Adding or removing noise to a signal (beginner)

[franchouze]

use fft to filter noise

Hello,

I have to add some noise to a signal knowing the spectral power of the noise. This noise can be additive or multiplicative but let's start with additive.

I have read that to remove noise to a signal you can do :

NoisySignal-->FFT-->Filter-->IFFT-->Signal where the filter is defined by :

|Filter|=1-SpectralPower(Noise)/(SpectralPower(Signal)+SpectralPower(Noise))

I tried to compute it on Matlab but I couldnt make it work... So I would like to be sure of the with the previous formula. Do you agree with it ?
If not, could you give me a hint to add noise to a signal knowing its spectral power ?

Thanks a lot for your help.

 

[franchouze]

add noise to signal

From what I have read, this can be done by using AR estimation

https://www.mathworks.com/access/he.../access/helpdesk/help/toolbox/signal/lpc.html

This methods try to estimates the coefficient of a filter using the autocorrekation function (IFT of the spectral power).

There are still some things I do not understand.
The number of used coefficient can be 4 or 8 for instance. However if my spectral power is on 1024 samples, the autocorelation function is therefore on 1024 samples. That means that I am using very few values of my autocorelation function and it seems that I may lost information. Can someone explain me clearly how AR does work plz ?
From what i have understood, when I have the AR coefficient. I used in input of the filter a white noise and got as output a signal that have the spectral power I wanted. Is that it ?

Help me please.

 

[urgull]

www.signalinfo.blogspot.com

for basic information about signals and system,
www.signalinfo.blogspot.com

 

[FvM]

adding noise to a signal

There may be a misunderstanding. Generally, you can't remove noise from a signal. In most cases, you can only improve SNR by optimal filtering, except noise and signal spectral components would be fully separated.

For the same reason, increasing the number of filter parameters most likely doesn't considerably improve the filter performance.

 

[madicalphy]

adding noise to extract signal

The detailed design of digital filters requires a level of theoretical knowledge, including the use of z-transform theory. Autocorrelation is a special digital signal processing technique that has the ability to extract a measurement signal when it is completely swamped by noise. I think what you need is ; go through the literature. If you got some time, please visit this webpage also.

**broken link removed**

**broken link removed**

 

[frankvh]

how to filter noise from a signal

NoisySignal-->FFT-->Filter-->IFFT-->Signal

Yes this can work, but understand what you're doing. Going through an FFT converts into the frequency domain. Then in the frequency domain you remove some stuff (hopefully noise), then you do an inverse FFT to return to the time domain.

This method will only work well if the noise frequency components are separate from the signal frequency components. For your classic gaussian noise, which is broadband, this won't work at all.

However, if indeed your noise is frequency limited, why use this FFT / IFFT method? Why not use a conventional FIR or IIR filter instead? This kind of FFT/IFFT method is better suited to very complex signals. For example to implement a comb filter.

If you post some details on what exactly your signal looks like, and what the noise is that you're adding, we can probably offer some other suggestions.