The Signum Function

Monday, 25 March 2019

5:09 PM

𝑓﷐𝑡﷯=﷐sgn﷮﷐𝑡﷯﷯=﷐﷐−1,𝑡<0﷮0,𝑡=0﷮1,𝑡>0﷯﷯ Ink Drawings Ink Drawings Ink Drawings Ink Drawings ℱ﷐﷐sgn﷮﷐𝑡﷯﷯﷯=ℱ﷐𝑢﷐𝑡﷯−𝑢﷐−𝑡﷯﷯ =ℱ﷐𝑢﷐𝑡﷯﷯−ℱ{𝑢﷐−𝑡﷯} (linearity) =﷐𝜋𝛿﷐ω﷯+﷐1﷮𝑗𝑤﷯﷯−﷐π𝛿﷐−ω﷯+﷐1﷮𝑗﷐−ω﷯﷯﷯ (reversal) =﷐𝜋𝛿﷐ω﷯+﷐1﷮𝑗𝑤﷯﷯−﷐π𝛿﷐ω﷯+﷐1﷮𝑗﷐−ω﷯﷯﷯ =﷐2﷮𝑗𝜔﷯ Ink Drawings Ink Drawings Ink Drawings Ink Drawings       

 

 (time differentiation)

 

 

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