Class Wiki - User contributions [en]

PSK31 Demodulation (Kurt & Michael)

2013-05-18T06:22:23Z

Michael.vonpohle: /* PID Controller Problems */

== Project Description ==

The goal of this project is to design and code a Matlab script that will encode and decode a PSK31 signal including signals with noise. The receiver should be able to read in signals (as a wav file) from other sources as well.

PSK31 is a audible text encoding that can be sent over the air by amateur radio operators. A computer's sound card can be used to send and receive the signal since the signal is audible. For more information regarding PSK31 see the Wikipedia article.[http://en.wikipedia.org/wiki/PSK31]

== Our Approach ==

=== Code Overview ===

==== Transmitter ====

Our code creates a PSK31 signal given an input carrier frequency and message. For testing our receiver code, the transmitter is setup to generate a random carrier frequency and phase. It also adds random noise to the signal before writing it to a wav file.
 
<pre>
clear all
close all
clc

fc = 100+rand(1)*3900 % Carrier Frequency
%fc = 1500;
Fs = 10000; % Sampling frequency
baud = 31.25;

%% Encode the message

phase = rand(1)*2*pi; % Phase of the signal
dt = 0:1/Fs:1/baud-1/Fs; % Time between samples
one = ones(size(dt)); % A 'One' signal
zero = cos(pi*dt*baud); % A 'Zero' signal

messageString = 'Hello World! The quick brown fox jumps over the lazy dog. ABCDEFGHIJKLMNOPQRSTUVWXYZ abcdefghijklmnopqrstuvwxyz 0123456789';
[message charTable] = make_bits(messageString);

baseband = [];
m=1;
for k = 1:length(message)
if(message(k)==0)
baseband = [baseband, zero*m];
m=-m;
else
baseband = [baseband, one*m];
end
end

t = 0:1/(Fs):length(baseband)/Fs-1/Fs;

v = baseband.*cos(2*pi*fc*t+phase);

% Noise
v = v+randn(size(v))*10^(-10/20);

wavwrite(v,Fs,'signal.wav');

figure(1)
subplot(2,1,1)
plot(t,baseband)
axis([0 2 -1.2 1.2])
title('\fontsize{14}Baseband')
xlabel('Time (s)')
ylabel('Amplitude')
subplot(2,1,2)
plot(t,v)
axis([0 2 -1.2 1.2])
title('\fontsize{14}Baseband with Carrier')
xlabel('Time (s)')
ylabel('Amplitude')
movegui('northwest')
</pre>

 [[Image:K&M_PSK31Signal.png|600px]]

==== Receiver ====
Our receiver is split into several steps:
<ol>
<li>We read in the signal from a wav file and generate utility variables and matrices.</li>

<pre>
%% Decode Message

clear all
baud = 31.25;

% [v,Fs] = wavread('PSK31_sample.wav');
% [v,Fs] = wavread('capture.wav');
[v,Fs] = wavread('signal.wav');

dt = 0:1/Fs:1/baud-1/Fs; % Time between samples
one = ones(size(dt)); % A 'One' signal
zero = cos(pi*dt*baud); % A 'Zero' signal
t = 0:1/(Fs):length(v)/Fs-1/Fs;

[sout charTable] = load_alpha();

upperNoiseCutOff = .75;
lowerNoiseCutOff = 1-upperNoiseCutOff;

% figure(1)
% plot(v)
</pre>

<li>We run the signal through an FFT and take an average over the range of the FFT spike to obtain a carrier frequency guess.</li>
<pre>
%% Determine Carrier Frequency

vFftShift = abs(fftshift(fft(v)));

freq = linspace(0,length(v)-1,length(v))*(Fs/length(v));
freqShift = (freq - Fs/2);

% remove noise components
noise = (vFftShift < lowerNoiseCutOff*max(vFftShift));
vFftShift(noise) = 0;

% uses the center(mean) of the fft spike as the frequency
freqRange = find(vFftShift(length(vFftShift)/2:length(vFftShift)) > 0);
carrierFreq = freqShift(round(mean([max(freqRange),min(freqRange)]))+length(vFftShift)/2-1)

figure(2)
plot(freqShift,vFftShift)
movegui('center')
</pre>
<li>A PID controller was implemented to help offset the fact that a carrier frequency derived from the FFT produces an inaccurate carrier frequency. An offset in the carrier frequency causes the constellation diagram to rotate in a circle. The PID tries to compensate for this by adding to or subtracting from the phase of the signal while trying to drive the Q-component of the signal to zero. The feedback loop is described by the code below.</li>
<code>
% PID controller constants
Kp = 25;
Ki = 50;
Kd = 1;
output = zeros(1, length(v)); % Init
setpoint = 0; % Sets the feedback point to control to.
previous_error = 0; % In this case, you want to set yt to 0.
integral = 0;
xt_filt = [];
yt_filt = [];
for k=51:length(v)
xt(k) = v(k)*cos(2*pi*u_fc*t(k)+output(k));
yt(k) = v(k)*sin(2*pi*u_fc*t(k)+output(k));

xt_filt(k:-1:k-50) = filter(b, a, xt(k:-1:k-50));
yt_filt(k:-1:k-50) = filter(b, a, yt(k:-1:k-50));

if(sign(xt(k)) == sign(yt(k)))
error = setpoint - yt_filt(k);
else
error = setpoint + yt_filt(k);
end

% PID Feedback Controller compensates for inaccurate fc guess.
% error = setpoint - yt_filt(k);
integral = integral + error*10;
derivative = (error - previous_error)/10;
output(k+1) = Kp*error + Ki*integral + Kd*derivative;
previous_error = error;
end

