7.1 MATLAB在信号与系统中的应用 7.2 MATLAB在数字信号处理中的应用 7.3 MATLAB辅助神经网络分析与设计 7.4 MATLAB辅助模糊系统分析与设计

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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 x[n] defined only for integer values of n and undefined for non-integer values of n

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

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

Stability Condition in Terms of the Pole Locations A causal LTI digital filter is BIBO stable if and only if its impulse response h[n] is absolutely summable, i.e., We now develop a stability condition in terms of the pole locations of the transfer function H(z)

Later in the course we shall review various methods of designing frequency-selective filters satisfying prescribed specifications We now describe several low-order FIR and IIR digital filters with reasonable selective frequency responses that often are satisfactory in a number of applications

The simple filters discussed so far are characterized either by a single passband and/or a single stopband There are applications where filters with multiple passbands and stopbands are required The comb filter is an example of such filters

It is nearly impossible to design a linear￾phase IIR transfer function It is always possible to design an FIR transfer function with an exact linear-phase response Consider a causal FIR transfer function H(z) of length N+1, i.e., of order N:

Discrete-Time Systems A discrete-time system processes a given input sequence x[] to generates an output sequencey[n] with more desirable properties In most applications, the discrete-time system is a single-input, single-output system: