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2. (a) Describe the steps used to test if a system is linear using the two methods additivity and homogeneity. [6 Marks] (ii) Use the additivity test method on a system that is given as y = v3 using the signals V1 = 4 and V2 = 5 for the input. [4 Marks] b). (0) A Fourier series analysis was applied to a signal x(t) that has a period of 1 ms. The Fourier series contained a fifth harmonic written as a sine wave plus a cosine wave with amplitudes an = 0.1 and bn = 0.1 respectively. Write down an expression to represent this harmonic as used in a Fourier series and describe each of the terms in the expression, include values in the expression. Describe how this harmonic could be represented as a single sine wave only. [6 Marks] A square wave signal x(t) is periodic with a period To = 4 ms, and has a duty cycle of 50%, the voltages used in x(t) are 5 V and OV. Write down an integration expression that would be used to find the 211 value for the 11th harmonic. Include as many values in the expression as you can. Describe how this integral is used to find a11. The a11 coefficient need not be fully calculated. [8 Marks] (c) (0) An impulse response of a system is given as h(t), and the input signal x(t). Write down an integration equation that is used to find the output of such a system at a time t = 0.1x10“, include as many numerical values in the equation as you can. Explain with reference to this integral how the output is calculated given h(t) and x(t). [5 Marks]