## Using the Matlab function filter to describe afirst-order LTI system

Draw the block diagram of the first-order system described by the differential equation below
$$y[n]=\frac{1}{2} y[n-1]+2 x[n]-x[n-2]$$

### FIR and IIR: definitions and discussion

• FIR: a system whose impulse response is time-limited (finite duration) is called a finite impulse response system o-th oro
• IIR: a system whose impulse response is not limited in time (infinite duration) is called an infinite impulse response system
• FIR systems are always stable $\quad n \geqslant 1$
• FIR systems are always stable $\sum_{k=n_{1}}^{n_{2}}|h[n]|<\infty$
• IIR systems are easy to implement via recursion: less memory, less computing
• However, IIR systems need to be designed carefully in order to avoid instability.

### Block diagram representations of first orderDT systems

Systems described by difference equations can be easily described by block diagrams;
Block diagrams are useful for:

• Pictorial representations (good for
interconnecting systems)
• Digital hardware representations
Block diagrams need only three basic operations:
• multiplication by a coefficient
• delay (time shift with $n=1$ )

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# 概率论代考

## ELEC 310 – Digital Signal Processing 1

### Instructor Office Hours

F. Gebali, P.Eng., Ph.D. Everyday email or phone first
E-mail: [email protected] Location: EOW 433

### Course Objectives

Generation of discrete-time signals through the sampling process and their spectral representation. Mathematical
representation and properties of digital signal processing (DSP) systems. Typical DSP systems, e.g., digital filters
and applications. The z-transform and its relation to the Laurent series. Evaluation of the inverse z transform using
complex series and contour integrals. Application of the z transform for representation and analysis of DSP systems.
The processing of continuous time signals using DSP systems. The discrete-?Fourier transform and the use of fast
Fourier transforms for its evaluation. Introduction to the design of DSP systems.

### Learning Outcomes

1. Understand linearity, time invariance and convolution
2. Explain relation between continuous- and discrete-time Fourier transform
3. Understand z-transform and its use in solving problems
4. Evaluate forward and inverse z and Fourier transforms for discrete signals
5. Demonstrate competency in working with both time- and frequency-domain representations of discrete-time
sampled signals
6. Design a discrete-time filtering algorithm based on given requirements
7. Use MATLAB effectively for analysis and design of sampled digital signals
8. Explain significance of sampling theorem and use it in the context of discrete-time processing of continuoustime signals