Terrain Profile & Path Loss

The site "Hey, what's that?" (http://www.heywhatsthat.com/) provides a great free tool for terrain profiles, coverage, and basic path calculations.

The Path Profiler is located at:
http://www.heywhatsthat.com/profiler-0904.html

Fourier Additivity Property

   

 The plot above shows two signals being added in the time domain and the spectrum of each time domain signal. The plot below shows the spectrum of each signal added in the frequency domain.

% Here we demonstrate the concept of additivity, that is, adding two or
% more signals in one domain results in the corresponding signals being
% added in the other domain.
close all;
    fs=125;   %sample frequency = 125Hz
    Ts=1/fs;  %sample period
    n=0:100*fs; %sample index (fs=samples per second), w=window lenght
    tn=n*Ts;
    x=cos(2*pi*5*tn);
% Time domain plot of x(t)=cos(2*pi*5*tn)
    figure('Color',[1 1 1]);
    subplot(3,2,1);
    h=plot(tn,x);box off;grid on;
    xlabel('Time(s)');
    ylabel('Amplitude');
    title(['Time Domain: x1(t)=cos(2*pi*5*tn)']);
    axis([0 1 -1.2 1.2]);
% Frequency domain plot of x(t)=cos(2*pi*5*tn)
    subplot(3,2,2);
    [X,f]=ComputeSpectrum(x,fs,2^14);
    sig1=X;
    h=plot(f,20*log(X));
    box off; grid on;
    set(h,'Linewidth',1);
    xlabel('Frequency(Hz)');
    ylabel('Amplitude(dB)');
    title(['Frequency Domain: x1(t)=cos(2*pi*5*tn)']);
    axis([4.4 5.8 -100 200]);
   
    x=cos(2*pi*10*tn);
  % Time domain plot of x(t)=cos(2*pi*10*tn)
    subplot(3,2,3);
    h=plot(tn,x);box off;grid on;
    xlabel('Time(s)');
    ylabel('Amplitude');
    title(['Time Domain: x2(t)=cos(2*pi*10*tn)']);
    axis([0 1 -1.2 1.2]);
% Frequency domain plot of x(t)=cos(2*pi*10*tn)
    subplot(3,2,4);
    [X,f]=ComputeSpectrum(x,fs,2^14);
    h=plot(f,20*log(X));
    sig2=X;
    box off; grid on;
    set(h,'Linewidth',1);
    xlabel('Frequency(Hz)');
    ylabel('Amplitude(dB)');
    title(['Frequency Domain: x2(t)=cos(2*pi*10*tn)']);
    axis([5 15 -100 250]);

    x=(cos(2*pi*5*tn)) + (cos(2*pi*10*tn)); % add two signal in time domain
% Time domain plot of x(t)=cos(2*pi*5*tn)+cos(2*pi*10tn)
    subplot(3,2,5);
    h=plot(tn,x);box off;grid on;
    xlabel('Time(s)');
    ylabel('Amplitude');
    title(['Time Domain: x1(t) + x2(t)']);
    axis([0 1 -3 3]);
% Frequency domain plot of x(t)=cos(2*pi*5*tn)+cos(2*pi*10tn)
    subplot(3,2,6);
    [X,f]=ComputeSpectrum(x,fs,2^14);
    h=plot(f,20*log(X));
    box off; grid on;
    set(h,'Linewidth',1);
    xlabel('Frequency(Hz)');
    ylabel('Amplitude(dB)');
    title(['Frequency Domain: x1(t) + x2(t)']);
    axis([0 30 -100 250]);
 % Now, let's simply add the specturm of each signa.
    figure('Color',[1 1 1]);
    subplot(3,1,1);
    h=plot(f,20*log(sig1));
    box off; grid on;
    set(h,'Linewidth',1);
    xlabel('Frequency(Hz)');
    ylabel('Amplitude(dB)');
    title(['Frequency Domain: x1(t) + x2(t)']);
    axis([0 30 -100 250]);
   
    subplot(3,1,2);
    h=plot(f,20*log(sig2));
    box off; grid on;
    set(h,'Linewidth',1);
    xlabel('Frequency(Hz)');
    ylabel('Amplitude(dB)');
    title(['Frequency Domain: x1(t) + x2(t)']);
    axis([0 30 -100 250]);

    subplot(3,1,3);
    h=plot(f,20*log(sig1+sig2));
    box off; grid on;
    set(h,'Linewidth',1);
    xlabel('Frequency(Hz)');
    ylabel('Amplitude(dB)');
    title(['Frequency Domain: x1(t) + x2(t)']);
    axis([0 30 -100 250]);

Normal Distributions in MatLab

%% Normal Distributions in Matlab
% James Eastham
% Member, IEEE
% Created on: 2/5/2012
%
% The following code creates multiple normal distributions

figure('Color',[1 1 1]);
x = 17:0.1:28; %Plot range

pop_average = 21.98; %population mean
sigma = .4; %population sigma
normal_dist = normpdf(x, pop_average, sigma);
plot(x, normal_dist,'LineWidth',3);hold on;

pop_average = 22.89;
sigma = .244;
normal_dist = normpdf(x, pop_average, sigma);
plot(x, normal_dist,'--r','LineWidth',3);hold on;

pop_average = 21.84;
sigma = .78;
normal_dist = normpdf(x, pop_average, sigma);
plot(x, normal_dist,'-.g','LineWidth',3);hold on;

pop_average = 22.24;
sigma = .91;
normal_dist = normpdf(x, pop_average, sigma);
plot(x, normal_dist,'-ko','LineWidth',3);hold on;

legend('build 1','build 2','build 3','overall')
grid on;
title('Design Build Performance');
xlabel('Gain(dB)');

Fourier Transform for Dummies: Matlab Implementation

The following code implements a simple Fourier Transform using cos and sin functions. This project was inspired by a short pdf I stumbled onto during an internet search on this topic. Here is a link to the original: FT for Dummies (I will gladly credit the author if contacted, I just have no idea who wrote the original document as it is not cited)

The following Matlab code, implements a simple Fourier Transform manually in Matlab.

