16.362: Signals and Systems: 1.1
Prof. K. Chandra
ECE, UMASS Lowell
September 6, 2007
1
System Characterization (Sec. 1.5)
A system is in general an interconnection of multiple components. Here, the
system is represented by a box that is driven by an inpu
Homework Solutions (Chapter 7)
P.7.1
From the Nyquist sampling theorem, we know that only if X(j) = 0 for
|>s/2, the signal will be recoverable from its samples. Therefore, X(j)=0
for |>5000.
P.7.2
From the Nyquist sampling theorem, the sampling frequency
Homework Solutions (Chapter 8)
P. 8.1
Taking the inverse Fourier transform of ( ), we have
() = 2() .
1
1
Therefore, () = 2 () and () = 2 .
P. 8.3
When () is multiplied by cos 2000), the output will be
(
1 () = () cos(2000)
= ()(2000) cos(2000)
= (1/2)(t)
16.362: Signals and Systems: 1.0
Prof. K. Chandra
ECE, UMASS Lowell
September 5, 2007
1
Background
Students in this course should have taken Engineering Math and Circuits I
and II. In these courses you have learnt about complex numbers and dierential equa
16.362: Linear Time-Invariant Systems: 2.0-2.1
Prof. K. Chandra
ECE, UMASS Lowell
February 11, 2008
1
Discrete-Time Linear Time-Invariant Systems
In this chapter, we examine in more detail, the relationshp between input
and output signals of a linear time
16.362: Inverse Laplace Transforms
Prof. K. Chandra
ECE, UMASS Lowell
October 3, 2008
1
Inverse Laplace Transforms
The inverse Laplace transform (ILT) is given by the equation,
x(t) =
1
2j
0 +j
X(s)est ds
(1)
0 j
where s = + j and 0 represents a arbitrari
16.362: Continuous Time Fourier Transforms
and Fourier Series
Prof. K. Chandra
ECE, UMASS Lowell
April 26, 2008
1
Continuous Time Fourier Transforms (Chapter. 4)
In this section we are interested in characterizing continuous time signals
x(t) in the frequ
16.362: Discrete Time Signals and
Z-Transforms
Prof. K. Chandra
ECE, UMASS Lowell
April 28, 2008
1
Z Transforms (Chapter. 10)
Consider discrete time signals x[n], < n < . The z-transform of x[n] is
X(z) and provides a characterization of x[n] in the compl
16.362: Linear Time-Invariant Systems: 2.2-2.3
Prof. K. Chandra
ECE, UMASS Lowell
September 21, 2007
1
Continuous-Time LTI Systems
Extending the concept of the impulse response of a LTI system to continuous
time systems, we represent h(t) as the response
16.362: Laplace Transforms: Chapter 9:
9.1-9.2
Prof. K. Chandra
ECE, UMASS Lowell
October 3, 2008
1
Laplace Transforms
We begin our study of representing signals in the frequency domain by starting with the Laplace Transform for continuous time signals. H