what does the statement “band limited signal of 5 KHz” mean

A band limited signal of $5$ kHz is observed at the output node whose sampling frequency is $600$ kHz. What is the minimum order of the filter?

Does it mean:

1. a signal that is from $0$ to $5$ kHz on the frequency axis when drawn

2. a signal from $-2.5$ kHz to $2.5$ kHz

3. a signal with bandwidth of $5$ kHz centered anywhere

• What is the context? Otherwise those exact words alone seem ambiguous. – hotpaw2 Nov 7 '13 at 20:20

4 Answers

The nature of the words in the question is slightly ambiguous.

• A Band-limited signal of bandwidth 5Khz means that the signal can be centered at any frequency but its extent around that frequency is 5Khz.
• A Band-limited signal of 5Khz is also used to represent a signal which is having a center frequency of 5Khz but which has a fixed band-width.
• It surely does not mean -2.5 to 2.5 because when mentioning the band-width usually the positive frequencies alone are counted.

I would advice you to revisit the text and look with respect to the above points.

• In communications, the last point is quite likely. Many people are confused at first when signals of 20MHz bandwidth are sampled with much less than 40MHz sampling rate. – jan Nov 8 '13 at 21:58
• @jan You are referring to case of bandpass sampling right. – Karan Talasila Dec 9 '13 at 7:05

Most likely this is a baseband signal with frequency content from 0 to 5 kHz. Although a sampling frequency of 600 kHz seems out of scale in that case.

Choice-1 : May be for real signals but wrong for complex signals. It's better to state it as; from $-5$ kHz to $5$ kHz baseband signal.

Choice-2 : Is wrong for real signals but may be for complex signals. Since a real signal with a frequency spectrum extending from $-2.5$ kHz to $2.5$ kHz is a baseband signal with a bandwidth of $2.5$ kHz by definition which is the max positive frequency for baseband (extending from -W to +W) real signals. If that was a complex signal, however, then its total bandwidth could be $5$ kHz in that case (extending from $-2.5$ kHz to $2.5$ kHz.)

Choice-3 : This can be true both for real and complex signals.

So, the statement is clearly missing necessary information and can be understood in multiple ways.

All the stuff about the filter and its order, and the sampling frequency, is apparently out of scope of the question: "what does the statement “band limited signal of 5 KHz” mean" and the three-fold choice.

The first options induce assumptions not present in the text:

• a signal that is from 0 to 5 kHz on the frequency axis when drawn
• a signal from -2.5 to 2.5

So according to the Holmes principle:

Once you eliminate the impossible, whatever remains, no matter how improbable, must be the truth.

we are left with:

• a signal with bandwidth of 5 kHz centered anywhere