% Fourier Transform for Dummies
% Matlab Implementation
% James Eastham
% Member, IEEE
% 1/22/2012
clear all; %clear all variables
close all; %close all figures
fs = 100; % sample freq
Ts=1/fs; % sample period
n=0:1*fs; % time window (fs=samples per second), 1 second
tn=n*Ts; % sample index
sig_a=5*sin(2*pi*5*tn+pi/3)+2*sin(2*pi*30*tn+pi/2)+2.3*sin(2*pi*8*tn); %create complex signal
sig_a = sig_a + 2*randn(size(tn)); % add noise
figure('Color',[1 1 1]); % plot orignial signal in time domain
subplot(2,1,1);hold on;
plot(tn,sig_a,'-r');
title('Time Domain Signal w/ Noise');
grid on;
% The following loop multiplies the original signal
% by sin and cos at each freq betwen 1 and fs/2
% each sample is then summed, after the loop
% the total sum for each freq is computed
for i=1:fs/2;
detect_sin=sin(2*pi*i*tn);
detect_cos=cos(2*pi*i*tn);
mult_sig_sin=detect_sin.*sig_a;
mult_sig_cos=detect_cos.*sig_a;
total_freq_sin(i)=sum(mult_sig_sin);
total_freq_cos(i)=sum(mult_sig_cos);
end;
total_freq_sin=total_freq_sin/(fs/2);
total_freq_cos=total_freq_cos/(fs/2);
total_freq=sqrt(total_freq_sin.^2+total_freq_cos.^2);
subplot(2,1,2);
stem(total_freq);
xlabel('Frequency');
ylabel('Amplitude');
Title('Frequency Domain');
axis('tight');
grid on;

Running MatLab 2007 (R2007a) 7.4.0 in Windows 7

If you are having a problem where Matlab errors out on startup running Windows 7, try this it solved my issue.

Switch your "theme" to "Windows Classic" (right click desktop, select preferences, find the classic theme in the Basic and High Contrast Themes area)

Open Matlab. Enjoy.

Don't ask why... I didn't have time to research it. Seems to be related to Java.

Here are the some of the errors I was getting:
java.lang.NullPointerException
javax.swing.border.EmptyBorder.(Unknown Source)
com.sun.java.swing.plaf.windows.WindowsTableHeaderUI$XPDefaultRenderer.getTableCellRendererComponent(Unknown Source)

Adding a NE5532 Op Amp Model to LTSpice

To add the NE5532 Model, follow the steps in my LM741 post (see link below), using the NE5532 model shown here below.

Special thanks to Uwe Beis who provided the TI 5534 updated model:
(http://www.beis.de/Elektronik/Electronics.html)

Adding the LM741 model to LTSpice

***** NE5532 Source: Texas Instruments NE5534
* C2 added to simulate compensated frequency response (Uwe Beis)

* NE5532 OPERATIONAL AMPLIFIER "MACROMODEL" SUBCIRCUIT
* CREATED USING NE5534 model from Texas InstrumentsAT 12:41
* (REV N/A)      SUPPLY VOLTAGE: +/-15V
* CONNECTIONS:   NON-INVERTING INPUT
*                | INVERTING INPUT
*                | | POSITIVE POWER SUPPLY
*                | | | NEGATIVE POWER SUPPLY
*                | | | | OUTPUT
*                | | | | |
.SUBCKT NE5532   1 2 3 4 5
*
C1   11 12 7.703E-12
C2    6  7 23.500E-12
DC    5 53 DX
DE   54  5 DX
DLP  90 91 DX
DLN  92 90 DX
DP    4  3 DX
EGND 99  0 POLY(2) (3,0) (4,0) 0 .5 .5
FB    7 99 POLY(5) VB VC VE VLP VLN 0 2.893E6 -3E6 3E6 3E6 -3E6
GA    6  0 11 12 1.382E-3
GCM   0  6 10 99 13.82E-9
IEE  10  4 DC 133.0E-6
HLIM 90  0 VLIM 1K
Q1   11  2 13 QX
Q2   12  1 14 QX
R2    6  9 100.0E3
RC1   3 11 723.3
RC2   3 12 723.3
RE1  13 10 329
RE2  14 10 329
REE  10 99 1.504E6
RO1   8  5 50
RO2   7 99 25
RP    3  4 7.757E3
VB    9  0 DC 0
VC    3 53 DC 2.700
VE   54  4 DC 2.700
VLIM  7  8 DC 0
VLP  91  0 DC 38
VLN   0 92 DC 38
.MODEL DX D(IS=800.0E-18)
.MODEL QX NPN(IS=800.0E-18 BF=132)
.ENDS

LM741 Datasheet

Many student projects use the LM741 op amp. Here is a link to the datasheet.




http://dl.dropbox.com/u/30278073/LM741_Datasheet.pdf