SAMPLING We live in a continuous-time world most of the signals we encounter are CT signals, e.g. x(). How do we convert them into Dt signals x[n? Sampling, taking snap shots of x(t) every Seconds

1. DTFT Properties and Examples 2. Duality in fs& ft 3. Magnitude/Phase of Transforms and Frequency Responses

Fourier series: Periodic signals and lti Systems ()=∑H(k k= ak一→H(ko)ak “g Soak-→|H(jkco)lkl H(7k)=1H(k0e∠B(ko) or powers of signals get modified through filter/system ncludes both amplitude phase akeJhwon

Fouriers derivation of the ct fourier transform x(t)-an aperiodic signal view it as the limit of a periodic signal as t→∞ For a periodic signal the harmonic components are spaced Oo=2π/ T apart. AsT→∞,Obo→>0, and harmonic components are space

Representation of ct signals Approximate any input x(t) as a sum of shifted, scaled

1Some examples of systems 2 System properties and examples CAusality

Can be continuous Trajectory of a space shuttle Mass density in a cross-section of a brain · Can be discrete dNa base sequence Digital image pixels Can be 1-D,2-D,·N-D For this course: Focus on a single(1-D) independent variable which we call“time

§1 波动稳定度概念 §2 惯性不稳定 §3 正压不稳定 §4 斜压不稳定 §5 K—H 不稳定

§4 重力外波和重力内波 §5 惯性振荡与惯性波 §6 水平无辐散的 Rossby 波 §7 有水平辐合辐散的 Rossby 波 §8 大气混合波—惯性重力外波 §9 群速度，波的频散效应