<transcript><audio_27>but this would have put you on a point in the imaginary axis its this which is creating a trouble here so the one thing is we want to do away with this term now how do you do away with this term you can't do away with this term but by multiplying by</transcript><caption><image_28>The image is a whiteboard with a hand holding a black marker. On the whiteboard, there is a mathematical equation written in black ink. The equation is written in a neat and organized manner, with the letters "7 =" and "1 =" written above and below the equation. 

The equation appears to be a trigonometric equation, which is a type of mathematical equation that is used to calculate the area of a given value. The x-axis of the equation is labeled as "7" and the y-axis is labeled with the corresponding values.

There is also a logo of the Indian Institute of Technology (CDEEP) on the top right corner of the white board. The logo is a shield with a blue background and a white star in the center. The text on the board reads "CDEEP" in bold letters.</caption><caption><image_29>The image is a screenshot from a video interview. It shows a man in a black suit and a white shirt, speaking into a microphone. He is standing in front of a purple background with a geometric pattern. The man appears to be giving a speech or presentation, as he is gesturing with his hands as if he is making a point. On the right side of the image, there is text that reads "CDEEP IT Bombay" and on the bottom right corner, there are logos for the company.</caption><transcript><audio_30>its complex conjugate or dividing by the same term so it's clear that we cannot be happy with just a polynomial in z or z inverse we need a rational a proper rational function</transcript><transcript><audio_31>in z or z inverse to replace s and that rational function in z should be such that it cancels out this factor that's the first observation the second observation is that when omega goes from</transcript><transcript><audio_32>minus pi to plus pi even if this term were to be absent you would be taken only from minus 2 to plus 2 here not from minus infinity to plus infinity</transcript><caption><image_33>The image shows a hand holding a black marker and writing on a whiteboard. The hand is positioned in the center of the image and is holding the marker in a way that it appears to be writing a mathematical equation. The equation is written in black ink and is in the form of a circle. The background is white and there is a logo on the top right corner that reads "CDEEP IT BOMB" and a stamp on the bottom right corner. The image appears to have been taken in a classroom or office setting.</caption> but this would have put you on a point in the imaginary axis its this which is creating a trouble here so the one thing is we want to do away with this term now how do you do away with this term you can't do away with this term but by multiplying by its complex conjugate or dividing by the same term so it's clear that we cannot be happy with just a polynomial in z or z inverse we need a rational a proper rational function in z or z inverse to replace s and that rational function in z should be such that it cancels out this factor that's the first observation the second observation is that when omega goes from minus pi to plus pi even if this term were to be absent you would be taken only from minus 2 to plus 2 here not from minus infinity to plus infinity
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