</code>
<li>We multiply the signal with a cosine wave at our guess frequency. This splits the signal into two parts: a high frequency component (with frequency equal to the sum of the ''actual'' carrier frequency and our ''guess'' frequency) and a low frequency component (due to the difference of the two frequencies). </li>
<li>We filter the multiplied signal through a butterworth filter with a 75Hz cutoff frequency to remove the high frequency component.</li>

<pre>
%% Mix and Filter

mix = v.*cos(2*pi*(carrierFreq)*t)';
% mix = v.*cos(2*pi*(fc)*t)';

figure(4)
subplot(2,2,1)
plot(t,mix)
axis([0 2 -1.2 1.2])
title('\fontsize{14}Signal Multiplied by Cosine')
xlabel('Time (s)')
ylabel('Amplitude')
subplot(2,2,3)
mixFft = abs(fftshift(fft(mix)));
plot(freqShift,mixFft)
title('\fontsize{14}FFT of Multiplied Signal')
xlabel('Frequency (Hz)')
ylabel('Amplitude')
text(150,.8*max(mixFft),sprintf('Low Frequency\n<- Component'))
text(300,.25*max(mixFft),sprintf('High Frequency\nComponent ->'))

[b,a] = butter(5,(75)/Fs);
mixFilter = filter(b,a,mix);
mixFilterFft = abs(fftshift(fft(mixFilter)));
subplot(2,2,2)
plot(t,mixFilter)
axis([0 2 -1.2 1.2])
title('\fontsize{14}Multiplied Signal Filtered')
xlabel('Time (s)')
ylabel('Amplitude')
subplot(2,2,4)
plot(freqShift,mixFilterFft)
title('\fontsize{14}FFT of Filtered Signal')
xlabel('Frequency (Hz)')
ylabel('Amplitude')
text(150,.8*max(mixFft),sprintf('Low Frequency\n<- Component'))
movegui('west')
</pre>

 [[File:K&M_Signal_Mixed_and_Filtered.png|600px]]
<li>We mark the locations where the filtered signal changes sign. This identifies possible "sync" points where zeros in the signal may occur.</li>

<li>We compare the length of time that occurs between each sync point with the baud rate to determine how many baud periods occur between each sync point. A single baud period indicates a zero. Each additional period over the first baud period indicates a one. (Ex. Three baud periods -> '110')</li>

<pre>
%% Sign Change Method
k = 1
for n = 1:length(v)-1
if (sign(mixFilter(n+1)) ~= sign(mixFilter(n)))
zeroLoc(k) = n;
k = k+1;
end
end

period = Fs/baud;

bitstream = []
for n = 1:length(zeroLoc)-1
periodDiff = zeroLoc(n+1)-zeroLoc(n);
cross = round(periodDiff/period) - 1;
if (cross == 0)
bitstream = [bitstream 0];
else if (cross > 0)
bitstream = [bitstream ones(1,cross) 0];
end
end
end

bitstream = [bitstream ones(1,10)]; %pad with ones for end of message

sample = zeros(1,length(v));
sample(zeroLoc) = 1;

figure(5)
plot(t,mixFilter,'b')
hold on
plot(t,sample,'k')
hold off
axis([0 2 -1.2 1.2])
title('\fontsize{14}Sign Change Sync Points')
xlabel('Time (s)')
ylabel('Amplitude')
legend('Filtered Signal','Sync Points','location','best')
</pre>

 [[File:K&M_Sync_Points.png|600px]]
<li>We send the resulting bit stream through a text decoder which translates the ones and zeros into a text message.</li>
<pre>
%% Bitstream to Characters

breakLoc = [];
k = 1;
for n = 1:length(bitstream)-2
% Finds '00' bits indicating new character
if(isequal(find(bitstream(n:n+1) == [0 0]),[1 2]))
breakLoc(k) = n;
k = k+1;
end;
end;

messageText = '';
for n = 1:length(breakLoc)-1
messageChunks = bitstream(breakLoc(n):breakLoc(n+1)-1);
temp = mat2str(messageChunks);
temp = strrep(temp,'[','');
temp = strrep(temp,'0 0 ','');
temp = strrep(temp,']','');
if (((breakLoc(n+1) - breakLoc(n)) <= 12) && (~isequal(temp,'0')) &&(bin2dec(fliplr(temp)) <= length(charTable)))
messageText = [messageText charTable(bin2dec(fliplr(temp)))];
end;
end

messageText
</pre>
</ol>

== Results/Problems ==
===Transmitter===
To our knowledge, our transmitter generates a signal without any problems.
===Receiver===
As long as our guess frequency is close to the actual frequency, (less than 0.1Hz off) our receiver can easily handle a 1dB SNR.
==== Frequency Errors ====
In most cases, our guess frequency is within 0.2Hz of the actual frequency. As the guess frequency exceeds these bounds, the text decode becomes increasingly garbled.
==== PID Controller Problems ====
The first iteration did not take into account the I component of the signal and was constantly trying to drive the signal to the positive I coordinates. A simple if-else statement solved this problem. However there are some bugs. There might be a singularity at (0,0) which causes the controller to perform in a strange fashion. Also, the code has very bad noise rejection. It can produce baseband but not very well once noise is added. Finally, it doesn't decode signals that we generate ourselves. When we produce our signal in MATLAB, the code works fine. However, the signal from wikipedia.com and Dr. Frohne's signal don't work. One problem with the wikipedia.com signal is that it's native format is .ogg which is lossy. This could've presented problems when we convert the signal to a wave file as high frequencies get chopped in lossy formats.

