How was this result obtained sorry due to an error some of...

How was this result obtained? Sorry, due to an error, some of the text duplicated, so don't pay attention to duplicates. Thanks!! Suppose we want to design a discrete-time LTI system which has the property that if the input is (-), then the output is: y[n] = Find the frequency response He(jw) of a discrete-time LTI system that has the foregoing property. He(jw) = 1/(1 - e^(-jw))^3 Ge 1/(1 - e^(-jw))^3 (1 - e^(-jw))/(1 - e^(-jw))^6 2/(1 - e^(-jw))^3 He(jw) = (1 - e^(-jw))/(1 - e^(-jw))^2 Correct Answer 1/(1 - e^(-jw))^3 2/(1 - e^(-jw))^3 He(jw) = (1 - e^(-jw))/(1 - e^(-jw))^2

Transcript

00:01 Here we are considering about the discrete time lti signal that is y of n from here is equals to y of n minus 0 .3 of y of n minus 1 minus 0 .04 of y of n minus 2 become equals to x of n plus 2 of x of n minus 1.

00:19 So this is given here with the initial conditions are having that is y of minus 1 is equals and y of minus 2 is equals to 0 and where we are given the value of the input that is represented by x of n that is equals to 0 .4 raise to the power n which is multiplied by the u of n.

00:38 So this is given here.

00:40 So in the first part we have to determine the zero input response.

00:45 So from here we can say that we are considering about the zero input response.

00:52 So we are using the unilateral z transform from here.

00:58 So for the unilateral z transform we can say that the value of y of z become equals to minus of 0 .3 which is multiplied by the z inverse of y of z plus y of minus of 1 minus 0 .04 of x raise to z raise to the power minus 2 multiplied by the y of z plus z inverse of y raise to the y of minus 1 plus y of z minus of z that is equals to x of z plus z of 2 of z inverse of y of z.

01:30 Simplifying the term we get the value that is equals to y of z multiplied by the 1 minus 0 .3 of z inverse multiplied by the y of z minus 0 .9 minus 0 .04 multiplied by the z raise to the power minus 2 y of z plus 0 .12 multiplied by z inverse become equals to x of z multiplied by the 1 plus 2 of z inverse.

01:55 So solving the term we can say that input that is x of n is equals to 0 .4 multiplied by the u of n.

02:02 So taking the transformation so x of z become equals to 1 that is equals to 1 divided by the 1 minus 0 .4 multiplied by the z inverse.

02:10 So from here this is the value or we can say that 1 minus 0 .3 of z inverse minus 0 .04 of z raise to the power minus 2 of y of z become equals to 0 .9 plus 0 .12 z inverse plus 1 plus 2 z inverse which is divided by 1 minus 0 .4 of z inverse.

02:34 Let's say this is the initial condition term and this from here is the input term...

Question

Please give Ace some feedback