Signals and Systems EE235 Leo Lam © 2010-2012.

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Signals and Systems EE235 Leo Lam © 2010-2012

Unstable Leo Lam © 2010-2011

Today’s menu Review Duality Sample Final Leo Lam © 2010-2011

Duality of Fourier Transform Duality (very neat): Duality of the Fourier transform: If time domain signal f(t) has Fourier transform F(), then F(t) has Fourier transform 2 f(-) i.e. if: Then: Changed sign 4 Leo Lam © 2010-2011

Duality of Fourier Transform (Example) Using this pair: Find the FT of Where T=5 5 Leo Lam © 2010-2011

Duality of Fourier Transform (Example) Using this pair: Find the FT of 6 Leo Lam © 2010-2011

Convolution/Multiplication Example Given f(t)=cos(t)e–tu(t) what is F() 7 Leo Lam © 2010-2011

More Fourier Transform Properties time domain Fourier transform Duality Time-scaling Multiplication Differentiation Integration Conjugation Dual of convolution 8 8 Leo Lam © 2010-2011

Fourier Transform Pairs (Recap) Review: 1 9 9 Leo Lam © 2010-2011

Sample Final Review: 10 10 Leo Lam © 2010-2011

Sample Final Review: 11 11 Leo Lam © 2010-2011

Sample Final Review: 12 12 Leo Lam © 2010-2011

Sample Final Review: 13 13 Leo Lam © 2010-2011

Sample Final Review: 14 14 Leo Lam © 2010-2011

Sample Final Review: 15 15 Leo Lam © 2010-2011

Sample Final Review: 16 16 Leo Lam © 2010-2011