==Authors==

[[User:Michael.vonpohle|Michael von Pohle]]

[[Hildebrand,_Kurt|Kurt Hildebrand]]

User:Michael.vonpohle

2013-04-16T22:57:50Z

Michael.vonpohle:

== General Information ==
I'm an electrical engineering major and have attended Walla Walla University since 2009. I plan to graduate in 2013. This page contains a summary of my contributions to the wiki.
== Projects/Pages ==
[[PSK31 Demodulation (Kurt & Michael)]]

Hildebrand, Kurt

2013-04-16T22:57:01Z

Michael.vonpohle:

== Contact Information ==

'''Phone:''' (909)528-3558

'''Prefered E-mail:''' kurthildebrand@gmail.com

'''School E-mail:''' kurt.hildebrand@wallawalla.edu

== PSK 31 Demodulation ==

Fall, 2012
*Partner [[User:Michael.vonpohle|Michael von Pohle]]
[[PSK31 Demodulation (Kurt & Michael)]]

PSK31 Demodulation (Kurt & Michael)

2012-12-14T10:33:31Z

Michael.vonpohle: /* Receiver */

== Project Description ==

The goal of this project is to design and code a Matlab script that will encode and decode a PSK31 signal including signals with noise. The receiver should be able to read in signals (as a wav file) from other sources as well.

PSK31 is a audible text encoding that can be sent over the air by amateur radio operators. A computer's sound card can be used to send and receive the signal since the signal is audible. For more information regarding PSK31 see the Wikipedia article.[http://en.wikipedia.org/wiki/PSK31]

== Our Approach ==

=== Code Overview ===

==== Transmitter ====

Our code creates a PSK31 signal given an input carrier frequency and message. For testing our receiver code, the transmitter is setup to generate a random carrier frequency and phase. It also adds random noise to the signal before writing it to a wav file.
 
<pre>
clear all
close all
clc

fc = 100+rand(1)*3900 % Carrier Frequency
%fc = 1500;
Fs = 10000; % Sampling frequency
baud = 31.25;

%% Encode the message

phase = rand(1)*2*pi; % Phase of the signal
dt = 0:1/Fs:1/baud-1/Fs; % Time between samples
one = ones(size(dt)); % A 'One' signal
zero = cos(pi*dt*baud); % A 'Zero' signal

messageString = 'Hello World! The quick brown fox jumps over the lazy dog. ABCDEFGHIJKLMNOPQRSTUVWXYZ abcdefghijklmnopqrstuvwxyz 0123456789';
[message charTable] = make_bits(messageString);

baseband = [];
m=1;
for k = 1:length(message)
if(message(k)==0)
baseband = [baseband, zero*m];
m=-m;
else
baseband = [baseband, one*m];
end
end

t = 0:1/(Fs):length(baseband)/Fs-1/Fs;

v = baseband.*cos(2*pi*fc*t+phase);

% Noise
v = v+randn(size(v))*10^(-10/20);

wavwrite(v,Fs,'signal.wav');

figure(1)
subplot(2,1,1)
plot(t,baseband)
axis([0 2 -1.2 1.2])
title('\fontsize{14}Baseband')
xlabel('Time (s)')
ylabel('Amplitude')
subplot(2,1,2)
plot(t,v)
axis([0 2 -1.2 1.2])
title('\fontsize{14}Baseband with Carrier')
xlabel('Time (s)')
ylabel('Amplitude')
movegui('northwest')
</pre>

 [[Image:K&M_PSK31Signal.png|600px]]

==== Receiver ====
Our receiver is split into several steps:
<ol>
<li>We read in the signal from a wav file and generate utility variables and matrices.</li>

<pre>
%% Decode Message

clear all
baud = 31.25;

% [v,Fs] = wavread('PSK31_sample.wav');
% [v,Fs] = wavread('capture.wav');
[v,Fs] = wavread('signal.wav');

dt = 0:1/Fs:1/baud-1/Fs; % Time between samples
one = ones(size(dt)); % A 'One' signal
zero = cos(pi*dt*baud); % A 'Zero' signal
t = 0:1/(Fs):length(v)/Fs-1/Fs;

[sout charTable] = load_alpha();

upperNoiseCutOff = .75;
lowerNoiseCutOff = 1-upperNoiseCutOff;

% figure(1)
% plot(v)
</pre>

<li>We run the signal through an FFT and take an average over the range of the FFT spike to obtain a carrier frequency guess.</li>
<pre>
%% Determine Carrier Frequency

vFftShift = abs(fftshift(fft(v)));

freq = linspace(0,length(v)-1,length(v))*(Fs/length(v));
freqShift = (freq - Fs/2);

% remove noise components
noise = (vFftShift < lowerNoiseCutOff*max(vFftShift));
vFftShift(noise) = 0;

% uses the center(mean) of the fft spike as the frequency
freqRange = find(vFftShift(length(vFftShift)/2:length(vFftShift)) > 0);
carrierFreq = freqShift(round(mean([max(freqRange),min(freqRange)]))+length(vFftShift)/2-1)

figure(2)
plot(freqShift,vFftShift)
movegui('center')
</pre>
<li>A PID controller was implemented to help offset the fact that a carrier frequency derived from the FFT produces an inaccurate carrier frequency. An offset in the carrier frequency causes the constellation diagram to rotate in a circle. The PID tries to compensate for this by adding to or subtracting from the phase of the signal while trying to drive the Q-component of the signal to zero. The feedback loop is described by the code below.</li>
<code>
% PID controller constants
Kp = 25;
Ki = 50;
Kd = 1;
output = zeros(1, length(v)); % Init
setpoint = 0; % Sets the feedback point to control to.
previous_error = 0; % In this case, you want to set yt to 0.
integral = 0;
xt_filt = [];
yt_filt = [];
for k=51:length(v)
xt(k) = v(k)*cos(2*pi*u_fc*t(k)+output(k));
yt(k) = v(k)*sin(2*pi*u_fc*t(k)+output(k));

xt_filt(k:-1:k-50) = filter(b, a, xt(k:-1:k-50));
yt_filt(k:-1:k-50) = filter(b, a, yt(k:-1:k-50));

if(sign(xt(k)) == sign(yt(k)))
error = setpoint - yt_filt(k);
else
error = setpoint + yt_filt(k);
end

