Experiment 1
Purpose:
The purpose of this experiment is to investigate using a Fourier series to represent a
continuous time periodic signal x(t).
Questions:
1a)
I) The purpose of the for loop is to assign different variables to the x vector that was
crea
Experiment 0
Purpose:
The purpose of this experiment is to understand how to represent signals in Matlab,
perform the convolution of signals, and study some simple LTI systems.
Theory:
A discrete signal can be considered as a vector, an ordered collection
function HW11(a,b)
if nargin = 0
a = 0.278;
b = 0.834;
end
disp(['a = ',num2str(a),', b = ',num2str(b)])
N = 5;
spoles = b*exp(j*pi*(1+(2*[1:N]-1)/N)/2);
p = real(spoles)*a + j*imag(spoles);
zpoles = (2+p)./(2-p);
D = real(poly(zpoles);
zzeros = [-1 -1 -1
Chapter Five
Roland Priemer
Discrete Fourier Transform
In practice, a function expression for a continuous time periodic signal is usually
not available. Therefore, we cannot directly apply the method developed in
Chapter Four to investigate the strengths
Chapter Three
Roland Priemer
Data Acquisition
A real-world signal varies continuously with time over a continuous range. A
real-world signal is usually an analog output of some transducer, which is a
voltage v(t ) or possibly a current. The voltage v(t )
Chapter Seven
Roland Priemer
Fourier Transform
The concept of representing a periodic continuous time function with a linear
combination of complex exponential functions has made a significant impact in
all fields of engineering and science. With the DFT,
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Chapter Two
Roland Priemer
Continuous and Discrete Time Systems
The term system is used to refer to an interconnection and interaction of devices
and processes such that by virtue of the interconnection, interaction and inputs
some particular system activ
Chapter Four
Roland Priemer
Fourier Series
Many natural phenomena and man-made devices and systems behave in
a cyclical manner. To study a cyclical phenomenon, it is useful to have a method
to model it. Since trigonometric functions are periodic functions
Homework Problems: DTFT pairs and properties
P4.1 Calculate the DTFT of each () using the definition cfw_() =
:
= ()
a) () = 3()
b) () = ( 1) + ( + 1)
c) () = rect 1 ()
d) () = 3 ()
1
P4.2 Calculate the IDTFT of each ( ) using the definition 1 ( ) = 2 2
Chapter Ten
Roland Priemer
Laplace Transform
The Fourier transform of a signal x(t ) exists if the signal is absolutely
integrable. Fourier transform analysis can only be applied to LTI continuous
time systems that are stable, which means that the impulse
Chapter Eleven
Roland Priemer
Bilateral z-Transform
The DTFT is useful for spectral analysis of signals and systems. However, while
signals that are absolutely summable have a DTFT, other kinds of signals, for
which a DTFT does not exist, are also of inte
Chapter Twelve
Roland Priemer
Unilateral z-Transform
The BZT is useful for LTI DTS analysis. However, we usually work with righthanded or causal signals. Some of the mechanics of working with the BZT
includes terms due to a left-handed part of a signal. I
Chapter Eight
Roland Priemer
Discrete Time Fourier Transform
The discrete Fourier transform (DFT) provides a means to study the spectral
nature of a periodic continuous time signal given samples of the signal. The
discrete time Fourier transform (DTFT) pr
Chapter Six
Roland Priemer
Fast Fourier Transform
Computing an N point DFT or inverse DFT of a sequence of N complex
numbers requires N 2 complex multiplications. For large N , computational
efficiency becomes an important factor. Under various restrictio