How are Fourier Series and Fourier transform are related?

Click For Summary
SUMMARY

Fourier Series and Fourier Transform are fundamentally related mathematical tools used in signal processing. Fourier Series applies to periodic sinusoidal signals, while Fourier Transform is utilized for aperiodic signals. The mathematical relationship allows for the derivation of the Fourier Transform from the Fourier Series by considering the limit as the period approaches infinity. This connection is essential for understanding how continuous signals can be analyzed in the frequency domain.

PREREQUISITES
  • Understanding of periodic and aperiodic signals
  • Familiarity with basic calculus and limits
  • Knowledge of signal processing concepts
  • Experience with mathematical transformations
NEXT STEPS
  • Study the derivation of the Fourier Transform from the Fourier Series
  • Explore the applications of Fourier Transform in signal analysis
  • Learn about the properties of Fourier Transforms
  • Investigate the implications of Fourier Series in digital signal processing
USEFUL FOR

Students and professionals in mathematics, engineering, and physics, particularly those focused on signal processing and analysis of periodic and aperiodic signals.

ramdas
Messages
78
Reaction score
0
We know that Fourier series is used for periodic sinusoidal signals and Fourier transform is used for aperiodic sinusoidal signals.

But i want to know that
  1. Is there any relation present between Fourier Series and Fourier transform ?
  2. Also,Can we derive mathematical formula of Fourier transform for a aperiodic signal using Fourier series formula or vice versa ?
 
Mathematics news on Phys.org

Similar threads

Undergrad The precise relationship between Fourier series and Fourier transform
  • · Replies 12 ·
Replies
12
Views
4K
Undergrad What does it mean when an integral is evaluated over a single limit?
  • · Replies 23 ·
Replies
23
Views
5K
Fourier Transform: Nonperiodic vs Periodic Signals
  • · Replies 5 ·
Replies
5
Views
2K
High School How to calculate the Fourier transform of sin(a*t)*exp(-t/b) ?
  • · Replies 7 ·
Replies
7
Views
2K
Graduate Can You Prove the Series Is Periodic?
  • · Replies 33 ·
2
Replies
33
Views
3K
High School Time-evolving Fourier transform
  • · Replies 2 ·
Replies
2
Views
2K
How Does Fourier Math Apply to Image Processing?
  • · Replies 2 ·
Replies
2
Views
2K
Undergrad Interpretation of the Fourier Transform of a Cauchy Distribution
  • · Replies 4 ·
Replies
4
Views
3K
Undergrad Can an FFT be used to extract individual sinusoids from a set of data points?
  • · Replies 5 ·
Replies
5
Views
2K
Fourier transform of PSD
  • · Replies 4 ·
Replies
4
Views
2K