Using Matlab do the following:

2. [3 points] Nonlinear systems produce "distortion", such as a cheap speaker due to the lack of linearity in the response stemming from shoddy materials. Your job here is to demonstrate how how different types of nonlinearity give rise to harmonic and intermodulation distortions. Consider an input signal ()such as the sum of two ("primary") sinusoids Now consider some mapping function that takes the input signal and "maps" it into a new output signal For a linear mapping, the amplitude and phase at a given frequency might be affected, but additional frequency components are not created. For example consider 3 r(I)I Such would have the effect of cubing two sinusoids and thereby create new frequencies, which would manifest as harmonics of the two primaries, as well as intermodulations (e.g., 2f? - f2) Consider A2 = 0 and 2(1) = 13. Briefly explain why new frequencies would arise (eg, 3h) would arise by virtue of the relevant trig identity Write a code to demonstrate the spectral amplitude of two quantized tones (A1A2 and f2 - 1.2fi) for the cubic mapping. Your code should produce a plot showing both the input spectra and the output. Briefly describe what distortion frequencies that are created . Now repeat for a quartic nonlinearity: 2(1)-14. Show the spectrum and describe differences, explaining briefly. What happens at the primary frequencies? Lastly consider a hyperbolic tangent: r(I) - tanh (I). Show the spectrum and describe differ- ences, explaining briefly. Wh at happens at the primary frequencies? You should submit your code, as well as an images created 2. [3 points] Nonlinear systems produce "distortion", such as a cheap speaker due to the lack of linearity in the response stemming from shoddy materials. Your job here is to demonstrate how how different types of nonlinearity give rise to harmonic and intermodulation distortions. Consider an input signal ()such as the sum of two ("primary") sinusoids Now consider some mapping function that takes the input signal and "maps" it into a new output signal For a linear mapping, the amplitude and phase at a given frequency might be affected, but additional frequency components are not created. For example consider 3 r(I)I Such would have the effect of cubing two sinusoids and thereby create new frequencies, which would manifest as harmonics of the two primaries, as well as intermodulations (e.g., 2f? - f2) Consider A2 = 0 and 2(1) = 13. Briefly explain why new frequencies would arise (eg, 3h) would arise by virtue of the relevant trig identity Write a code to demonstrate the spectral amplitude of two quantized tones (A1A2 and f2 - 1.2fi) for the cubic mapping. Your code should produce a plot showing both the input spectra and the output. Briefly describe what distortion frequencies that are created . Now repeat for a quartic nonlinearity: 2(1)-14. Show the spectrum and describe differences, explaining briefly. What happens at the primary frequencies? Lastly consider a hyperbolic tangent: r(I) - tanh (I). Show the spectrum and describe differ- ences, explaining briefly. Wh at happens at the primary frequencies? You should submit your code, as well as an images created