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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

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    $\begingroup$ What is the context? Otherwise those exact words alone seem ambiguous. $\endgroup$
    – hotpaw2
    Commented Nov 7, 2013 at 20:20

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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.

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    $\begingroup$ 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. $\endgroup$
    – jan
    Commented Nov 8, 2013 at 21:58
  • $\begingroup$ @jan You are referring to case of bandpass sampling right. $\endgroup$
    – Karan Talasila
    Commented Dec 9, 2013 at 7:05
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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.

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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.

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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
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