0.2 Lab 2 - discrete-time systems  (Page 2/3)

The following two continuous-time systems are commonlyused in electrical engineering:

For each of these two systems, do the following:

• i. Formulate a discrete-time system that approximates the continuous-time function.
• ii. Write down the difference equation that describes your discrete-time system. Your difference equation should be inclosed form, i.e. no summations.
• iii. Draw a block diagram of your discrete-time system as in [link] .

Stock market example

One reason that digital signal processing (DSP) techniques are so powerful is thatthey can be used for very different kinds of signals. While most continuous-time systems only process voltage and current signals,a computer can process discrete-time signals which are essentially just sequences of numbers.Therefore DSP may be used in a very wide range of applications. Let's look at an example.

A stockbroker wants to see whether the average value of a certain stock is increasing or decreasing.To do this, the daily fluctuations of the stock values must be eliminated.A popular business magazine recommends three possible methods for computing this average.

Do the following:

• For each of the these three methods: 1) write a difference equation,2) draw a system diagram, and 3) calculate the impulse response.
• Explain why methods [link] and [link] are known as moving averages.

Example discrete-time systems

Write two Matlab functions that will apply the differentiator and integrator systems, designed in the "Example Discrete-time Systems" section, to arbitrary input signals. Then apply the differentiator and integrator to the followingtwo signals for $-10\le n\le 20$ .

• $\delta \left(n\right)-\delta (n-5)$
• $u\left(n\right)-u(n-(N+1\left)\right)$ with $N=10$

Hint: To compute the function $u\left(n\right)$ for $-10\le n\le 20$ , first set n = -10:20 , and then use the Boolean expression u = (n>=0) .

For each of the four cases, use the subplot and stem commands to plot each input and output signal on a single figure.

Difference equations

In this section, we will study the effect of two discrete-time filters.The first filter, $y=S_1\left[x\right]$ , obeys the difference equation

and the second filter, $y=S_2\left[x\right]$ , obeys the difference equation

Write Matlab functions to implement each of these filters.