Fourier and Laplace transformations

Click For Summary
SUMMARY

The discussion clarifies the differences between Fourier Transform (FT) and Laplace Transform (LT). The FT is defined as a two-sided integral ranging from negative infinity to positive infinity, utilizing a purely imaginary transform variable. In contrast, the LT is typically a single-sided integral from zero to positive infinity, employing a complex variable that is not limited to purely imaginary values. Understanding these distinctions is crucial for applications in signal processing and control systems.

PREREQUISITES
  • Understanding of integral calculus
  • Familiarity with complex numbers
  • Basic knowledge of signal processing concepts
  • Experience with mathematical transformations
NEXT STEPS
  • Research the applications of Fourier Transform in signal processing
  • Learn about the properties and applications of Laplace Transform
  • Explore the relationship between Fourier and Laplace Transforms
  • Study examples of solving differential equations using Laplace Transform
USEFUL FOR

Students in engineering and mathematics, signal processing professionals, and anyone interested in understanding advanced mathematical transformations.

karthik3k
Messages
149
Reaction score
0
Im sorry. I am really new to this. Whats the Difference between FT and LT ?
 
Physics news on Phys.org
The FT is two sided (integral from -infinity to +infinity) and uses a purely imaginary transform variable.

The LT is usually single sided (integral from zero to +infinity) and uses a complex variable that is not restricted to pure imaginary.
 

Similar threads

Undergrad Solving ODE with Laplace transform and Existence and Uniqueness Theorem
  • · Replies 19 ·
Replies
19
Views
4K
Undergrad Laplace transform of a simple equation (Simple question)
  • · Replies 4 ·
Replies
4
Views
2K
Graduate Polar Fourier transform of derivatives
  • · Replies 4 ·
Replies
4
Views
3K
Undergrad Understanding the Laplace Transform of cos(t)/t
  • · Replies 7 ·
Replies
7
Views
8K
Graduate A discussion about Fourier and Laplace transforms and calculus
  • · Replies 4 ·
Replies
4
Views
4K
Undergrad Solution of delayed forcing function
  • · Replies 5 ·
Replies
5
Views
4K
Graduate Why is the Heat equation solved with separation of variables but not with Fourier transformations?
  • · Replies 4 ·
Replies
4
Views
4K
Graduate Laplace transform of derivatives
  • · Replies 6 ·
Replies
6
Views
3K
MHB Inverse laplace transform pf infinite product
  • · Replies 1 ·
Replies
1
Views
1K
Undergrad Convergence of this Laplace transformation
  • · Replies 3 ·
Replies
3
Views
2K