Hi Mohammadreza,

SNR is the acronym for Signal to Noise Ratio which in turn is an abbreviated term for "Signal Power to Noise Power Ratio." This idea was developed in the very early days of radio communication to characterize the quality of the reception of radio signals.

If I remember correctly, H. Friis and D. O. North worked on the definition of Noise Factor (Noise Figure) back in the 1940s. Noise factor is the ratio of the SNR at the input to the SNR of the output of any device such as a filter or amplifier. These are both measured in the "information bandwidth" of the desired signal.

One of the most important issues that affect the computation of SNR is the precise definitions of the Signal Power and Noise Power. In radio communication this is usually the Power in the transmitted signal (or its information content) and the equivalent noise power within the bandwidth of a filter used to filter the signal with the minimum bandwidth possible.

In the case of an ECG, the "signal" is a pseudo-stationary waveform, and over short time durations, a "power" can be defined. The "noise" is a combination of random noise in the tranducers and electronics.

Here are the steps I would apply to your efforts:

1. Define the power of the ECG signal. This is related to its variance or mean-square value.

2. Define the power of the noise. This is the variance or mean-square value of the ECG instrument output when the transducers are not connected to a patient.

3. Calculate the input SNR (SNRin) as the ratio of these input values.

4. Design or acquire a matched filter for the ECG signal or, less optimally, a minimum bandwidth filter that passes nearly all of the spectrum of the ECG signal as determined by an FFT. This is effectively the "information bandwidth."

5. Repeat steps #1 and #2 for the output of the filter.

6. Calculate the output SNR (SNRout) as the ratio of these output values.

7. Compute the SNR improvement factor (analogous to Noise Factor) as the ratio of OUTPUT SNR to INPUT SNR.

Hope this helps. Good luck.

Dear sir,

Power and variance are the same.

A good comparison before and after would be to calculate the SNR at the output of the filter (SNRout = Power of Ouput signal/ Noise of Output Signal) as a function of SNR as if not filter was present. Note that you should really be careful to the noise at the output of the filter, as it might not be the same as the noise power before introducing the filter.

SNR is usually expressed in logarithmic scale, and the usual definition is SNR=20log(std (signal))/std(noise))= 20 log (rms(signal)/rms(noise)).

Dear Bazzi

for example i have a signal+noise!  the amplitude of noise in 50Hz, is 500 mv !

i use a filter to eliminate the effect of noise. now i have a rather pure signal. do you mean in calculating the SNR for output signal(rather pure signal), i have to define new power to noise?! if not, so what you mean "Noise of Output Signal"?

Best way to calculate SNR is in terms of Power ratios and expressed in dB.

Hi,

If you are able to calculate EVM fro your received symbols. Then you can easily calculate SNR from it by 1/(EVM^2) 

Dears

It is better to calculate power SNR

Regards

If you express the SNR using power the expression is SNR=10log(var (signal))/var(noise)).

Dear Mr. Meidani,

Can you attach two figures:

1) a signal + noise sinusoid at a given SNR as an input to the filter.

2) the output of the filter for the input in (1).

the best relation is 

SNR= the power of the message / power for noise 

Dear Samer,

This is true, but the question is to find a relation between the SNR before/after the filter

Hi Mohammadreza,

SNR is the acronym for Signal to Noise Ratio which in turn is an abbreviated term for "Signal Power to Noise Power Ratio." This idea was developed in the very early days of radio communication to characterize the quality of the reception of radio signals.

If I remember correctly, H. Friis and D. O. North worked on the definition of Noise Factor (Noise Figure) back in the 1940s. Noise factor is the ratio of the SNR at the input to the SNR of the output of any device such as a filter or amplifier. These are both measured in the "information bandwidth" of the desired signal.

One of the most important issues that affect the computation of SNR is the precise definitions of the Signal Power and Noise Power. In radio communication this is usually the Power in the transmitted signal (or its information content) and the equivalent noise power within the bandwidth of a filter used to filter the signal with the minimum bandwidth possible.

In the case of an ECG, the "signal" is a pseudo-stationary waveform, and over short time durations, a "power" can be defined. The "noise" is a combination of random noise in the tranducers and electronics.

Here are the steps I would apply to your efforts:

1. Define the power of the ECG signal. This is related to its variance or mean-square value.

2. Define the power of the noise. This is the variance or mean-square value of the ECG instrument output when the transducers are not connected to a patient.

3. Calculate the input SNR (SNRin) as the ratio of these input values.

4. Design or acquire a matched filter for the ECG signal or, less optimally, a minimum bandwidth filter that passes nearly all of the spectrum of the ECG signal as determined by an FFT. This is effectively the "information bandwidth."

5. Repeat steps #1 and #2 for the output of the filter.

6. Calculate the output SNR (SNRout) as the ratio of these output values.

7. Compute the SNR improvement factor (analogous to Noise Factor) as the ratio of OUTPUT SNR to INPUT SNR.

Hope this helps. Good luck.

Dear Dr.Russel

thanks for your perfect answer.

regards

Ah, just another thing. Power and variance are not the same. Variance of x is defined as E[(x-mean(x))**2)=integral from -infinity to +infinity (x-mean(x))**2*p(x)dx. They are only the same if the mean is zero.

So it seems i have to calculate SNR using relationship which uses power of signal to calculate SNR. because the mean of ECG signal is not zero!