MATLAB discrete time systems in time domain and frequency domain analysis

Purpose

Become more familiar with and master the system function H (Z) analysis of discrete-time systems in time domain and frequency domain characteristics;

Review how MATLAB language in time domain and frequency domain analysis of discrete-time systems

Content

(1) the use of the MATLAB command to draw a discrete-time system pole-zero diagram, impulse response and frequency response curve

Two pole-zero diagram of the system to analyze the stability of the discrete system

Principle

System function of the discrete-time system that is: XXXXXX

To note is that the system function of the discrete-time system may have two forms, one is the numerator and denominator polynomial according to Z Positive Power term arrangement, the other is the numerator and denominator polynomial according to Z negative power times the Arrangement. Either arrangement, the dimensions of the numerator and denominator polynomial coefficient vector must be the same, different use 0 filled, otherwise Z = 0 the zero or pole can be left out.

Pole-zero distribution of the system function H (Z) can determine the characteristics of the system has very important significance to the analysis of the discrete system characteristics. Through the analysis of poles and zeros of the system function for discrete systems, the characteristics of the following aspects:

Time-domain characteristics of a system impulse response h (n)

(2) stability of discrete systems

3 the frequency characteristics of the discrete system (amplitude-frequency response and phase frequency response)

MATLAB provides us with the solving of these features and draw the pole-zero diagram of the system function-related functions, such as zplane, impz, freqz, the use of these functions see the book 6.5 and 6.6.

The implementation of the procedures required by the graphics, as shown below.

From pole-zero diagram of Figure 1 you can see, the function of the system poles inside the unit circle, so the system is a stable system.

Task

A system function XX known discrete systems, try using MATLAB analysis of the system in time domain and frequency domain characteristics. Requirements: pole-zero diagram, respectively, to draw in a window system, impulse response, amplitude frequency and phase-frequency characteristics, and determine the stability of the system.

Known a discrete-time system block diagram shown in Figure 2, try using MATLAB analysis of the frequency characteristics of the system. Requirements: pole-zero diagram, respectively, to draw in a window system, the phase frequency response curve, 0-π and 0-2π range of the amplitude-frequency characteristics, and analyze the stability of the system and to complete the function.

Thinking title

If you want to show the frequency characteristics of the 0-of π and 0-2π range in order to observe the cyclical nature of the frequency response of discrete-time system, how to adjust your MATLAB command?