MATLAB Filtering Gaussian noise with Matlab

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To design a filter for a 1 kHz square wave contaminated with Gaussian noise at 0 dB SNR using MATLAB, it's essential to understand the frequency characteristics of both the square wave and the noise. The square wave is generated at 1 kHz, while the noise is produced using a random Gaussian function. The sampling frequency is set at 100 kHz, which means the Nyquist frequency is 50 kHz. This indicates that the cut-off frequency for the filter should be below 50 kHz to avoid aliasing. The design can utilize Butterworth or Chebyshev filters, and the MATLAB function filter(B,A,x) will facilitate the time-domain filtering process. Understanding the frequency components of the signals will aid in determining the appropriate cut-off frequency for effective noise reduction.
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I’m generating a 1 kHz square wave and adding Guassian noise to obtain a SNR of 0 dB (using Matlab6.5). The task is to design a filter that will filter out as much noise as possible from the square wave plus noise signal.
The sampling frequency is 100kHz.
Noise signal: 100.0*randn(1, length(t))
Square wave: 100*square(2*pi*1000*t)
What else do I need to know in order to design this filter using Butterworth or Chebyshev I or any filter? How do I determine the cut-off frequency for my filter?
The MATLAB function filter(B,A,x) will be used for the time-domain filtering operation.
I've started out by considering the frequency characteristics of each signal, but don't know how that will help i the design process.
Any help will be greatly appreciated.
Thanks
 
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You can design a low, high, or bandpass filter with the bessel function in matlab. Here is the link to it:
https://www.mathworks.com/help/signal/ref/besself.html

So, if the sampling frequency is 100khz, you should cut it off at 50khz. That is the Nyquist Frequency.
 

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