<transcript><audio_15>is not going to help us in fact let us use some more cues to lead us to a transformation of choice let us do it the other way let us put z equal to e raised to the power j</transcript><caption><image_16>The image is a screenshot from a TV show. It shows a man in a suit and tie sitting in front of a microphone. He appears to be in a studio or a news studio, as there is a large screen in the background with a map of India on it. The man has a mustache and is looking off to the side with a serious expression on his face. The text on the screen reads "CDEEP HIT BOMBAY".</caption><caption><image_17>The image shows a hand holding a black marker and writing on a whiteboard. The hand is positioned in a way that the marker is pointing towards the right side of the image. The background is plain white and there is a logo of a company on the top right corner. On the bottom right corner, there is text that reads "CDEEP HIT BOMB 3". The image appears to be a screenshot from a video or presentation.</caption><transcript><audio_18>omega and the same transformation and we get 1 minus e raised to the power minus j omega and that can be rewritten as e raised to</transcript><transcript><audio_19>the power j minus j omega by 2</transcript><caption><image_20>The image shows a person's hand holding a black marker and writing on a whiteboard. The whiteboard has a logo of the Indian Institute of Technology (CDEEP) on the top right corner. Below the logo, there is a text written in Hindi that reads "CDEEP HIT BOMB 11". The text appears to be a mathematical equation or mathematical problem. The person is writing on the whiteboard with the marker.</caption> is not going to help us in fact let us use some more cues to lead us to a transformation of choice let us do it the other way let us put z equal to e raised to the power j omega and the same transformation and we get 1 minus e raised to the power minus j omega and that can be rewritten as e raised to the power j minus j omega by 2
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