with x(0)=I exist and are unique on the time interval t E [ 0, 1] for allTER\.Then discrete time system(4. 1)with f(5)=r(, i)describes the evolution of continuous time system(4.)at discrete time samples. In particular, if a is continuous then so is f Let us call a point in the closure of X locally attractive for system(4. 1)if there exists

9.0 Introduction 9.1 Direct Computation Of The Discrete Fourier Transform 9.2 decimation-in-time FFT Algorithms 9.3 decimation-in-frequency FFT Algorithms 9.4 practical considerations

4.0 Introduction 4.1 Periodic Sampling 4.2 Frequency-Domain Representation of Sampling 4.3 Reconstruction of a Bandlimited Signal from its Samples 4.4 Discrete-Time Processing of Continuous Time signals 4.5 Continuous-time Processing of Discrete Time Signal

Expectations and Conditional Expectations Definition 1 Discrete Random Variable random wariable is discrete f the set of outcomes is either finite in number or countably

Sampling Sampling provides a discrete-time representation of a continuous waveform Sample points are real-valued numbers In order to transmit over a digital system we must first convert into discrete valued numbers

4.1 LTI Discrete-Time Systems in the Transform Domain · Such transformdomain- representations provide additional insight into the behavior of such systems It is easier to design and implement these systems in the transform-domain for certain applications We consider now the use of the DtFt and the z-transform in developing the transform- domain representations of an LTI system

Introduction Basic signal properties(dc, rms, dBm. and power) Fourier transform and spectra Linear systems and linear distortion Bandlimited signal and sampling Discrete Fourier transform · Bandwidth of signal

长期以来,快速傅氏变换(Fast Fourier Transform)和离散小波变换(Discrete Wavelet Transform)在数字信号处理、石油勘探、地震预报、医学断层诊断、编码理论

5. Aggregating Consumers Consumer Heterogeneity and a Discrete good b. The Properties of Aggregate Demand The Existence of a representative Consumer d. Externalities e. The Social Multiplier

100.1 Models Classes of Systems to Be Modeled • Two Major Approaches to Modeling • Forms of the Model • Nonuniqueness • Approximation of Continuous Systems by Discrete Models 100.2 Dynamic Response