If we have the full sequence of Fourier coefficients for a periodic signal, we can reconstruct it by multiplying the complex sinusoids of frequency ω0k by the weights Xk and summing:

**Inverse Transforms**

If we
have the full sequence of Fourier coefficients for a periodic signal, we can
reconstruct it by multiplying the complex sinusoids of frequency ω0k by the
weights Xk and summing:

We can
perform a similar reconstruction for aperiodic signals

These are
called the **inverse transforms**.

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