The Spectrum of the Unit Impulse
Explore the concept of the unit impulse and its spectrum through the Discrete Fourier Transform. Understand how a unit impulse in time corresponds to an all-ones sequence in frequency, and examine the effects of shifting the impulse on its DFT output. This lesson helps you grasp fundamental DFT properties relevant for digital signal processing.
We'll cover the following...
We'll cover the following...
Understanding the DFT starts with the spectrum of a unit impulse. This case gives us an interesting result, as we will now see.
The signal
A unit impulse is a signal that is everywhere, except at time index where its value is . In mathematical terms, we say:
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