![]() 2.2 The impulse response of an ideal lowpass filter is given byįor all t, where w and to are constants. ( y1 + y 2 ) = a1 * u1 + a 2 * u 2 So it does not has the property of additivity, therefore, is not a linear system. Choose two different input, get the outputs: Y = a (u ) * u a(u) is a function of input u. The input-output relation in Fig 2.1(c) can be described as: ![]() Easy to testify that it is a linear system. Z = y −b z = a *u z is the new output introduced. But we can introduce a new output so that it is linear. ( y1 + y 2 ) = a * (u1 + u 2 ) + 2 * b So it does not has the property of additivity, therefore, is not a linear system. Testify whether it has the property of additivity. Y = a *u + b Here a and b are all constants. The input-output relation in Fig 2.1(b) can be described as: 2.1 Consider the memoryless system with characteristics shown in Fig 2.19, in which u denotes the input and y the output.
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