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Fourier Transform vs Laplace Transform-Difference between Fourier Transform and Laplace Transform

This page on Fourier Transform vs Laplace Transform describes basic difference between Fourier Transform and Laplace Transform.

Fourier Transform

The Fourier Transform provides a frequency domain representation of time domain signals. It is expansion of fourier series to the non-periodic signals.

Following are the fourier transform and inverse fourier transform equations.

Fourier Transform

Following table mentions fourier transform of various signals.

Fourier Transform of signals table1 Fourier Transform of signals table2

• Fourier Transform of a real signal is always even conjugate in nature.
• Shifting in time domain changes phase spectrum of the signal only.
• Compression in time domain leads to expansion in frequency domain and vice-versa.

Laplace Transform

The main drawback of fourier transform (i.e. continuous F.T.) is that it can be defined only for stable systems. Where as, Laplace Transform can be defined for both stable and unstable systems.

Following are the Laplace transform and inverse Laplace transform equations.

Laplace Transform

Following table mentions Laplace transform of various functions.

Laplace Transform of functions

To convert Laplace transform to Fourier tranform, replace s with j*w, where w is the radial frequency. in units of radians per second (rad/s).

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