Fourier Transform Pairs Some Basic Functions Information at x(t) X(ω) © 2015, Erik Cheever (Synthesis) (Analysis) (impulse) (constant) (unit rectangular pulse, width=1) (sinc) (constant) (impulse) (complex exponential) (shifted impulse) (causal exponential) (same as Laplace w/ s=jω) (Gaussian) (Gaussian) Derived Functions (using basic functions and properties) x(t) X(ω) (time scaled rectangular pulse, width=Tp) (rectangular pulse in ω) (triangular pulse, width=2) (scaled triangular pulse, width=2Tp) γ(t) (unit step function) Using these functions and some Fourier Transform Properties (next page), we can derive the Fourier Transform of many other functions.
Fourier Transform Pairs Some Basic Functions x(t) X(ω) (Synthesis) (Analysis) (impulse) (constant) (unit rectangular pulse, width=1) (sinc) (constant) (impulse) (complex exponential) (shifted impulse) (causal exponential) (same as Laplace w/ s=jω) (Gaussian) (Gaussian) Derived Functions (using basic functions and properties) x(t) X(ω) (time scaled rectangular pulse, width=Tp) (rectangular pulse in ω) (triangular pulse, width=2) (scaled triangular pulse, width=2Tp) γ(t) (unit step function) Using these functions and some Fourier Transform Properties (next page), we can derive the Fourier Transform of many other functions. Information at © 2015, Erik Cheever
FTPairsProps.docx