% PID Feedback Controller compensates for inaccurate fc guess.
% error = setpoint - yt_filt(k);
integral = integral + error*10;
derivative = (error - previous_error)/10;
output(k+1) = Kp*error + Ki*integral + Kd*derivative;
previous_error = error;
end

</code>
<li>We multiply the signal with a cosine wave at our guess frequency. This splits the signal into two parts: a high frequency component (with frequency equal to the sum of the ''actual'' carrier frequency and our ''guess'' frequency) and a low frequency component (due to the difference of the two frequencies). </li>
<li>We filter the multiplied signal through a butterworth filter with a 75Hz cutoff frequency to remove the high frequency component.</li>

<pre>
%% Mix and Filter

mix = v.*cos(2*pi*(carrierFreq)*t)';
% mix = v.*cos(2*pi*(fc)*t)';

figure(4)
subplot(2,2,1)
plot(t,mix)
axis([0 2 -1.2 1.2])
title('\fontsize{14}Signal Multiplied by Cosine')
xlabel('Time (s)')
ylabel('Amplitude')
subplot(2,2,3)
mixFft = abs(fftshift(fft(mix)));
plot(freqShift,mixFft)
title('\fontsize{14}FFT of Multiplied Signal')
xlabel('Frequency (Hz)')
ylabel('Amplitude')
text(150,.8*max(mixFft),sprintf('Low Frequency\n<- Component'))
text(300,.25*max(mixFft),sprintf('High Frequency\nComponent ->'))

[b,a] = butter(5,(75)/Fs);
mixFilter = filter(b,a,mix);
mixFilterFft = abs(fftshift(fft(mixFilter)));
subplot(2,2,2)
plot(t,mixFilter)
axis([0 2 -1.2 1.2])
title('\fontsize{14}Multiplied Signal Filtered')
xlabel('Time (s)')
ylabel('Amplitude')
subplot(2,2,4)
plot(freqShift,mixFilterFft)
title('\fontsize{14}FFT of Filtered Signal')
xlabel('Frequency (Hz)')
ylabel('Amplitude')
text(150,.8*max(mixFft),sprintf('Low Frequency\n<- Component'))
movegui('west')
</pre>

 [[File:K&M_Signal_Mixed_and_Filtered.png|600px]]
<li>We mark the locations where the filtered signal changes sign. This identifies possible "sync" points where zeros in the signal may occur.</li>

<li>We compare the length of time that occurs between each sync point with the baud rate to determine how many baud periods occur between each sync point. A single baud period indicates a zero. Each additional period over the first baud period indicates a one. (Ex. Three baud periods -> '110')</li>

<pre>
%% Sign Change Method
k = 1
for n = 1:length(v)-1
if (sign(mixFilter(n+1)) ~= sign(mixFilter(n)))
zeroLoc(k) = n;
k = k+1;
end
end

period = Fs/baud;

bitstream = []
for n = 1:length(zeroLoc)-1
periodDiff = zeroLoc(n+1)-zeroLoc(n);
cross = round(periodDiff/period) - 1;
if (cross == 0)
bitstream = [bitstream 0];
else if (cross > 0)
bitstream = [bitstream ones(1,cross) 0];
end
end
end

bitstream = [bitstream ones(1,10)]; %pad with ones for end of message

sample = zeros(1,length(v));
sample(zeroLoc) = 1;

figure(5)
plot(t,mixFilter,'b')
hold on
plot(t,sample,'k')
hold off
axis([0 2 -1.2 1.2])
title('\fontsize{14}Sign Change Sync Points')
xlabel('Time (s)')
ylabel('Amplitude')
legend('Filtered Signal','Sync Points','location','best')
</pre>

 [[File:K&M_Sync_Points.png|600px]]
<li>We send the resulting bit stream through a text decoder which translates the ones and zeros into a text message.</li>
<pre>
%% Bitstream to Characters

breakLoc = [];
k = 1;
for n = 1:length(bitstream)-2
% Finds '00' bits indicating new character
if(isequal(find(bitstream(n:n+1) == [0 0]),[1 2]))
breakLoc(k) = n;
k = k+1;
end;
end;

messageText = '';
for n = 1:length(breakLoc)-1
messageChunks = bitstream(breakLoc(n):breakLoc(n+1)-1);
temp = mat2str(messageChunks);
temp = strrep(temp,'[','');
temp = strrep(temp,'0 0 ','');
temp = strrep(temp,']','');
if (((breakLoc(n+1) - breakLoc(n)) <= 12) && (~isequal(temp,'0')) &&(bin2dec(fliplr(temp)) <= length(charTable)))
messageText = [messageText charTable(bin2dec(fliplr(temp)))];
end;
end

messageText
</pre>
</ol>

== Results/Problems ==
===Transmitter===
To our knowledge, our transmitter generates a signal without any problems.
===Receiver===
As long as our guess frequency is close to the actual frequency, (less than 0.1Hz off) our receiver can easily handle a 1dB SNR.
==== Frequency Errors ====
In most cases, our guess frequency is within 0.2Hz of the actual frequency. As the guess frequency exceeds these bounds, the text decode becomes increasingly garbled.
==== PID Controller Problems ====
The first iteration did not take into account the I component of the signal and was constantly trying to drive the signal to the positive I coordinates. A smiple if-else statement solved this problem. However there are some bugs. There might be a singularity at (0,0) which causes the controller to perform in a strange fashion. Also, the code has very bad noise rejection. It can produce baseband but not very well once noise is added. Finally, it doesn't decode signals that we generate ourselves. When we produce our signal in MATLAB, the code works fine. However, the signal from wikipedia.com and Dr. Frohne's signal don't work. One problem with the wikipedia.com signal is that it's native format is .ogg which is lossy. This could've presented problems when we convert the signal to a wave file as high frequencies get chopped in lossy formats.

