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EE 5410 Signal Processing Semester A 2022-2023 Assignment 1
发布时间：2022-09-18
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EE 5410 Signal Processing
Semester A 2022-2023
Assignment 1
Due Date: 7 October 2022
1. Find the Fourier series coefficients for the following continuous-time signal:
with fundamental period of 
.
2. Given the following periodic signal:
(a) Determine the fundamental period of .
(b) Determine the Fourier transform of .
(c) Determine the Fourier transform of 
.
3. The impulse response of a RL circuit has the form of:
where 
and 
represent the values of resistor and inductor, respectively.
(a) Find the Fourier transform of , i.e., .
(b) Determine the magnitude, phase, real part and imaginary part of 
.
4. Consider a continuous-time linear time-invariant (LTI) system with continuous-time input and impulse response . Determine the system continuous-time output in terms of . Is the system stable? Is the system causal? Is the system memoryless? Briefly explain your answers.
5. Given a discrete-time system with input 
and output 
:
Determine whether the system is memoryless, stable, causal, linear, and/or time- invariant. Briefly explain your answers.
6. Consider two discrete-time signals 
and .
(a) Compute (b) Compute
using the convolution formula.
using 
transform.
7. Consider the following discrete-time signals:
and 
where is an integer. Let with and .
Determine the value of 
.
8. Figure 1 shows a discrete-time system which consists of an interconnection of 2 discrete-time systems with impulse responses 
and 
.
Figure 1
(a) Determine the overall impulse response of the system, , in terms of
and .
(b) Determine 
when 
and 
.
9. Given a continuous-time signal:
We sample it with a sampling period sec. to produce the discrete-time
signal 
. Find 
, 
, 
, 
and 
. Is 
a periodic signal?
10. Consider a LTI system whose transfer function 
is:
(a) If the system is stable, determine the system impulse response .
(b) If the system is causal, determine the system impulse response 
.
