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### calculating SNR from PSD

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```i have two signals, one is the tranmission waveform, the other is receive
one,

can any one tell me how to get the SNR of my received waveform,.

the waveform consists of bits which has shape of raised cosines,

i tried to get the power of the signal from the PSD but i dont know how t
integrate the power at all frequencies to get the power of the signal

ne clues

```
 0
Reply aneeq (7) 9/3/2007 4:28:24 PM

See related articles to this posting

```On Mon, 03 Sep 2007 11:28:24 -0500, bizoo wrote:

> i have two signals, one is the tranmission waveform, the other is received
>
> one,
>
> can any one tell me how to get the SNR of my received waveform,.
>
> the waveform consists of bits which has shape of raised cosines,
>
> i tried to get the power of the signal from the PSD but i dont know how to
>
> integrate the power at all frequencies to get the power of the signal
>
>
> ne clues

You should be able to take the calculated PSD of your signal alone,
then multiply it frequency-by-frequency with both the noise alone and the
noise+signal and get a "signal+noise"/noise ratio -- then subtract one.

Note that this is going to give you a rather approximate figure.  The
random nature of noise means that any measurements of noise (such as it's
PSD) will themselves be noisy.  What you'll _really_ be calculating is
"measured signal and noise" / "measured noise", or "signal + noise +
measurement noise" / "signal + noise + measurement noise".  As your signal
level drops, your SNR calculation will become more and more noisy, until
it ends up being meaningless.

--
Tim Wescott
Control systems and communications consulting
http://www.wescottdesign.com

Need to learn how to apply control theory in your embedded system?
"Applied Control Theory for Embedded Systems" by Tim Wescott
Elsevier/Newnes, http://www.wescottdesign.com/actfes/actfes.html
```
 0
Reply tim177 (4434) 9/3/2007 5:34:43 PM

```Hello,

I have a code example here:
http://www.elisanet.fi/mnentwig/webroot/SNR_FFT_correlation_example/index.html
But it requires the actual samples, the PSD alone won't do.

Cheers

Markus
```
 0
Reply mnentwig (306) 9/3/2007 6:02:51 PM

```bizoo wrote:
> i have two signals, one is the tranmission waveform, the other is received
> one,
>
> can any one tell me how to get the SNR of my received waveform,.
>
> the waveform consists of bits which has shape of raised cosines,
>
> i tried to get the power of the signal from the PSD but i dont know how to
> integrate the power at all frequencies to get the power of the signal

Integrate with respect to time. You need to restore the original
amplitude before integrating the received signal. A narrow band filter
might help with that.

Jerry
--
Engineering is the art of making what you want from things you can get.
¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯
```
 0
Reply jya (12872) 9/3/2007 8:41:16 PM

```>On Mon, 03 Sep 2007 11:28:24 -0500, bizoo wrote:
>
>> i have two signals, one is the tranmission waveform, the other i
>>
>> one,
>>
>> can any one tell me how to get the SNR of my received waveform,.
>>
>> the waveform consists of bits which has shape of raised cosines,
>>
>> i tried to get the power of the signal from the PSD but i dont know ho
to
>>
>> integrate the power at all frequencies to get the power of the signal
>>
>>
>> ne clues
>
>You should be able to take the calculated PSD of your signal alone,
>then multiply it frequency-by-frequency with both the noise alone an
the
>noise+signal and get a "signal+noise"/noise ratio -- then subtract one.
>
>Note that this is going to give you a rather approximate figure.  The
>random nature of noise means that any measurements of noise (such a
it's
>PSD) will themselves be noisy.  What you'll _really_ be calculating is
>"measured signal and noise" / "measured noise", or "signal + noise +
>measurement noise" / "signal + noise + measurement noise".  As you
signal
>level drops, your SNR calculation will become more and more noisy, until
>it ends up being meaningless.
>
>--
>Tim Wescott
>Control systems and communications consulting
>http://www.wescottdesign.com
>
>Need to learn how to apply control theory in your embedded system?
>"Applied Control Theory for Embedded Systems" by Tim Wescott
>Elsevier/Newnes, http://www.wescottdesign.com/actfes/actfes.html
>

I have one query Tim,

You said to take the psd of my transmitted signal and multiply it freq b
freq with the psd of  received signal (signal which also contains noise
and with the noise signal alone

and then take ratio of (S+N)/N  -1

why do i need to multiply with the original signal

i mean if i take the ratio of psd of my received signal with the psd o
noise alone , will it not be the same thing as above, in general i a
wondering why You said of multiplying with the original transmitte
signal

br

```
 0
Reply aneeq (7) 9/6/2007 5:48:26 AM

```>Hello,
>
>I have a code example here:
>http://www.elisanet.fi/mnentwig/webroot/SNR_FFT_correlation_example/index.html
>But it requires the actual samples, the PSD alone won't do.
>
>Cheers
>
>Markus
>

Hi mike interesting technique
Can You give me some reference to the this technique, some book or som
research article
in general i am looking to find out the limitations of this approach
for example as You have also mentioned on this page that signals must b
well synchronized otherwise SNR would vary remarkably,

So i want to dig deep into this technique and see if i can use it with m
work
br
```
 0
Reply aneeq (7) 9/6/2007 5:50:53 AM

```Hello,

unfortunately I can't remember any textbook reference.

I picked one related reference from the web at random. Relevant is fo
example the text prior to equation (2):
http://www4.ncsu.edu/~kggard/kg_papers/ARFTG_1204_SNR_EVM.pdf

If you experiment with the tolerable timing error, try to plot th
spectrum of the uncorrelated signal. Any timing error shows up a
triangle-shaped artifacts on the frequency axis (the higher the frequency
the more damage caused by a fixed time offset).

If you find something, please let me know, I'll add it to my web page.

Cheers

Markus
```
 0
Reply mnentwig (306) 9/6/2007 6:12:55 AM

```On Sep 3, 12:28 pm, "bizoo" <an...@kth.se> wrote:
> i have two signals, one is the tranmission waveform, the other is received
> one,
>
> can any one tell me how to get the SNR of my received waveform,.
>
> the waveform consists of bits which has shape of raised cosines,
>
> i tried to get the power of the signal from the PSD but i dont know how to
> integrate the power at all frequencies to get the power of the signal
>
> ne clues

For the PSD calculation:

Look at "Fundamentals of Acoustics" by Kinsler, Frey, Coppens, and
Sanders, in chapter 11 on Noise Signal Detection, Hearing and Speech.
I have the 3rd edition,

```
 0
Reply stan.pawl (69) 9/11/2007 12:15:29 PM

7 Replies
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