==Authors==

[[User:Michael.vonpohle|Michael von Pohle]]

[[Hildebrand,_Kurt|Kurt Hildebrand]]

PSK31 Demodulation (Kurt & Michael)

2012-12-14T10:32:42Z

Michael.vonpohle: /* Receiver */

== Project Description ==

The goal of this project is to design and code a Matlab script that will encode and decode a PSK31 signal including signals with noise. The receiver should be able to read in signals (as a wav file) from other sources as well.

PSK31 is a audible text encoding that can be sent over the air by amateur radio operators. A computer's sound card can be used to send and receive the signal since the signal is audible. For more information regarding PSK31 see the Wikipedia article.[http://en.wikipedia.org/wiki/PSK31]

== Our Approach ==

=== Code Overview ===

==== Transmitter ====

Our code creates a PSK31 signal given an input carrier frequency and message. For testing our receiver code, the transmitter is setup to generate a random carrier frequency and phase. It also adds random noise to the signal before writing it to a wav file.
 
<pre>
clear all
close all
clc

fc = 100+rand(1)*3900 % Carrier Frequency
%fc = 1500;
Fs = 10000; % Sampling frequency
baud = 31.25;

%% Encode the message

phase = rand(1)*2*pi; % Phase of the signal
dt = 0:1/Fs:1/baud-1/Fs; % Time between samples
one = ones(size(dt)); % A 'One' signal
zero = cos(pi*dt*baud); % A 'Zero' signal

messageString = 'Hello World! The quick brown fox jumps over the lazy dog. ABCDEFGHIJKLMNOPQRSTUVWXYZ abcdefghijklmnopqrstuvwxyz 0123456789';
[message charTable] = make_bits(messageString);

baseband = [];
m=1;
for k = 1:length(message)
if(message(k)==0)
baseband = [baseband, zero*m];
m=-m;
else
baseband = [baseband, one*m];
end
end

t = 0:1/(Fs):length(baseband)/Fs-1/Fs;

v = baseband.*cos(2*pi*fc*t+phase);

% Noise
v = v+randn(size(v))*10^(-10/20);

wavwrite(v,Fs,'signal.wav');

figure(1)
subplot(2,1,1)
plot(t,baseband)
axis([0 2 -1.2 1.2])
title('\fontsize{14}Baseband')
xlabel('Time (s)')
ylabel('Amplitude')
subplot(2,1,2)
plot(t,v)
axis([0 2 -1.2 1.2])
title('\fontsize{14}Baseband with Carrier')
xlabel('Time (s)')
ylabel('Amplitude')
movegui('northwest')
</pre>

 [[Image:K&M_PSK31Signal.png|600px]]

==== Receiver ====
Our receiver is split into several steps:
<ol>
<li>We read in the signal from a wav file and generate utility variables and matrices.</li>

<pre>
%% Decode Message

clear all
baud = 31.25;

% [v,Fs] = wavread('PSK31_sample.wav');
% [v,Fs] = wavread('capture.wav');
[v,Fs] = wavread('signal.wav');

dt = 0:1/Fs:1/baud-1/Fs; % Time between samples
one = ones(size(dt)); % A 'One' signal
zero = cos(pi*dt*baud); % A 'Zero' signal
t = 0:1/(Fs):length(v)/Fs-1/Fs;

[sout charTable] = load_alpha();

upperNoiseCutOff = .75;
lowerNoiseCutOff = 1-upperNoiseCutOff;

% figure(1)
% plot(v)
</pre>

<li>We run the signal through an FFT and take an average over the range of the FFT spike to obtain a carrier frequency guess.</li>
<pre>
%% Determine Carrier Frequency

vFftShift = abs(fftshift(fft(v)));

freq = linspace(0,length(v)-1,length(v))*(Fs/length(v));
freqShift = (freq - Fs/2);

% remove noise components
noise = (vFftShift < lowerNoiseCutOff*max(vFftShift));
vFftShift(noise) = 0;

% uses the center(mean) of the fft spike as the frequency
freqRange = find(vFftShift(length(vFftShift)/2:length(vFftShift)) > 0);
carrierFreq = freqShift(round(mean([max(freqRange),min(freqRange)]))+length(vFftShift)/2-1)

figure(2)
plot(freqShift,vFftShift)
movegui('center')
</pre>
<li>A PID controller was implemented to help offset the fact that a carrier frequency derived from the FFT produces an inaccurate carrier frequency. An offset in the carrier frequency causes the constellation diagram to rotate in a circle. The PID tries to compensate for this by adding to or subtracting from the phase of the signal while trying to drive the Q-component of the signal to zero. The feedback loop is described by the code below.</li>
<code>
% PID controller constants
Kp = 25;
Ki = 50;
Kd = 1;
output = zeros(1, length(v)); % Init
setpoint = 0; % Sets the feedback point to control to.
previous_error = 0; % In this case, you want to set yt to 0.
integral = 0;
xt_filt = [];
yt_filt = [];
for k=51:length(v)
xt(k) = v(k)*cos(2*pi*u_fc*t(k)+output(k));
yt(k) = v(k)*sin(2*pi*u_fc*t(k)+output(k));

xt_filt(k:-1:k-50) = filter(b, a, xt(k:-1:k-50));
yt_filt(k:-1:k-50) = filter(b, a, yt(k:-1:k-50));

if(sign(xt(k)) == sign(yt(k)))
error = setpoint - yt_filt(k);
else
error = setpoint + yt_filt(k);
end

