1. S. Mandayam/ ECOMMS/ECE Dept./Rowan University Electrical Communications Systems ECE.09.331 Spring 2008 Shreekanth Mandayam ECE Department Rowan University http://engineering.rowan.edu/~shreek/spring08/ecomms/ A Guide to Signals & Transforms

2. S. Mandayam/ ECOMMS/ECE Dept./Rowan University All those signals………. Amplitude time discrete continuous discrete-time analog signal w(nT s ) TsTs sampling discrete discrete discrete-time digital signal C n 111 110 101 100 011 010 001 000 sampling Time Amplitude Signal w(t) continuous continuous continuous-time analog signal w(t) discrete continuous discrete-time sequence w[n] n=0 1 2 3 4 5 indexing

3. S. Mandayam/ ECOMMS/ECE Dept./Rowan University …..and all those transforms Continuous-time analog signal w(t) Continuous-time analog signal w(t) Discrete-time analog sequence w [n] Discrete-time analog sequence w [n] Sample in time, period = T s  =2  f  =  T s, scale amplitude by 1/T s Sample in frequency,  = 2  n/N, N = Length of sequence Continuous Fourier Transform W(f) Continuous Fourier Transform W(f) Discrete Fourier Transform W(k) Discrete Fourier Transform W(k) Discrete-Time Fourier Transform W(  Discrete-Time Fourier Transform W(  Laplace Transform W(s) Laplace Transform W(s) z-Transform W(z) z-Transform W(z) z = e j  s = j   f C C C C C D D D C Continuous-variable Discrete-variable