<transcript><audio_52>the power minus j omega divided by 1 plus e raised to the power j omega please check that so easy and therefore we have the answer to the</transcript><transcript><audio_53>s equal to 1 minus z inverse by 1 plus z inverse and now let us check that this transformation indeed does all the jobs that we wanted of course one job we have already</transcript><caption><image_54>The image is a whiteboard with black text written on it. The text reads "We are therefore asking for" and is written in a cursive font. Below the text, there are three equations written in black marker. The equations are:

1 = 1 = 1, 2 = 2, and 3 = 1. The first equation is written as "1+2" and the second equation is "1 + 2". The third equation is also written as "+1+1".

On the right side of the image, there is a logo for CDEEP, a company that sells CDEEP products. The logo is a shield with a crown on top and the words "CDEEP" written in the center. The background of the whiteboard is plain white.</caption><video><caption><image_55>The image is a screenshot from a video interview. It shows a man in a suit sitting at a desk with a microphone in front of him. He appears to be deep in thought, with his eyes closed and his head tilted downwards. The background is a dark purple color with a map of the world in the top left corner. On the right side of the image, there is a logo for NPTEL and the words "CDEEP" in white text. The overall tone of the interview is serious and focused.</caption><caption><image_56>The image is a screenshot from a video. It shows a person's hand holding a pen and writing on a whiteboard. The whiteboard is blank and the person is in the process of writing on it. On the top right corner of the image, there is a logo of a company called "CDEEP" and on the top left corner, there are two lines of text that appear to be instructions or instructions. The text on the bottom right corner reads "CDEEP HIT BOMBAY". The image appears to be taken from a top-down perspective.</caption></video><transcript><audio_57>verified let's start with that thing that we have already done so let's start with z equal to e raised to the power j omega we will just it's a formality but we'll just complete it</transcript><transcript><audio_58>and we've seen that you know s becomes j tan omega by 2 here so the good thing is omega going from minus pi towards plus pi</transcript><video><caption><image_59>The image shows a person's hand holding a black marker and writing on a whiteboard. The text on the whiteboard is written in black ink and appears to be a mathematical equation. The equation is written as "z = jian" and "jian" is written below it. On the right side of the image, there is a logo of the company "CDEEP" and the text "NPTEL" on the bottom right corner. The background is plain white.</caption><caption><image_60>The image shows a hand holding a black marker and writing on a whiteboard. The text on the whiteboard is written in black ink and appears to be mathematical equations. The equations are written in a neat and organized manner, with the letters and numbers clearly visible. The background of the image is blurred, but it seems to be a classroom or a classroom setting. On the top right corner, there is a logo for a company called "CDEEP" and on the bottom left corner, it reads "NPTEL".</caption><caption><image_61>The image shows a hand holding a piece of paper with a mathematical equation written on it. The equation is written in black ink and is written on a whiteboard. The hand is holding the paper with one hand and the other hand is pointing towards the right side of the image. The background is plain white. On the top right corner, there is a logo of the Indian Institute of Science and Technology (IIT Bombay) and on the top left corner, it reads "CDEEP". On the bottom right corner of the whiteboard, there are two logos, one for NPTEL and one for CDEEP. The image appears to be a screenshot from a video or presentation.</caption></video> the power minus j omega divided by 1 plus e raised to the power j omega please check that so easy and therefore we have the answer to the s equal to 1 minus z inverse by 1 plus z inverse and now let us check that this transformation indeed does all the jobs that we wanted of course one job we have already verified let's start with that thing that we have already done so let's start with z equal to e raised to the power j omega we will just it's a formality but we'll just complete it and we've seen that you know s becomes j tan omega by 2 here so the good thing is omega going from minus pi towards plus pi
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