with matlab? Any ideas?
The function in question looks like this:
f(s,z)=exp(-v*z)*s*(1-v)
where v=sqrt(1-2/s)
and I want to perform the inverse transform s -> u, and I am
interested in the solution when z=0.
My analytical approach resulted in the solution:
f(z,u)=DiracDelta(u)+(1/pi)*integral{from 0 to
2}(s*(sin(k*z)+k*cos(k*z))
where k=sqrt(2/s-1)
th...

**Laplace transform #2 1002804**1. f(t) = (2t+4)u(t)
2. g(t) = (4+3e^-2t)u(t)
3. h(t) = (6sin(3t) + 8 cos(3t))u(t)
4. g(t) = d[2e^-4tcos(2t)]/dt
On 04/26/2012 04:17 PM, iam wrote:
> 1. f(t) = (2t+4)u(t)
> 2. g(t) = (4+3e^-2t)u(t)
> 3. h(t) = (6sin(3t) + 8 cos(3t))u(t)
> 4. g(t) = d[2e^-4tcos(2t)]/dt
Have you even tried anything?
tried searching for the command laplace? try searching
for heaviside for unit step u(t).
try using diff() first for the 4th case
--Nasser
On 04/26/2012 06:06 PM, Nasser M. Abbasi wrote:
> On 04/26/2012 04:17 PM, iam wrote:
>> 1. f(t) = (2t+4)u(t)
&g...

**inverse laplace transform #2**
Is anybody familiar with on line notebooks regarding
inversion of laplace transforms via Bromwich integral
formula, within Mathematica?
For example, the function Cosh[x*Sqrt[s]]/(s*Cosh[Sqrt[s]])
has infinitely many singularities (note that s=0 is not a branch point
as a quick look might indicate).
It can be deduced that the function has poles at s=0 and s=s[n]
where s[n]=-(n^2-1/2)^2 Pi^2, n=1,2,3,...
I can perform its inversion by hand, (Mathematica
InverseLaplaceTransform
at least in vrsion 5.2 fails for this task) but I wonder if somebody
has worked
with such Bomwich integr...

**Finding the inverse Laplace transform when there is not a closed form expression for the Laplace transform**Hi,
I'm trying to use ilaplace to find the inverse Laplace transform where the Laplace transform is as follows:
L(s) = exp(integral wrt x from 0 to inf of (exp(-s*x)-1)*k(x)/x) where k(x) is a known function.
In other words, the Laplace transform is not known in closed form. I'm running into some problems so my question is whether it possible to find the inverse Laplace transform in this case?
Thanks!
...

**Differences between laplace transform, z transform and fourier transform**Hi All,
I have studied three diff kinds of transforms, The laplace transform, the
z transform and the fourier transform. As per my understanding the usage of
the above transforms are:
Laplace Transforms are used primarily in continuous signal studies, more
so in realizing the analog circuit equivalent and is widely used in the
study of transient behaviors of systems.
The Z transform is the digital equivalent of a Laplace transform and is
used for steady state analysis and is used to realize the digital circuits
for digital systems.
The Fourier transform is a particular case of z-transform, ...

**Problem with inverse laplace transform #2**
Hello,
I am a new user of Mathematica, and want to get the following inverse
Laplace transform problem:
I have 3 parameters, h,m,n. Parameters m and n are integers. I tried
to find inverse Laplace transform of function:
but mathematica can not give me an answer. Can it be solved by
Mathematica?
Thank you very much!
Alexey.
On 11 , 01:52, "Alexey Nikitin" <niki...@proc.ru> wrote:
> Hello,
>
> I am a new user of Mathematica, and want to get the following inverse
> Laplace transform problem:
>
> I have 3 para...

**Re: inverting Laplace transforms #2**Thank you for the link. Here's one I've been looking for a long time and it's not in those tables:
InverseLaplaceTransform[1/(s+Exp[-s]), s, t]
Mathematica can't seem to do much at all in the way of inverse transforms, nothing more than Exp[-s] as far as I can find.
...

**Fourier Transform #2 #2**I have a problem with one of my assignments and I hope any of you
could help me out.
Take the phase of the clown image(file clown.tif) and the magnitude of
the Mandrill image (Mandrill.tiff) and combine them into a new
synthetic image. Show the magnitude plot for the clown image,the phase
plot for the mandrill image and inverse transformation of the result
using(ifft2).
We can help. Send mail to bharat[at]arithos[dot]com
Regards
Bharat Pathak
Arithos Designs
www.Arithos.com
On Aug 1, 12:53=A0am, "bharat pathak" <bha...@arithos.com> wrote:
> We can help. Send mail to b...

**Factor 2 error in Inverse Laplace Transform**Hi,
InverseLaplaceTransform is an extremely useful part of Mathematica
(since v 4.1).
However, in the following simple problem it gives the wrong answer:
Problem 1:
InverseLaplaceTransform[s/(s+1),s,t]
-1/(2*E^t)+DiracDelta[t]
where the factor 2 is completely wrong.
To see that I slightly rewrite Problem 1 into
Problem 1a:
InverseLaplaceTransform[Apart[s/(s+1)],s,t]
and then I get the correct answer:
-E^(-t)+DiracDelta[t]
Of course one can "Unprotect" InverseLaplaceTransform and teach it to
give the correct answer but that is not the point.
(Also one can s...

**Re: Inverse / Laplace Transform Halved #2**Sir, I see that the LT* LT^-1 thing worked but why can't one get just the inverse transform itself? I ask this because I can't get M7 to produce anything other than very simple inverse transforms. In your example:
InverseLaplaceTransform[E^(-a Sqrt[s]) s, s, t]
just comes back unevaluated. For a while I thought one needed some kind of package loaded but now I think not; I'm now thinking it just doesn't work very well. Am I missing something?
Rob
...

**Problem with inverse laplace transform (FIX) #2**Hello,
I am very sorry that my function wasn't in my mail at first time. I
am a new user of Mathematica, and want to get the following inverse
Laplace transform problem:
I have 3 parameters h,m,n. Parameters m and n are integers. I tried
to find inverse Laplace transform of function:
InverseLaplaceTransform[-1/h - ((((-h+p)/(h+p))^(m-2n)) * (h+p)^2) /
(h*(h-p)*p),p,x]
*-*-*-*-*- Mathematica code *-*-*-*-*
\!\(InverseLaplaceTransform[\(-\(1\/h\)\) - \(\((\(\(-h\) + p\)\/\(h +
p\))\)\
\^\(m - 2\ n\)\ \((h + p)\)\^2\)\/\(h\ \((h - p)\)\ p\), p, x]\)
-*-*-*-*...

**maple 9.5.2, inverse laplace transform problem**
Maple 9.5.2 seems to be unable to solve this:
>restart;
>g:=inttrans[invlaplace]( exp(-s*T),s,t);
But when I give assumptions on T, it will then solve it:
>restart;
>assume(T,integer); assume(T,positive);
>g:=inttrans[invlaplace]( exp(-s*T),s,t);
giving the answer as
g := Dirac(-t+T)
my question is that, why the assumptions are needed? in
the text book I am looking at it gives the inverse laplace
of exp(-s T) as above but with no assumptions on T. I do not
see why the assumptions as needed as T can be real, or
negative.
Am I missing somethi...

**linspace(2,2,2) returns [2 2] ??**May be the help for linspace should change?
It says:
"LINSPACE(X1, X2, N) generates N points between X1 and X2."
Notice, it says BETWEEN.
But when I ask for 2 points, between 2 and 2:
----------------
EDU>> linspace(2,2,2)
ans =
2 2
---------------
May be mathematically this is ok? i.e. there are infinite points between
the point and itself? (on the real line), but from programming point of
view, it is confusing. no?
--Nasser
Maybe it should say "generates N points between X1 and X2, inclusive."
What did you expect to...

