Selected Continuous Fourier Theorems

This section presents continuous-time Fourier theorems that go beyond obvious analogs of the DTFT theorems proved in §2.3 above. The differentiation theorem comes up quite often, and its dual pertains as well to the DTFT. The scaling theorem provides an important basic insight into time-frequency duality. The Poisson Summation Formula (PSF) in continuous time extends the discrete-time version presented in §8.3.1. Finally, the extremely fundamental uncertainty principle is derived from the scaling theorem.

- Radians versus Cycles
- Differentiation Theorem
- Differentiation Theorem Dual
- Scaling Theorem
- Shift Theorem
- Modulation Theorem (Shift Theorem Dual)
- Convolution Theorem
- Flip Theorems
- Power Theorem
- The Continuous-Time Impulse
- Gaussian Pulse
- Rectangular Pulse
- Sinc Impulse
- Impulse Trains
- Poisson Summation Formula
- Sampling Theory
- The Uncertainty Principle

- Relation of Smoothness to Roll-Off Rate

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