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how get rid of transient response?

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farhadi

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we have a third order filter of length 800.at point 600 ,h[n] becomes negligible,i thinked if we create an input signal(zero mean,unit power Gaussian) of length n0 and run signal through filter,will get rid off any transient response and can use its output,such as another filter but its not true because if we convolve another signal with it,end of this output have a lot of distortion,can help me how i should remove transient response?
 

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