Name:

Section:

Laboratory Exercise 1
DISCRETE-TIME SIGNALS: TIME-DOMAIN REPRESENTATION

1.1 GENERATION OF SEQUENCES

Project 1.1 Unit sample and unit step sequences

A copy of Program P1_1 is given below.

Answers:

Q1.1 The unit sample sequence u[n] generated by running Program P1_1 is shown
below:

< Insert MATLAB figure(s) here. Copy from figure window(s) and
paste. >

Q1.2 The purpose of clf command is -

The purpose of axis command is -

The purpose of title command is -

The purpose of xlabel command is -

The purpose of ylabel command is -

Q1.3 The modified Program P1_1 to generate a delayed unit sample sequence ud[n]
with a delay of 11 samples is given below along with the sequence generated by
running this program.

< Insert program code here. Copy from m-file(s) and paste. >

< Insert MATLAB figure(s) here. Copy from figure window(s) and
paste. >

Q1.4 The modified Program P1_1 to generate a unit step sequence s[n] is given below
along with the sequence generated by running this program .

< Insert program code here. Copy from m-file(s) and paste. >

< Insert MATLAB figure(s) here. Copy from figure window(s) and
paste. >

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Q1.5 The modified Program P1_1 to generate a unit step sequence sd[n] with an ad-
vance of 7 samples is given below along with the sequence generated by running
this program.

< Insert program code here. Copy from m-file(s) and paste. >

< Insert MATLAB figure(s) here. Copy from figure window(s) and
paste. >

Project 1.2 Exponential signals

A copy of Programs P1_2 and P1_3 are given below.

< Insert program code here. Copy from m-file(s) and paste. >

Answers:

Q1.6 The complex-valued exponential sequence generated by running Program P1_2 is

< Insert MATLAB figure(s) here. Copy from figure window(s) and
paste. >

Q1.7 The parameter controlling the rate of growth or decay of this sequence is -

The parameter controlling the amplitude of this sequence is -

Q1.8 The result of changing the parameter c to (1/12)+(pi/6)*i is -

Q1.9 The purpose of the operator real is -

The purpose of the operator imag is -

Q1.10 The purpose of the command subplot is -

Q1.11 The real-valued exponential sequence generated by running Program P1_3 is

< Insert MATLAB figure(s) here. Copy from figure window(s) and
paste. >

Q1.12 The parameter controlling the rate of growth or decay of this sequence is -

The parameter controlling the amplitude of this sequence is -

Q1.14 The sequence generated by running Program P1_3 with the parameter a changed
to 0.9 and the parameter K changed to 20 is shown below:

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 < Insert MATLAB figure(s) here. Copy from figure window(s) and
paste. >

Q1.15 The length of this sequence is -

It is controlled by the following MATLAB command line :

It can be changed to generate sequences with different lengths as follows (give an

Q1.16 The energies of the real-valued exponential sequences x[n]generated in Q1.11

Project 1.3 Sinusoidal sequences

A copy of Program P1_4 is given below.

< Insert program code here. Copy from m-file(s) and paste. >

Answers:

Q1.17 The sinusoidal sequence generated by running Program P1_4 is displayed below .

< Insert MATLAB figure(s) here. Copy from figure window(s) and
paste. >

Q1.18 The frequency of this sequence is -

It is controlled by the following MATLAB command line :

A sequence with new frequency _____ can be generated by the following command
line:

The parameter controlling the phase of this sequence is -

The parameter controlling the amplitude of this sequence is -

The period of this sequence is -

Q1.19 The length of this sequence is -

It is controlled by the following MATLAB command line :

A sequence with new length _____ can be generated by the following command
line:

Q1.20 The average power of the generated sinusoidal sequence is -

Q1.21 The purpose of axis command is -

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 The purpose of grid command is -

Q1.22 The modified Program P1_4 to generate a sinusoidal sequence of frequency 0.9 is
given below along with the sequence generated by running it .

< Insert program code here. Copy from m-file(s) and paste. >

< Insert MATLAB figure(s) here. Copy from figure window(s) and
paste. >

A comparison of this new sequence with the one generated in Question Q1.17
shows -

A sinusoidal sequence of frequency 1.1 generated by modifying Program P1_4 is

< Insert MATLAB figure(s) here. Copy from figure window(s) and
paste. >

A comparison of this new sequence with the one generated in Question Q1.17
shows -

Q1.23 The sinusoidal sequence of length 50, frequency 0.08, amplitude 2.5, and phase
shift of 90 degrees generated by modifying Program P1_4 is displayed below .

