DEPARTMENT OF COMPUTER SYSTEMS ENGINEERING
SUKKUR INSTITUTE OF BUSINESS ADMINISTRATION
Digital Signal Processing (Lab)
Name: __________________________________________ Date: _________________________
Score: _____________________Signature of Instructor_________________________________
Lab # 08 Handout
LTI Discrete Time Systems and Continuous Time Signals
1. LTI Discrete Time Systems
A linear, time-invariant (LTI) discrete-time system is completely characterized in the time domain by
its impulse response sequence, and the output sequence of the LTI system can be computed for any
input sequence by convolving the input sequence with its impulse response sequence. Certain classes
of LTI discrete-time systems are characterized also by a linear, constant-coefficient difference
equation. For such systems, the output sequence can be computed recursively for any input sequence.
By applying the DTFT or the z-transform to either the convolution sum description or to the difference
equation representation, the LTI discrete-time system can also be characterized in the frequency
domain. Such transform domain representations provide additional insight into the behavior of such
systems, in addition to making it simpler to design and implement them for specific applications.
2. Laboratory Ethics
Students are expected to behave ethically both in and out of the lab. Unethical behavior includes, but
is not limited to, the following:
 Possession of another person’s laboratory solutions from the current or previous years.
 Reference to, or use of another person’s laboratory solutions from the current or previous
years.
 Submission of work that is not done by your laboratory group.
 Allowing another person to copy your laboratory solutions or work
 Cheating on quizzes.
3. Background Review
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4. Matlab Commands Used
5. Transfer Function Analysis
The frequency response of an LTI discrete-time system characterized by a difference equation of the
form of Eq. (2.11) is given by Eq. (4.9). The frequency response can thus be easily evaluated at a set
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of discrete frequency points using the command freqz. In fact, Program P3_1 can be used for this
purpose, as was done earlier in Question Q3.41 in the lab-6.
Q4.1 Modify Program P3_1 to compute and plot the magnitude and phase spectra of a moving
average filter of Eq. (2.13) for three different values of length M(3, 7, 10 ) and for 0 ≤ ω ≤ 2π.
Justify the type of symmetries exhibited by the magnitude and phase spectra. What type of filter
does it represent?
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6. Continuous Time Signals
Digital signal processing algorithms are often used to process continuous-time signals. To this end, it
is necessary to convert a continuous-time signal into an equivalent discrete-time signal, apply the
necessary digital signal processing algorithm to it, and then convert back the processed discrete-time
signal into an equivalent continuous-time signal. In the ideal case, the conversion of a continuous-time
signal into a discrete-time form is implemented by periodic sampling and, to prevent aliasing, an
analog anti-aliasing filter is often placed before sampling to band limit the continuous-time signal.
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Q5.4 Run Program P5 1 for four other values of the sampling period T(0.004, 0.02, 0.15, 0.02) with
two lower and two higher than that listed in Program P5 1. Comment on your results.
Q5.5 Repeat Program P5 1 by changing the frequency of the sinusoidal signal to 3 KHz and 7 KHz,
respectively. Is there any difference between the corresponding equivalent discrete-time signals and
the one generated in Question Q5.1?
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Q5.8 Restore the original display range and repeat Program P5 2 by changing the frequency of the
sinusoidal signal to 3 KHz and 7 KHz, respectively. Is there any difference between the
corresponding equivalent discrete-time signals and the one generated in Question Q5.6?
Lab Submission: Attach the prints of the plots you obtain in the exercises above with proper
headings including the function name and description.
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