Rules and Tables of Fourier Transform

 

Definition 

Rules on Functions 

Linearity 

Differentiation in time 

Differentiation in frequency 

Integration in time 

Convolution in Time 

Convolution in Frequency 

Time scaling 

Time Reversal 

Shifting in time 

Shifting in frequency 

Duality 

Unit (Step) Function 

Unit Impulse (Delta) Function 

Periodic Function with period T 

Table of Transforms 

Algebraic 

Exponential 

Trigonometric 

Mixed 

Parseval’s Relations 

 

 

 

Definition

 

The above equations can also be used with the following form:

(The product of the coefficients before the integration of the forward and inverse transform must be equal to: 1/2π)

 

 

 

Rules on Functions

 

Linearity:

 

Differentiation in time:

 

Differentiation in frequency:

 

Integration in time:

 

Convolution in Time

 

Convolution in Frequency

 

Time scaling

 

Time Reversal

 

Shifting in time:

 

Shifting in frequency:

 

Duality:

 

Unit (Step) Function:

 

Unit Impulse (Delta) Function:

 

Periodic Function with period T:

 

 

 

Table of Transforms

 

Algebraic:

 

Exponential:

 

 

Trigonometric:

 

Mixed:

 

Parseval’s Relations: