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The given equation, x=2*sin(4*pi*t)+5*cos(8*pi*t), can be analyzed through Fast Fourier Transform (FFT) to obtain the frequency components of the signal. To make the analysis more robust, Gaussian noise can be added to the signal to simulate real-world conditions. Once the signal with noise is obtained, FFT can be performed again to obtain the frequency components of the noisy signal. By comparing the frequency components of the original signal with those of the noisy signal, it is possible to analyze the effect of noise on the signal. This type of analysis can be helpful in a variety of fields, such as audio signal processing and image processing.