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Discrete-Time Signals: Time-Domain Representation Signals are represented as sequences of numbers, called samples Sample value of a typical signal or sequence denoted as x[n] with n being an integer in the range-∞≤n≤∞ ·x[n] defined only for integer values of and undefined for non-integer values
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the Transform Domain An LTI discrete-time system is completely characterized in the time-domain by its impulse response {h[n]} We consider now the use of the DTFT and the z-transform in developing the transform￾domain representations of an LTI system
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◆ Background ◆ Preliminary Concepts ◆ Sampling and the Fourier Transform of Sampled Functions ◆ The Discrete Fourier Transform of One Variable ◆ Extension to Functions of Two Variables ◆ Some Properties of the 2-D Discrete Fourier Transform ◆ The Basics of Filtering in the Frequency Domain ◆ Image Smoothing Using Frequency Domain Filters ◆ Image Sharpening Using Frequency Domain Filters ◆ Selective Filtering
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◆7.0 Introduction ◆7.1 Design of Discrete-Time IIR Filters From Continuous-Time Filters ◆7.2 Design of FIR Filters by Windowing ◆7.3 Examples of FIR Filters Design by the Kaiser Window Method ◆7.4 Optimum Approximations of FIR Filters ◆7.5 Examples of FIR Equiripple Approximation ◆7.6 Comments on IIR and FIR Discrete-Time Filters
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The dtft provides a frequency-domain representation of discrete-time signals and lti discrete-time systems Because of the convergence condition, in many cases. the dtft of a sequence may not exist as a result. it is not possible to make use of such frequency-domain characterization in these cases Copyright C 2001, S K. Mitra
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2.1 Discrete-time LTI Systems : The Convolution Sum (卷积和) 2.1.1 The Representation of Discrete-Time Signals in Terms of impulses
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BIBO Stability Condition - A discrete-time LTI system is BIBO stable if the output sequence {y[n]} remains bounded for any bounded input sequence{x[n]}
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◆7.0 Introduction ◆7.1 Design of Discrete-Time IIR Filters From Continuous-Time Filters ◆7.2 Design of FIR Filters by Windowing ◆7.3 Examples of FIR Filters Design by the Kaiser Window Method ◆7.4 Optimum Approximations of FIR Filters ◆7.5 Examples of FIR Equiripple Approximation ◆7.6 Comments on IIR and FIR Discrete-Time Filters
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一、傅立叶变换-离散时间傅立叶变换(Discrete-Time Fourier Transform,DTFT)(定义、收敛条件、性质)– 离散傅立叶变换(Discrete Fourier Transform,DFT)(定义、性质) 二、Z变换(定义、收敛条件、逆变换、性质)
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◆7.0 Introduction ◆7.1 Filter Specifications ◆7.2 Design of Discrete-Time IIR Filters From Continuous-Time Filters ◆7.3 Discrete-Time Butterworth, Chebyshev and Elliptic Filters ◆7.4 Frequency Transformations of Lowpass IIR Filters ◆7.5 Design of FIR Filters by Windowing ◆7.6 Examples of FIR Filters Design by the Kaiser Window Method
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