Statistics Assignment: Tensile Strength of Concrete
Student ID: S1451713
Abstract
The report aims to analyse the effect of accelerators and plasticisers and their combination on
the tensile strength of concrete. The data is collected using the Split Cylin

A The H EAVISIDE and D IRAC Functions
The H EAVISIDE unit function , also called the unit step function, is dened
according to
7
1 for t > a,
1 for t a,
H(t a) :=
or H(t a) : 12 for t = a, (A.1a,b)
0 for t < a,
0 for t < a,
where t is the time variable a

Fourier Magnitude and Phase
Complex Nature of X (j)
Recall, Fourier Transform:
Z
X (j)
Magnitude and Phase
=
x(t)e jt dt
C
and Inverse Fourier Transform:
Z
1
X (j)e jt d
x(t) =
2
Z 0
Z
1
1
=
X (j)e jt d +
X (j)e jt d
2
2 0
Professor Deepa Kundur
Unive

The Heaviside Function or Step Function.
We define the Heaviside function or step function as:
0, if t < a
Ha (t) =
1, if t > a
(See figure 1)
Note: Ha (t) has a jump at t = a and therefore is piecewise continuous!
(because it takes the constant values