The Fourier transform has several interesting properties.
Linearity means that if we can add two signals in time, their Fourier transforms will also add. If we amplify or attenuate a signal in time, its Fourier transform will also amplify or attenuate by the same amount.
If a signal is real in time, it will be complex conjugate symmetric. This means, that we only really need to look at half the Fourier transform.
Time shifting, will be described in detail in a later slide.
Shifting the frequency of a signal is the same as multiplying the signal in time by a rotating complex exponential
Finally, multiplying two signal in the frequency domain is the same as complicated process called convolution in the time domain.