< Insert MATLAB figure(s) here. Copy from figure window(s) and
paste. >

The period of this sequence is -

Q1.24 By replacing the stem command in Program P1_4 with the plot command, the
plot obtained is as shown below:

< Insert MATLAB figure(s) here. Copy from figure window(s) and
paste. >

The difference between the new plot and the one generated in Question Q1.17 is -

Q1.25 By replacing the stem command in Program P1_4 with the stairs command the
plot obtained is as shown below:

< Insert MATLAB figure(s) here. Copy from figure window(s) and
paste. >

The difference between the new plot and those generated in Questions Q1.17 and
Q1.24 is -

Project 1.4 Random signals

Answers:

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Q1.26 The MATLAB program to generate and display a random signal of length 100 with
elements uniformly distributed in the interval [–2, 2] is given below along with the
plot of the random sequence generated by running the program :

< Insert program code here. Copy from m-file(s) and paste. >

< Insert MATLAB figure(s) here. Copy from figure window(s) and
paste. >

Q1.27 The MATLAB program to generate and display a Gaussian random signal of length
75 with elements normally distributed with zero mean and a variance of 3 is given
below along with the plot of the random sequence generated by running the
program:

< Insert program code here. Copy from m-file(s) and paste. >

< Insert MATLAB figure(s) here. Copy from figure window(s) and
paste. >

Q1.28 The MATLAB program to generate and display five sample sequences of a random
sinusoidal signal of length 31

{X[n]} = {Acos(on + )}

where the amplitude A and the phase  are statistically independent random
variables with uniform probability distribution in the range 0  A  4 for the
amplitude and in the range 0     for the phase is given below. Also shown
are five sample sequences generated by running this program five different times .

< Insert program code here. Copy from m-file(s) and paste. >

< Insert MATLAB figure(s) here. Copy from figure window(s) and
paste. >

1.2 SIMPLE OPERATIONS ON SEQUENCES

Project 1.5 Signal Smoothing

A copy of Program P1_5 is given below.

< Insert program code here. Copy from m-file(s) and paste. >

Answers:

Q1.29 The signals generated by running Program P1_5 are displayed below :

< Insert MATLAB figure(s) here. Copy from figure window(s) and
paste. >

Q1.30 The uncorrupted signal s[n]is -

The additive noise d[n]is -

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Q1.31 The statement x = s + d CAN / CANNOT be used to generate the noise
corrupted signal because -

Q1.32 The relations between the signals x1, x2, and x3, and the signal x are -

Q1.33 The purpose of the legend command is -

Project 1.6 Generation of Complex Signals

A copy of Program P1_6 is given below.

< Insert program code here. Copy from m-file(s) and paste. >

Answers:

Q1.34 The amplitude modulated signals y[n] generated by running Program P1_6 for
various values of the frequencies of the carrier signal xH[n] and the modulating
signal xL[n], and various values of the modulation index m are shown below:

< Insert MATLAB figure(s) here. Copy from figure window(s) and
paste. >

Q1.35 The difference between the arithmetic operators * and .* is -

A copy of Program P1_7 is given below.

< Insert program code here. Copy from m-file(s) and paste. >

Answers:

Q1.36 The swept-frequency sinusoidal sequence x[n] generated by running Program

< Insert MATLAB figure(s) here. Copy from figure window(s) and
paste. >

Q1.37 The minimum and maximum frequencies of this signal are -

Q1.38 The Program 1_7 modified to generate a swept sinusoidal signal with a minimum
frequency of 0.1 and a maximum frequency of 0.3 is given below :

< Insert program code here. Copy from m-file(s) and paste. >

1.3 WORKSPACE INFORMATION

Q1.39 The information displayed in the command window as a result of the who
command is -

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Q1.40 The information displayed in the command window as a result of the whos
command is -

1.4 OTHER TYPES OF SIGNALS (Optional)

Project 1.8 Squarewave and Sawtooth Signals

Answer:

Q1.41 MATLAB programs to generate the square-wave and the sawtooth wave sequences
of the type shown in Figures 1.1 and 1.2 are given below along with the sequences
generated by running these programs :

< Insert program codes here. Copy from m-file(s) and paste. >

< Insert MATLAB figure(s) here. Copy from figure window(s) and
paste. >

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