What exactly do we mean the signal bandwidth is the range of frequencies the signal is made of?Is this referring to the Fourier transform of the signal in the frequency domain?
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\$\begingroup\$ Bandwidth can be defined in different ways. Sometimes starting at 0Hz and other times not (like when a carrier is involved). \$\endgroup\$DKNguyen– DKNguyen2021-12-14 16:14:46 +00:00Commented Dec 14, 2021 at 16:14
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\$\begingroup\$ That definition of bandwidth is correct regardless of anything to do with Fourier transform (which is merely one way of illustrating a signal in the frequency domain). \$\endgroup\$user16324– user163242021-12-14 20:30:13 +00:00Commented Dec 14, 2021 at 20:30
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3 Answers
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What exactly do we mean the signal bandwidth is the range of frequencies the signal is made of?
It's the range of frequencies over which the majority of the signal's power* is contained.
Is this referring to the Fourier transform of the signal in the frequency domain?
If you're doing analysis, yes. If you're actually transmitting a signal it has more to do with how it interacts with the physical world. Specifically, if I'm broadcasting a signal at some frequency, a radio receiver that's set up to have a very narrow bandwidth will receive my signal over a range of frequencies, even if that receiver is implemented with vacuum tubes, coils, capacitors, resistors, and some quartz crystals. That range of frequencies will be the representative of my transmitted signal's bandwidth.
* Or the signal's energy, if it's a one-time event. Usually "bandwidth" is for a signal that goes on and on, like a phone conversation or a datastream sent over radio.
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Yes, it is; Fourier tells us that signals can be represented by an orthogonal projection to single-frequency basis functions. So, without the Fourier transform the phrase
the range of frequencies the signal is made of
isn't meaningful.
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Signals don't have bandwidths.
You shape signals to occupy the bandwidth required for the particular application.
Signals can be broken down into frequency components as a result of Fourier analysis. Non-periodic signals will occupy a spectrum of freqencies.
e.g. A square wave has harmonics that go on and on? What is the bandwidth of the square wave? Obviously you can say "infinite" but then can a square wave retain its shape, if it passes through any real network?
It is entirely possible and indeed common usage, to say that the signal power is concentrated in a certain bandwidth and peaks at a certain frequency. The key idea (especially in the communications world) is that signals must be limited to occupy their own assigned bands and not create out-of-band interference. If you use this strategy you must clearly mention upper and lower limits.
Circuits/networks have bandwidths
At some point, the signal has to pass through a circuit or an electrical network that will have certain frequency selective characteristics. Such characteristics are referred to as low-pass, high-pass or band-pass. There is the theoretical all-pass too. These words often appear without hyphens. You can talk about the bandwidth of circuits, filters, cables, transmission lines or channels of various types. Here I use the word network to refer to an electrical network more popularly known as a circuit.
Communication networks
I must use the word network more carefully. Networks that are exchanging packets define bandwidth as the number of packets that can be sent/received in a given time interval. The upstream and downstream bandwidths could be different. The raw physical bandwidth of a network may be high, but then with the overhead of the protocol, it reduces further. When talking about communication networks, a standard is often used for resolving verbal ambiguities. e.g. SATA, FiberChannel, T1/E1 etc.