% PID Feedback Controller compensates for inaccurate fc guess.
% error = setpoint - yt_filt(k);
integral = integral + error*10;
derivative = (error - previous_error)/10;
output(k+1) = Kp*error + Ki*integral + Kd*derivative;
previous_error = error;
end

</code>
<li>We multiply the signal with a cosine wave at our guess frequency. This splits the signal into two parts: a high frequency component (with frequency equal to the sum of the ''actual'' carrier frequency and our ''guess'' frequency) and a low frequency component (due to the difference of the two frequencies). </li>
<li>We filter the multiplied signal through a butterworth filter with a 75Hz cutoff frequency to remove the high frequency component.</li>

<pre>

%% Mix and Filter

mix = v.*cos(2*pi*(carrierFreq)*t)';
% mix = v.*cos(2*pi*(fc)*t)';

figure(4)
subplot(2,2,1)
plot(t,mix)
axis([0 2 -1.2 1.2])
title('\fontsize{14}Signal Multiplied by Cosine')
xlabel('Time (s)')
ylabel('Amplitude')
subplot(2,2,3)
mixFft = abs(fftshift(fft(mix)));
plot(freqShift,mixFft)
title('\fontsize{14}FFT of Multiplied Signal')
xlabel('Frequency (Hz)')
ylabel('Amplitude')
text(150,.8*max(mixFft),sprintf('Low Frequency\n<- Component'))
text(300,.25*max(mixFft),sprintf('High Frequency\nComponent ->'))

[b,a] = butter(5,(75)/Fs);
mixFilter = filter(b,a,mix);
mixFilterFft = abs(fftshift(fft(mixFilter)));
subplot(2,2,2)
plot(t,mixFilter)
axis([0 2 -1.2 1.2])
title('\fontsize{14}Multiplied Signal Filtered')
xlabel('Time (s)')
ylabel('Amplitude')
subplot(2,2,4)
plot(freqShift,mixFilterFft)
title('\fontsize{14}FFT of Filtered Signal')
xlabel('Frequency (Hz)')
ylabel('Amplitude')
text(150,.8*max(mixFft),sprintf('Low Frequency\n<- Component'))
movegui('west')
</pre>

 [[File:K&M_Signal_Mixed_and_Filtered.png|600px]]
<li>We mark the locations where the filtered signal changes sign. This identifies possible "sync" points where zeros in the signal may occur.</li>

<li>We compare the length of time that occurs between each sync point with the baud rate to determine how many baud periods occur between each sync point. A single baud period indicates a zero. Each additional period over the first baud period indicates a one. (Ex. Three baud periods -> '110')</li>

<pre>
%% Sign Change Method
k = 1
for n = 1:length(v)-1
if (sign(mixFilter(n+1)) ~= sign(mixFilter(n)))
zeroLoc(k) = n;
k = k+1;
end
end

period = Fs/baud;

bitstream = []
for n = 1:length(zeroLoc)-1
periodDiff = zeroLoc(n+1)-zeroLoc(n);
cross = round(periodDiff/period) - 1;
if (cross == 0)
bitstream = [bitstream 0];
else if (cross > 0)
bitstream = [bitstream ones(1,cross) 0];
end
end
end

bitstream = [bitstream ones(1,10)]; %pad with ones for end of message

sample = zeros(1,length(v));
sample(zeroLoc) = 1;

figure(5)
plot(t,mixFilter,'b')
hold on
plot(t,sample,'k')
hold off
axis([0 2 -1.2 1.2])
title('\fontsize{14}Sign Change Sync Points')
xlabel('Time (s)')
ylabel('Amplitude')
legend('Filtered Signal','Sync Points','location','best')
</pre>

 [[File:K&M_Sync_Points.png|600px]]
<li>We send the resulting bit stream through a text decoder which translates the ones and zeros into a text message.</li>
<pre>
%% Bitstream to Characters

breakLoc = [];
k = 1;
for n = 1:length(bitstream)-2
% Finds '00' bits indicating new character
if(isequal(find(bitstream(n:n+1) == [0 0]),[1 2]))
breakLoc(k) = n;
k = k+1;
end;
end;

messageText = '';
for n = 1:length(breakLoc)-1
messageChunks = bitstream(breakLoc(n):breakLoc(n+1)-1);
temp = mat2str(messageChunks);
temp = strrep(temp,'[','');
temp = strrep(temp,'0 0 ','');
temp = strrep(temp,']','');
if (((breakLoc(n+1) - breakLoc(n)) <= 12) && (~isequal(temp,'0')) &&(bin2dec(fliplr(temp)) <= length(charTable)))
messageText = [messageText charTable(bin2dec(fliplr(temp)))];
end;
end

messageText
</pre>
</ol>

== Results/Problems ==
===Transmitter===
To our knowledge, our transmitter generates a signal without any problems.
===Receiver===
As long as our guess frequency is close to the actual frequency, (less than 0.1Hz off) our receiver can easily handle a 1dB SNR.
==== Frequency Errors ====
In most cases, our guess frequency is within 0.2Hz of the actual frequency. As the guess frequency exceeds these bounds, the text decode becomes increasingly garbled.
==== PID Controller Problems ====
The first iteration did not take into account the I component of the signal and was constantly trying to drive the signal to the positive I coordinates. A smiple if-else statement solved this problem. However there are some bugs. There might be a singularity at (0,0) which causes the controller to perform in a strange fashion. Also, the code has very bad noise rejection. It can produce baseband but not very well once noise is added. Finally, it doesn't decode signals that we generate ourselves. When we produce our signal in MATLAB, the code works fine. However, the signal from wikipedia.com and Dr. Frohne's signal don't work. One problem with the wikipedia.com signal is that it's native format is .ogg which is lossy. This could've presented problems when we convert the signal to a wave file as high frequencies get chopped in lossy formats.

