# Incorrect lecture notes relating Bandwidth with speed?

1. Mar 9, 2013

### ericeng

My understanding of Bandwidth in the context in which I learn it (Analogue and Digital Communications) is that it is the spectral width of a signal, BW = f[upper] - f[lower].

However, my lecture notes then define 'fundamental limitations' as,

Bandwidth:
- A measure of "speed"
- When a signal changes rapidly with time, the frequency content (or spectrum) extends over a wide range; i.e. has "large bandwidth"
- The faster data is sent, the more bandwidth it uses (is needed)

This confuses me. I don't get how bandwidth is a measure of speed, other than how frequency in general relates to signals in the time domain. Are the bullet points above factually correct?

How rapidly a signal changes with time only determines at which frequency(s) it lies, not the width of the range of frequencies?

I understand how sending data faster could require more bandwidth; by increasing bandwidth, more simultaneous signals could be sent. But to say that increasing the speed of transmission will result in an increase in bandwidth, I just don't understand that.

Insight is most welcome.

Thanks!

2. Mar 9, 2013

### milesyoung

This isn't strictly true since a high frequency sinusoid "changes rapidly with time" but its spectral content is limited to a single frequency. It is, however, true for a trapezoidal waveform (which is a common approximation used for digital signals) - as you decrease its rise time, you increase the bandwidth (using your definiton) of the waveform.

I think its fair to say that higher bandwidth provides for more throughput. I understand "faster" in this context to mean an increase in data transmission rate.

What do you mean by 'speed of transmission'?

3. Mar 9, 2013

### ericeng

Okay, this I understand. Thanks.

So shouldn't this read that the more data sent simultaneously, the more bandwidth is required? Because the data could be being transmitted at the same rate but more data per unit time could result as an increase in bandwidth? ''Speed'' seems like the wrong word here. It's like suggesting "speed" is the cause of faster transmission due to a shorter cable.

Sorry, by speed I meant rate as you used above, not propagation speed.

4. Mar 9, 2013

### milesyoung

If I saw those slides/notes, I would just think "speed" was used as a kind of umbrella term for rise time, data transmission rate etc. - just a way to get you to think of "things that move/change fast".

It doesn't strictly make sense but it _is_ presented in quotes ;)

5. Mar 9, 2013

### ericeng

Okay, thanks for your replies. I also came across the Shannon-Hartley theorem which defines channel capacity in bits/s. BW goes up, bits/s goes up. Simple!