Hello all,

I would really appreciate it if anyone could help me understand the "normalized frequency response" of any system. I am having trouble deducing any useful information from "normalized frequency response" of a system, like this one below:



As per Nyquist theorem, the sampling frequency should be at least twice the maximum input frequency. From that perspective, the x-axis of the normalized frequency response of any system should never exceed 0.5. Why is this plot's x-axis ending at 5? Moreover, what do these bumps and ripples in the plot reveal?

Thank you.

 

Normalized, in this case the graph is normalized to 0 db. Normalization
is used to compare disparate systems, with same response typically
except for an overall G factor. Also used in filter design, eg. to normalize
everything to 1F, 1H, 1 ohm, do the design, then un-normalize to get actual
values.

http://www.ee.surrey.ac.uk/Projects/CAL/linear-systems/m306-normalization.htm

The response graph is from basic sampling theory -

http://www.cppsim.com/BasicCommLectures/lec10.pdf

The periodic nature of sampling.


Regards, Dana.

 

Thank you very much, danadak, for your quick response.

I do know what normalization is, but I do not know how to interpret a normalized frequency response.

None of the links mentioned by you discusses anything about understanding a plot normalized in the x-axis or plotting a graph with respect to normalized x-axis.

Interpreting a simple, non-normalized frequency response is a lot easier.

 

understanding a plot normalized in the x-axis or plotting a graph with respect to normalized x-axis.

It's quite simple.
In the graph, fin is an input frequency of interest that is being sampled and fdr is the sampling frequency relative to the input frequency.
Thus, for example, if the input frequency exactly equals the sample frequency (fin/fdr = 1), then the sampled output is zero.

So to use the graph you just substitute you actual input frequency for fin and the actual sample frequency for fdr.
If you want a non-normalized plot, then change the X-axis to fin with the normalized "0" point being where fin equal to the sample frequency. That gives you a non-normalized plot
That's not so hard, is it?

 

Hello all,

I would really appreciate it if anyone could help me understand the "normalized frequency response" of any system. I am having trouble deducing any useful information from "normalized frequency response" of a system, like this one below:

As per Nyquist theorem, the sampling frequency should be at least twice the maximum input frequency. From that perspective, the x-axis of the normalized frequency response of any system should never exceed 0.5. Why is this plot's x-axis ending at 5? Moreover, what do these bumps and ripples in the plot reveal?

Thank you.

I'm not sure what the "DR" stands for (it should say somewhere in the document where you got that plot from), but it looks like it is probably the sampling frequency.

Just because you might not WANT any frequency greater than the Nyquist frequency does not mean that they don't exist. The system WILL have some response to higher frequencies, although they will be aliased down to lower frequencies in the output.

The ripples in that plot are for THAT specific response (a particularly circuit topology).

 

At the most basic level the frequency response shown is, in a system with
no filter, the frequency response of the sampler, eg. the act of sampling
and creating a series of weighted impulses of the continuous time input signal.

https://ocw.mit.edu/resources/res-6...pling-aliasing-and-frequency-response-part-1/
Following this with a f(Z) further modifies this basic response.


Regards, Dana.

 

Yes, that's pretty easy. Thanks crutschow.

https://ocw.mit.edu/resources/res-6...pling-aliasing-and-frequency-response-part-1/
Following this with a f(Z) further modifies this basic response.

That was certainly helpful. Thanks a lot, danadak.

I'm not sure what the "DR" stands for (it should say somewhere in the document where you got that plot from), but it looks like it is probably the sampling frequency.

Yes, that's it!

Just because you might not WANT any frequency greater than the Nyquist frequency does not mean that they don't exist. The system WILL have some response to higher frequencies, although they will be aliased down to lower frequencies in the output.

Yes, of course. But that's why I want to ask! What do they tell the designer? I mean If I am making sure sampling frequency is at least twice the input frequency, why should the designer bother about any frequencies beyond half the sampling frequency?

 

Here is a discussion on over and under sampling.

http://www.ti.com/lit/an/slaa594a/slaa594a.pdf

https://inst.eecs.berkeley.edu/~ee247/fa05/lectures/L24_f05.pdf The case for oversampling

Regards, Dana.

 

why should the designer bother about any frequencies beyond half the sampling frequency?

Because those high frequency signals will appear (are aliased) into the sampled signal, as shown in the graph.
So if you don't want those higher frequencies in the sampled signal (whether they are noise or actual signal), then any signal above half the sample frequency must be filtered out before it is sampled (appropriately called an anti-aliasing filter).

 

Because those high frequency signals will appear (are aliased) into the sampled signal, as shown in the graph.
So if you don't want those higher frequencies in the sampled signal (whether they are noise or actual signal), then any signal above half the sample frequency must be filtered out before it is sampled (appropriately called an anti-aliasing filter).

This is what I was looking for. Thank you very much crutschow.

I know what anti-aliasing filters are, but never thought about it this way! Now I can see a clear picture of the entire system.

 

Caution, there are designs that purposely alias signals as pointed out by the TI
paper link I posted. So not all is bad with aliasing. Nyquist violation in appropriate
designs can bring one more tool into the designers toolbox depending on goals.

Regards, Dana.

 

Yes, of course. But that's why I want to ask! What do they tell the designer? I mean If I am making sure sampling frequency is at least twice the input frequency, why should the designer bother about any frequencies beyond half the sampling frequency?

Ever hear of noise?

Can the designer ever ensure that the input signal contains NO content above the Nyquist frequency? No matter how much you filter it, there will always still be content there -- and there's a practical limit to how much filtering you can do.

So buy knowing how the system will respond to higher frequency content, you can determine how much filtering you HAVE to do in order to achieve acceptable performance from the system.

 

If you have a lot of noise/ unwanted signals above the highest frequency of interest, you can also use a higher sampling frequency, and do some of the filtering digitally in the processor.
That allows the use of a simpler, lower-order anti-alias analog filter for the same noise suppression.
For example, this is inherently done in sigma-delta converters, which have a much higher sample frequency than twice the highest signal frequency.

 

http://www.ti.com/lit/an/slaa594a/slaa594a.pdf

Excellent article. Thanks danadak.