Signal Denoising with Fourier/Z-Transform & Filters

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In summary, the conversation discusses the use of filters and basic knowledge of Fourier/Z-Transform to improve the signal-to-noise ratio in a Simulink block-diagram for signal denoising. The possibility of using a bandpass filter to eliminate noise is suggested, but limitations arise when the noise frequency components span from -infinity to +infinity. The idea of encoding data as modulation on a carrier wave is also mentioned as a better alternative for transmission.
  • #1
bakaneko
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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 alot
 
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  • #2
bakaneko said:
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 alot

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?
 
  • #3
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?
 
  • #4
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.
 

FAQ: Signal Denoising with Fourier/Z-Transform & Filters

What is signal denoising?

Signal denoising is the process of removing unwanted noise from a signal while preserving the useful information. This is commonly done in applications such as audio and image processing, where noise can distort the signal and make it difficult to extract meaningful information.

What are Fourier and Z-transforms?

Fourier and Z-transforms are mathematical techniques used to analyze signals in the frequency domain. They allow us to decompose a signal into its individual frequency components, which can then be manipulated or filtered to remove noise and extract useful information.

How do filters help with signal denoising?

Filters are used in signal denoising to remove specific frequency components from a signal. This can be done using various types of filters, such as low-pass, high-pass, or band-pass filters. Filters are designed to selectively attenuate certain frequencies while preserving others, thus reducing the noise in the signal.

What is the difference between Fourier and Z-transforms in signal denoising?

The main difference between Fourier and Z-transforms is the type of signals they are typically used for. Fourier transforms are used for continuous signals, while Z-transforms are used for discrete-time signals. However, both techniques can be used for signal denoising, and the choice between them depends on the nature of the signal being analyzed.

Is signal denoising with Fourier/Z-transforms and filters always effective?

No, signal denoising is not always effective, as it depends on the type and amount of noise present in the signal. In some cases, noise may be too strong or too similar to the useful signal, making it difficult to remove without also losing important information. It is important to carefully choose the appropriate techniques and parameters for each specific signal to achieve the best results.

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