Seems no other helper here has a printer at hand as well.
I looked at your code, and their is nothing strange in it. Nevertheless, i polished it up a bit.
Code: Select all
\listfiles
\documentclass[10pt]{article}
\usepackage[T1]{fontenc}
\usepackage{lmodern}
\usepackage{amsmath}
\usepackage{geometry}
\geometry{top=1in,textheight=9in,textwidth=7in,
}
\usepackage{parskip}
\usepackage{pgfplots}
\pgfplotsset{ compat=1.12 }
%\setlength{\oddsidemargin}{-.250in}
%\setlength{\topmargin}{0in}
%\setlength{\textheight}{9.0in}
%\setlength{\textwidth}{7in}
%\setlength{\parindent}{0in}
%\setlength{\headsep}{0.1in}
%\setlength{\parskip}{10pt}
%\newcommand{\chart}[1]{\includegraphics[width=5.0in]{#1}}
\begin{document}
\begin{center}
\LARGE{\textbf{Using an FFT to Evaluate Periodic Signals}}
\vspace{.25in}
{\small\setlength{\parskip}{0pt}
Andrew Gentile, P.E.\par
Gentile Engineering, LLC\par
andrewkgentile@gmail.com\par}
\end{center}
\vspace{.25 in}
\thispagestyle{empty}
\noindent\textbf{Abstract}\hspace{.25in} {\itshape This paper discusses the concept of a fast Fourier transform and how it can be used for analyzing periodic signals. The algorithm itself is fairly simple and can be implemented using Microsoft Excel. However, the selection of sampling parameters is not intuitive. This paper will describe how to select appropriate parameters, and how to verify that the algorithm results are accurate. The code samples included in this document are written in Excel VBA. }
\section{Introduction}
The FFT is an algorithm which can convert a signal in the time
domain into a discrete frequency domain. The immediate practical
value of this is analysis of periodic signals, such as vibration
signals, electrical harmonics, and induced signal noise. Knowing
the frequencies at which a signal is occurring is very valuable
in troubleshooting. Given that an accurate sampling of a
periodic signal can be obtained, the FFT can be used to break
down a periodic signal into individual frequency components.
\section{The Equation}
The FFT equation is as follows:
\begin{equation}\label{ffteq}
X_k = \sum_{n=0}^{N-1}x[n] {e}^{-j\cdot2\cdot\pi\cdot n\cdot k/N}
\end{equation}
Where $X_k$ is a complex value corresponding to the $k$-th
frequency. $N$ is the number of samples collected. And $x[n]$
are the samples, which are real numbers. Each value of $X_k$ has
a real part and an imaginary part. The magnitude of $X_k$ is
related to the magnitude of the signal at the $k$-th frequency.
The angle of $X_k$ is related to the phase shift of the signal at
the $k$-th frequency.
\section{Example Data Set}
A sample data set was created in Excel using $y(t) =
1+2\cos(10t+\frac{\pi}{4})+3\cos(20t-\frac{\pi}{3})+4\cos(30t)$.
This discrete array uses a time vector of 102 Hz, or a time
interval of $\frac{1}{102}$ seconds. There are 128 samples in
the set. The sampling rate was chosen in order to maximize the
periodicity of this signal and to select integer values for
frequency bins. Note that the signal is not perfectly periodic.
Table 1 shows how many periods are present in the signal for each
frequency. These are very close to an integer number, which
would make them perfectly periodic. However even the small error
will show up in the data. In this case the error will be small
enough to ignore.
\begin{figure}[b]
\centering
\begin{tikzpicture}
\begin{axis}[xlabel={time $t$},ylabel={Magnitude
$y(t)$}]
\addplot [domain=0:1.2,samples=100]
{1+2*cos(deg(10*x)+(pi/4))+3*cos(deg(20*x)-(pi/3))+4*cos(deg(30*x))};
\end{axis}
\end{tikzpicture}
\caption{$y(t) =
1+2\cos(10t+\frac{\pi}{4})+3\cos(20t-\frac{\pi}{3})+4\cos(30t)$}
\label{sample}
\end{figure}
\end{document}
You can try if their are any differences, but i guess not.
Asking other TeX enthusiasts, the printed output looked normal.
it would at least be a good idea to know (1) Which Program did he use to print, (2) was that program set to print in eco mode?
When it comes to strange printed output, it is almost always the printer(driver) that does some monkey business. Have you tried printing from a different computer with a different printer?
The smart way: Calm down and take a deep breath, read posts and provided links attentively, try to understand and ask if necessary.
