The linearity property of Z-transform states that the z-transform of a weighted sum of two signals is equal to the weighted sum of individual z-transforms. Group of answer choicesTrueFalse

1. Which of the following justifies the linearity property of z-transform?[x(n)↔X(z)].a) x(n)+y(n) ↔ X(z)Y(z)b) x(n)+y(n) ↔ X(z)+Y(z)c) x(n)y(n) ↔ X(z)+Y(z)d) x(n)y(n) ↔ X(z)Y(z)

As per the convolution property of z-transformGroup of answer choicesnonethe z-transform of convolution of two sequences is the product of their respective z-transforms.the z-transform of convolution of two sequences is the convolution of their respective z-transforms.the z-transform of convolution of two sequences is the addition of their respective z-transforms.

Given 5.0||)5.0(4)( 2 >+= zzzzX Find the Z-Transform of the following signals.(a) y[n] = x[ n – 2] (b) e[n] = x[–n] (c) d[n] = 2n x[n] (d) s[n] = x[n] * x[n]A N S :4(a) 2)5.0z(zz4)z(Y += |Z| > 0.5 (b) 2)2(16)(+=zzE (c)1||:)1(8)( 2 >+=

With reference to Time shifting property of z-transform, if X(z) is the z-transform of x(n) then what is the z-transform of x(n-k)? Group of answer choicesx(z+k)Zk X(z)x(z-k)Z-k X(z)

Weighted superposition of time-shifted impulse responses is termed as _______ for discrete-time signals.Group of answer choicesConvolution IntegralNoneConvolution SumConvolution Multiple