Can you denoise a signal with random noise using only filters?

[bakaneko]

Hi,
I was given a homework to design a block-diagram in Simulink to do signal denoising.

With only knowing Fourier/Z-Transform, filters, and some other basic stuff, is it possible to get it done? I was thinking to use a filter to cut down the noise, but the problem is that the noise is random, we don't know the frequency of the noise at a given time. so, I guess it's not possible to do it with only filter.

can I have other hint to solve this problem? I really got stuck at the start

thanks a lot

 

[berkeman]

Hi,
I was given a homework to design a block-diagram in Simulink to do signal denoising.

With only knowing Fourier/Z-Transform, filters, and some other basic stuff, is it possible to get it done? I was thinking to use a filter to cut down the noise, but the problem is that the noise is random, we don't know the frequency of the noise at a given time. so, I guess it's not possible to do it with only filter.

can I have other hint to solve this problem? I really got stuck at the start

thanks a lot

Welcome to the PF. You can improve your signal/noise (SNR) ratio if you can wrap a banpass filter around your data (signal) frequency. If you have to let all frequencies through your system for some reason, then it is very difficult to improve your SNR (you need some "correlation" signal to your data signal).

What are the frequency characteristics of your signal, and of your noise components?

 

[bakaneko]

hi, thank you so much for helping!

I think I got the idea..

Let say I'm using a single pulse of square wave as my signal.

x(t) = 1 , (-T/2 < t < T/2)
x(t) = 0 , otherwise

so, I got a SINC wave for X(jw).. because it is a sinc, it spans from -infinity to +infinity

what if the noise also has its frequency components span from -inf to +inf? This is actually what bothers me sooo much..

I remember that the prof talked about anti-aliasing filter, where we 'sacrifice' the smaller frequency components, so that we can get X(jw) limited from A to B, not from -inf to +inf. Is it ok if I anti-alias that SINC wave, and put it into bandpass filter like you said?

 

[berkeman]

A pulse is not a good way to encode data for transmission, partly because of what you point out about the width of the frequency content in a pulse.

Instead, you should encode your data as modulation on a carrier wave. Bandpass the received signal around the frequency of the carrier, and you eliminate much of the noise in the channel.