Fourier considered a non-periodic or aperiodic function as a
periodic function whose period tends to infinity.
Thus the function that is represented as Fourier series was
made to approach an aperiodic function by le
Response functions and Greens functions
When an external stimulation F(t) is applied to a physical
system, if the measured response is A(t),
(t , t ') F (t ')dt '
where (t , t ') is the response function
A point in N-dimensional space is denoted by x1 , x2 ,., xN
known as coordinates.
Let x1 , x2 ,., xN and x '1 , x '2 ,., x 'N are coordinates of
a point in two different frames of references.
Suppose N independent relations between the
A four-vector A in spacetime will be defined as a
quantity which transform under Lorentz transformation in
the same way as coordinates of a point x in the fourdimensional space-time.
A four-vector is a vector in a four-dimensi
mathematician and engineer, Joseph Fourier
(1768-1830) claimed that an arbitrary
function defined in a finite interval by an
arbitrary graph could always be resolved into
a sum of pure sine and c
Zeros and Singularities
Suppose f(z) is analytic in region R, except at finite
number of exceptional points, these points are called
f ( z) z
f(z) has a zero of order k at z = .
f ( z)
Fourier transforms can be used to analyse transient
waveforms. In this section the Fourier transforms of simple
functions that appear frequently in physical applications are
f (t )
Single Rectangular Pulse
f (t )
F ( )
A monochromatic plane wave of frequency and
wavelength travel in z-direction to meet an arbitrary
diffraction screen in x- direction in the plane z=0. (No
variation in the y-direction)
P ( x, z)
When z < 0 the
Special Theory of Relativity
The Four-Vectors (4-Vectors) and Lorentz
Invariants of Special Relativistic (SR)
theory are fundamental entities that
accurately, precisely, and beautifully
describe the physical properties of the
world around us.
While it i
The convolution combines two functions of a variable to
produce a new function of a new variable, which is introduced
as a parameter.
The convolution of the functions f(t) and g(t) over the interval
[-, +] is denoted by and def
Correlation and Transfer Functions
Suppose f(t) and g(t) are two disturbances with zero mean
and their spectrums are F() and G() respectively.
Parsevals second theorem can be written in the form
g (t ) f (t )
G( ) F
( ) d
c a ib
is called a complex number
a and b are real numbers and i which is called the
imaginary unit has the property i 2 1
Complex conjugate is denoted by
c a ib
a ib c id