Difference Between Laplace Transform and Fourier Transform
Basically the Fourier transform is mostly similar to the Laplace transform, but there are a few key differences. In that the Fourier transform is defined for continuous-time signals, mean while the Laplace transform is defined for both the continuous-time and discrete-time signals. Additionally, the Fourier transform is not a well-suited for analyzing transient signals, while the Laplace transform is useful in it.
Property |
Laplace Transform |
Fourier Transform |
---|---|---|
Domain |
Time and frequency |
Frequency only |
Definition |
X(s)=∫ −∞ ∞ ​ x(t)e −st dt |
X(f)=∫ −∞ ∞ ​ x(t)e −j2πft dt |
Applications |
Circuit analysis, signal processing, control theory |
Circuit analysis, signal processing, image processing, quantum mechanics |
Fourier Transform in Circuit Analysis
In this article, we will study about the Fourier transform analysis or Fourier Transform in Circuit Analysis. The Fourier transform is basically a mathematical operation that decomposes a signal into its constituent frequency components. In simple words, it converts a signal from the time domain to the frequency domain. The time domain will represent the signal as a function of time, while the frequency domain represents the signal as a function of frequency.