Properties of the Fourier Transform

We now develop some properties of the Fourier transform that are useful in finding the transforms of complicated functions from the transforms of simple functions. For each property, we will first state and derive it, and then illustrate it with some examples.

• Linearity
• Time Scaling
• Time Shifting
• Frequency Shifting (or Amplitude Modulation)
• Time Differentiation
• Time Integration
• Reversal
• Duality
• Convolution