**2 * 2 * 2 * 2 or pow(2, 4)?**Hi ,
I hope this isn't too trivial to ask, but I'm evaluating a polynomial
that involve lots of terms like x^2y^2z^3, and although I can use the
power function pow(a, b), I wonder if just writing x*x*y*y*z*z*z for
example wouldn't be more efficient than pow(x, 2)*pow(y, 2)*pow(z,3).
Or is it all the same?
Thanks,
- Olumide
Olumide wrote:
> I hope this isn't too trivial to ask, but I'm evaluating a polynomial
> that involve lots of terms like x^2y^2z^3, and although I can use the
> power function pow(a, b), I wonder if just writing x*x*y*y*z*z*z for
> exam...

**2**2**2**2**2 wrong? Bug?**In Python 2.5 on intel, the statement
2**2**2**2**2
evaluates to
>>> 2**2**2**2**2
20035299304068464649790723515602557504478254755697514192650169737108940595563114
53089506130880933348101038234342907263181822949382118812668869506364761547029165
04187191635158796634721944293092798208430910485599057015931895963952486337236720
30029169695921561087649488892540908059114570376752085002066715637023661263597471
44807111774815880914135742720967190151836282560618091458852699826141425030123391
10827360384376787644904320596037912449090570756031403507616256247603186379312648
4703743782954975613770...

**Question about fourier transform and laplace transform**Hi
I am a computer engineering student.I have to know the difference betwee
Fourier transform and Laplace transform. Because we have studied laplac
transform previous semester, that time to find a frequency response of
system we replaced s by jw in a s domain transfer function, but now we ar
using Fourier transform. Can we get
Fourier transform by replacing s by jw in a Laplace transform?
pls make me clear any one.
Hi,
There was a discussion on this topic earlier.
http://www.dsprelated.com/showmessage/89022/1.php
Regards
Bharat
www.arithos.com
>I am a computer engineering stud...

**equivalence between Z-transform and Laplace-Transform**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 response to an unit step than the one I would get in the
discret domain (one being the discretized version of the other).
I thought I just had to replace z by 1+p in H(z). doing the
approximation e(p)=1+p. But it ...

**Laplace Transform vs Fourier transform**Hello Forum,
everyone is familiar with the Fourier transform and its importance.
Its independent variable, the angular frequency w, is a measurable
physical quantity.
What about the Laplace transform? What is, conceptually, the advantage of
taking the Laplace transform of a signal instead of the Fourier transform?
I know that by looking at its zeros and poles we can assess the stability
of the system for example.... is that not possible with the FT alone?
Does the Laplace transform show information on the system that the FT does
not?
thanks
fisico32
On Oct 27, 8:39=A0pm, "fisico32&q...

**Downsampling by 2: What happens the Spectrum? (Not the Fourier Transform). #2**Given a stationary discrete-time stochastic process x(n) with
discrete-time Fourier transform X(e^jw) and spectrum Sx(w). If x(n) is
downsampled by two to give y(n) it is well known that
Y(e^jw) = 0.5 [X(e^jw/2) + X(e^j(pi+w/2))]. (A)
My question is, what is the resulting spectrum, not just the Fourier
Transform. I know that Sx(w) = E[X(e^jw)X*(e^jw)] and Sy(w) =
E[Y(e^jw)Y*(e^jw)]. From (A), this gives
Sy(w) = 0.25[ Sx(w/2) + Sx(pi+w/2)
+ E[X(e^jw)X*(e^j(pi+w/2))
+ E[X*(e^jw)X(e^j(pi+w/2))] ]
I understand the first two terms which are the original spectrum in
...

**2.2.2 Annoyance**Caveat:
Python 2.2.2 (#37, Oct 14 2002, 17:02:34)
Type "help", "copyright", "credits" or "l
>>> l = [1,2,3]
>>> l[1]
2
>>> l.__getitem__(1)
2
>>> l.__getitem__(slice(1))
Traceback (most recent call last):
File "<stdin>", line 1, in ?
TypeError: an integer is required
>>>
According to the manuals of Python 2.2.2, passing a slice object to
__getitem__ is all right and should work...
Cost a few (grey) hairs of mine, while debugging a largish program, this is
not so.
Would someone care to pass on th...