==Authors==

[[User:Michael.vonpohle|Michael von Pohle]]

[[Hildebrand,_Kurt|Kurt Hildebrand]]

PSK31 Demodulation (Kurt & Michael)

2012-12-14T10:25:37Z

Michael.vonpohle: /* Receiver */

User:Michael.vonpohle

2012-12-14T05:48:17Z

Michael.vonpohle:

== General Information ==
I'm an Electrical Engineering Major and have attended Walla Walla since 2009. I plan to graduate in 2013. This page contains a summary of my contributions to the wiki.
== Projects/Pages ==
[[PSK31 Demodulation (Kurt & Michael)]]

User:Michael.vonpohle

2012-12-14T05:48:00Z

Michael.vonpohle: /* General Information */

== General Information ==
I'm an Electrical Engineering Major and have attended Walla Walla since 2009. I plan to graduate in 2013. This page contains a summary of my contributions to the wiki.

== Projects/Pages ==

[[PSK31 Demodulation (Kurt & Michael)]]

Signals and Systems

2012-12-14T05:47:46Z

Michael.vonpohle: /* 2012-2013 Contributors */

== Topics ==
[[Fourier series - by Ray Betz|Overview of Signals and Systems]]

===Individual Subjects===
*[[Linear Time Invariant System|Linear Time Invariant Systems]]
**[[The Game|"The Game"]]
*[[Orthogonal functions|Orthogonal Functions]]
*[[Energy in a signal|Finding the Energy in a Signal]]
**[[Rayleigh's Theorem]]
*[[Fourier series|Fourier Series]]
*[[Fourier transform|Fourier Transforms]]
**[[Discrete Fourier transform]]
*[[Sampling]]
*[[FIR Filter Example]]
*[[Relationship between e, sin and cos]]

== Some Useful Links to Suppliment or Substitute for a Textbook ==
===Books on Signal Processing===
*[https://ccrma.stanford.edu/~jos/sasp/sasp.html Spectral Audio Signal Processing, by Julius O. Smith III]
*[http://www.dspguide.com/ The Scientist and Engineer's Guide to Digital Signal Processing by Steven W. Smith, Ph.D.] The professor likes this one.
*[http://ocw.mit.edu/courses/electrical-engineering-and-computer-science/6-003-signals-and-systems-spring-2010/readings/ Discrete Time Signals & Systems]

===Fourier Series===
*[http://www.intmath.com/Fourier-series/Fourier-intro.php Interactive Mathematics (like a textbook with some examples)]
*[http://mathworld.wolfram.com/FourierSeries.html Mathworld]
*[http://en.wikipedia.org/wiki/Fourier_series Wikipedia]
*[http://web.mit.edu/2.14/www/Handouts/FreqDom.pdf MIT handout on Fourier Series, Fourier Transform, and Laplace Transform]
*[http://www.maths.mq.edu.au/~bon/Fourier%20Theory.pdf Fourier Theory B..M..N.. Clarke]

===Dirac Delta Function and Convolution===
*[http://web.mit.edu/2.14/www/Handouts/Convolution.pdf MIT handout on Dirac Delta Function and Convolution]

===Multi-rate Filtering===

[http://www.google.com/url?url=http://www.mds.com/tech/filter/multirate_article.pdf&rct=j&sa=U&ei=pD_UTJqtKY6ksQPbzPWMCw&ved=0CBUQFjAA&q=Purcell+Multirate+Filters&usg=AFQjCNFsHM7ROpUdrQ6py9ZH_RhQ_BeigA Multirate Filters Introduction]

[http://www.ws.binghamton.edu/fowler/fowler%20personal%20page/EE521_files/IV-05%20Polyphase%20FIlters_2007.pdf Slides from a Presentation on Polyphase Decimation and Interpolation by Mark Fowler]

===FIR Filters===

[http://www.dspguru.com/dsp/faqs/fir This is a very easy-to-understand summary of FIR basics, properties, design, and implementation]

[http://www.dspguru.com/dsp/faqs/multirate/decimation Another easy-to-understand article about decimation]

[http://www.dspguru.com/dsp/faqs/multirate/interpolation Another easy-to-understand article about interpolation]

===Adaptive FIR Filters===
[http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.42.6386&rep=rep1&type=pdf Introduction to Adaptive Filters, Simon Haykin]

[http://saba.kntu.ac.ir/eecd/taghirad/E%20books/TOC/Adaptive%20Filters.pdf Simon Haykin's book chapter]

[http://www.latticesemi.com/documents/doc22982x20.pdf?jsessionid=f0308ccf0f735471e49a6054323c5c177969 Adaptive LMS in an FPGA]

[[Adaptive Filters In the Frequency Domain]]

====Constant Modulus Algorythm====
[http://ens.ewi.tudelft.nl/Education/courses/et4147/sheets/cma_leus.pdf Using the CMA on antenna arrays]

===Course Pages===
[[2005-2006 Assignments]]

[[2006-2007 Assignments]]

[[2008-2009 Assignments]]

[[2009-2010 Assignments]]

[http://people.wallawalla.edu/~Rob.Frohne/ClassNotes/engr455index.htm Class notes for Signals & Systems]

