# 0.1 Lab 1 - discrete and continuous-time signals  (Page 4/5)

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## Processing of speech signals

Digital signal processing is widely used in speech processing for applications ranging from speech compression and transmission,to speech recognition and speaker identification. This exercise will introduce the process of reading and manipulatinga speech signal.

First download the speech audio file speech.au , and then do the following:

1. Use the auread command to load the file speech.au into Matlab.
2. Plot the signal on the screen as if it were a continuous-time signal (i.e. use the plot command).
3. Play the signal via the digital-to-analog converter in your workstation with the Matlab sound function.
Submit your plot of the speech signal.

## Attributes of continuous-time signals

In this section you will practice writing .m-files to calculate the basic attributes of continuous-time signals.Download the function signal1.p . This is a pre-parsed pseudo-code file (P-file), which isa “pre-compiled” form of the Matlab function signal1.m . To evaluate this function,simply type y = signal1(t) where t is a vector containing values of time.Note that this Matlab function is valid for any real-valued time, t , so y = signal1(t) yields samples of a continuous-time function.

First plot the function using the plot command. Experiment with different values for the sampling periodand the starting and ending times, and choose values that yield an accurate representation of the signal.Be sure to show the corresponding times in your plot using a command similar to plot(t,y) .

Next write individual Matlab functions to compute the minimum, maximum, and approximate energy of this particular signal.Each of these functions should just accept an input vector of times, t , and should call signal1(t) within the body of the function. You may use the built-in Matlab functions min and max . Again, you will need to experiment with the sampling period,and the starting and ending times so that your computations of the min, max, and energy are accurate.

Remember the definition of the energy is

$\text{energy}={\int }_{-\infty }^{\infty }{\left|\text{signal1},\left(,t,\right)\right|}^{2}dt\phantom{\rule{4pt}{0ex}}.$
Submit a plot of the function, and the computed values of the min, max, and energy.Explain your choice of the sampling period, and the starting and ending times.Also, submit the code for your energy function.

## Special functions

Plot the following two continuous-time functions over the specified intervals. Write separate script files if you prefer.Use the subplot command to put both plots in a single figure, and be sure to label the time axes.

• $\text{sinc}\left(t\right)$ for $t$ in $\left[-10\pi ,10\pi \right]$
• $\text{rect}\left(t\right)$ for $t$ in $\left[-2,2\right]$
The function rect(t) may be computed in Matlab by using a Boolean expression.For example, if t=-10:0.1:10 , then $y=rect\text{(}t\text{)}$ may be computed using the Matlab command y=(abs(t)<=0.5) .

Write an .m-script file to stem the following discrete-time function for $a=0.8$ , $a=1.0$ and $a=1.5$ . Use the subplot command to put all three plots in a single figure.Issue the command orient('tall') just prior to printing to prevent crowding of the subplots.

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