Time-Bandwidth Duality is the principle that a signal’s duration and bandwidth are inversely related: compressing a signal’s duration expands its its bandwidth, and vice versa. This is expressed by the time-bandwidth product inequality:
where equality holds for a Gaussian Pulse. In practice, to transmit symbols faster (shorter ), more bandwidth is required.
Intuition
Imagine a signal that starts at zero, briefly peaks, and then returns to zero. To make a signal that cancels out somewhere, there must be destructive interference. However, in order to get both the destructive interference almost everywhere and the brief peak where there is constructive interference, you need many sinusoids, spanning a broad spectrum. If we only had a narrow band of frequencies, the sinusoids would not be different enough to both totally cancel out in most of the time domain, but also peak in the middle.