<transcript><audio_90>sigma is less than 0 then 1 plus sigma squared is strictly less than 1 minus sigma squared and nothing changes if you add omega</transcript><caption><image_91>The image shows a person's hand holding a black marker and writing on a whiteboard. The whiteboard has the logo of the Indian Institute of Technology (CDEEP) and the text "It Bombay" written on it. The text is written in black ink and appears to be a mathematical equation. The equation is written on the whiteboard in a neat and precise manner. The background is blurred, but it seems like the person is focused on the task at hand.</caption><transcript><audio_92>and therefore it is very clear that the numerator by the denominator is strictly less than 1</transcript><transcript><audio_93>so we have what we wanted we have a satisfactory mapping of between the imaginary axis and the unit circle the outside of the unit circle corresponds to the right half of the s plane that is the real part of</transcript> sigma is less than 0 then 1 plus sigma squared is strictly less than 1 minus sigma squared and nothing changes if you add omega and therefore it is very clear that the numerator by the denominator is strictly less than 1 so we have what we wanted we have a satisfactory mapping of between the imaginary axis and the unit circle the outside of the unit circle corresponds to the right half of the s plane that is the real part of
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