Signals are digitized using an ADC. The process involved is known as sampling the analogue signal. If the message spectrum looks like the diagram shown below what is the minimum sampling frequency?



I know that Sampling Frequency is Twice the Max Freq.
But I don't know which number to choose 1 or 5 ??

 

The sampling theorm requires sampling at least twice the highest frequency component of interest in the original signal. Where is most of the information in the spectrum you posted?

 

This is All I got !!

 

Gee let's see.

Twice the max frequency.

Uhm... 1 Hz or 5 Hz? 1 Hz or 5 Hz?

Figuring out which is the max is a tough one, alright.

 

The sampling theorm requires sampling at least twice the highest frequency component of interest in the original signal. Where is most of the information in the spectrum you posted?

It doesn't really matter where most of the information is located. This is orthogonal to the issue of which is the highest frequency component of interest since there may only be a little bit of information there, but it is still of interest.

 

I am cofused which one to pick 1 or 5? As information given is limited.

 

What is the specific point you are confused about? What the term "maximum frequency" means?

 

1 Hz is minimum.
5 Hz is maximum.

Apply sampling theorem.

 

So 5*2 = 10 so answer will be 10 right ??

 

It doesn't really matter where most of the information is located. This is orthogonal to the issue of which is the highest frequency component of interest since there may only be a little bit of information there, but it is still of interest.

I have converted many signals whose signals had high frequency components that I didn't care about. I had a choice, sample high enough so that I didn't alias the high-freq stuff into the region of interest, or low-pass filter first, and then reduce the sampling rate...

 

So 5*2 = 10 so answer will be 10 right ??

10 Hz. That would have been my answer.

 

I have converted many signals whose signals had high frequency components that I didn't care about. I had a choice, sample high enough so that I didn't alias the high-freq stuff into the region of interest, or low-pass filter first, and then reduce the sampling rate...

Well, if you didn't care about them, then pretty much by definition they weren't of interest.

But it brings up the point that the sampling frequency needs to be at least twice the highest frequency present, whether it is of interest or not. If signals are present above the highest frequency of interest, then -- as you've pointed out -- they need to be filtered out before you can safely lower your sampling rate.

 

There is one sampling theorem that states that the sampling frequency must be at least twice the highest frequency present in the signal being sampled.

There is another that we call the corollary of the sampling theorem:

There must be no frequency content that is greater than one-half the sampling frequency.

In reality, they both say the same thing but from different perspectives.

 

...

There is another that we call the corollary of the sampling theorem:

There must be no frequency content that is greater than one-half the sampling frequency.

In reality, they both say the same thing but from different perspectives.

It is usually the corollary that drives system design. If using a PIC A/D, for example, the max. conversion rate and RAM depth drives what filtering needs to be done. Much of the information content of might be discarded just to make it work...

 

I agree. The corollary is usually brought to students' attention because it is not the sampling frequency that is so important but the necessity for an effective anti-aliasing filter on the sampled signal.