# Tag Info

### Is the Laplace transform redundant?

The Fourier and the Laplace transform obviously have many things in common. However, there are cases where only one of them can be used, or where it's more convenient to use one or the other. First ...
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### What is the difference between $X(j\omega)$ and $X(\omega)$ notation?

Both notations are common and correct. As pointed out by Yuri Nenakhov, the advantage of the argument $j\omega$ is that it coincides with the complex (Laplace transform) variable $s$ when its real-...

### Is the Laplace transform a special case of Fourier transform? (Not the other way around)

The Fourier Transform is the Laplace Transform with the complex variable s restricted to be the imaginary axis on the s plane. For this reason the Fourier Transform only exists when the imaginary axis ...

### How to compute Laplace Transform in Python?

Given the approach started in the OP's Github code I have this suggestion: Observe that the unilateral Laplace Transform given as: $$X(s) = \int_0^\infty x(t)e^{-st}dt$$ Is just the Fourier Transform ...
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### Why does the separable filter reduce the cost of computing the operator?

Assume you have a $N\times M$ sized image. If you know take what is classically used, a square filter kernel, of let's say size $L\times L$, you'd need to convolve that with the picture – which gives ...
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### Relation between Laplace and Fourier transforms

The Laplace transform evaluated at $s=j\omega$ is equal to the Fourier transform if its region of convergence (ROC) contains the imaginary axis. This is also true for the bilateral (two-sided) Laplace ...

### Intuitive interpretation of Laplace transform

Why is the fourier transform a special case of the laplace transform? The Laplace transform produces a 2D surface of complex values, while the Fourier transform produces a 1D line of complex values. ...

### Confusion Regarding Bi Linear Transform

The bi linear transform is the transform from the Laplace Transform Domain to the Z Transform. The Laplace Transform Domain is a regular plane. This transform transforms vertical lines in the Laplace ...

### Why is a negative exponent present in Fourier and Laplace transform?

Matt is correct that the sign is convention. I think that there is a reason for it beyond that though. If we look at complex frequencies in the complex plane, they look like a constant vectors that ...
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### Why the unilateral Laplace transform?

The widespread use of the unilateral Laplace transform reflects the fact that in practice we often deal with causal systems and signals that have a defined starting time (usually chosen as $t_0=0$). ...

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### Help with my first (simple) Z-transform

First of all, it's important to understand that there is no single best way to transform a continuous-time system to a discrete-time system. The method you're using is called backward Euler method, ...
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### Confusions regarding differences between Fourier transform & Laplace transform?

Concerning your first question, both, the Laplace and the Fourier transform, are frequency domain representations of a function or signal. In the Fourier transform we deal with a real-valued frequency ...
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### Product of Doublet and Arbitrary Function

Your first equation is correct. For derivatives of the Dirac delta impulse you get slightly more involved expressions. For $\delta'(t)$ the following holds: f(t)\delta'(t)=f(0)\delta'(t)-f'(0)\delta(...