==Articles==

===Octave Tutorials===
[[Installing Octave on a Mac]] (Chris Lau)

[[Octave and Scilab on a Mac]] (Ben Henry)

[[ASN2 - Octave Tutorial]] (Jodi S. Hodge)

[[A u(t) function example]]

[[FIR Filter Example Code for Octave]]

[[Leakage Example Octave Script]]

[[Interpolation using the DFT Example Script]]

[[Tuner Upper Removal Demonstration]]

[[Airplane Noise Removal Demonstration]]

===Final Project (2011)===
[[Matlab/Octave deMorse.m]]

[[morse.m This is the one from mathworks]]

===[[Table of Fourier Transform Properties]]===

==Homework Assignments==
Please put your name next to the assignment, linking it to your submission
* HW #1 - Make a personal page on this wiki ([[Christopher Garrison Lau I|Chris Lau]])([[Jodi S. Hodge]])([[user:chris.wills|Chris Wills]])[[Shepherd,Victor|(Victor Shepherd)]]
* HW #2 - Write a tutorial about installing and/or using Octave ([[Installing Octave on a Mac|Chris Lau]])([[Jodi S. Hodge]])([[Octave|Victor Shepherd]])
* HW #3 - Show graphically that <math> \int_{-\infty}^{\infty} e^{j2\pi f(t-u)}\, df = \delta (t-u)</math> ([[HW 3|Chris Lau]])([[Jodi S. Hodge]])([[user:chris.wills/HW3|Chris Wills]])([[Hw3|Victor Shepherd)]]

* HW #4 - Given a linear time-invariant system where <math>\ u(t) </math> produces an output <math>\ w(t) </math>, find the output due to any function <math>\ x(t) </math> ([[HW 4|Chris Lau]])
* HW #5: ([[HW 5|Chris Lau]])
** Part 1 - Find <math> \mathcal{F}[e^{- \sigma t} x(t)u(t)] </math> and relate it to the Laplace Transform. Derive the Inverse Laplace Transform of this from the inverse Fourier Transform.
** Part 2 - [[Image:20101006KeyDSCN3161.jpg|thumb|300px|center]]

* HW #6 - Pick a property of the Fourier Transform & present it on the Wiki. Make a table with all your properties. Interpret your property. ([[HW 6|Ben Henry]])([[Table of Fourier Transform Properties|Chris Lau]])([[Table of Fourier Transform Properties|Victor Shepherd]])
* HW #7 - Finish the practice tests
* HW #8 - Make a page about interpolating FIR filters. Note how many multiply/add operations.([[Jodi S. Hodge]])([[Interpolating FIR filters|Chris Lau]])([[Hw8|Victor Shepherd]])
* HW #9 - Add to #8 writeup how to do a decimating filter and figure out how many multiply & adds are needed for a n/2 decimating low pass filter.([[Jodi S. Hodge]])([[Decimating FIR filters|Chris Lau]])([[Hw9|Victor Shepherd)]]
* HW #10 - Use Octave (or Mathlab or Silab) to plot the frequency response of low pass filters with cut off frequencies of 1/32T, 1/8T, and 1/4T and compare how many coeffficients are needed with an eye to answer the question "Is it less calculation to decimate and then filter, or better to put the filter in the pre-decimation filter?" ([[Jodi S. Hodge]])([[Hw10|Victor Shepherd)]]
* HW #11 - Is our method the same as Mark Fowler's? See
[http://www.ws.binghamton.edu/fowler/fowler%20personal%20page/EE521_files/IV-05%20Polyphase%20FIlters_2007.pdf Wiki]. Same # multiply and adds? See Notes 11/3/10. ([[Jodi S. Hodge]])([[Hw11|Victor Shepherd)]]
* HW #12 - Experiment with a variety of signals having a 3Khz bandwidth to determine the resolution you can get when doing a cross correlation <math> \ r(m) =

\displaystyle\sum\limits_{n=0}^{N-1} x(n) x(n+m) </math>. You can generate the signals randomly and filter them to obtain the band-limited signals. ([[Jodi S. Hodge]])
* HW #13 - Derive the following realtions:
**a) <math>DFT(x(k-l))\!</math>
**b) <math> DFT(e^{j2 \pi lk/N}x(k)\!</math>
**c) <math>\sum\limits_{k=0}^{N-1} x(k)y(k)^{*}=c\sum\limits_{k=0}^{N-1} X(n)Y(n)^{*}</math> ([[Hw13|Victor Shepherd)]]

* HW #14 - Come up with a use for an adaptiveFIR filter and make an Octave script to demonstrate it. ([[Jodi S. Hodge]])([[Hw14|Victor Shepherd)]]
* HW #15 - Do Practice Exam II ([[Hw15|Victor Shepherd)]]
* [[CW-Robot Octave Simulation]]

==People Involved with this Wiki==

===2012-2013 Contributors===
[[Brian Haddad]]

[[Kurt Hildebrand]]

[[Denver Lodge]]

[[User:michael.vonpohle|Michael von Pohle]]

===2011-2012 Contributors===
[[Matthew Blaire]]

[[Cody Lorenz]]

===2010-2011 Contributors===
[[Ben Henry|Ben Henry]]

[[Christopher Garrison Lau I]]

[[user:chris.wills|Chris Wills]]

[[Jodi S. Hodge]]

[[Luke Chilson]]

[[Shepherd,Victor|Victor Shepherd]]

===2009-2010 Contributors===
[[Nick Christman]]

[[Joshua Sarris]]

[[Kevin Starkey]]

[[Max Woesner]]

[[Jodi Hodge]]

[[Corneliu Turturica]]

===2008-2009 Contributors===
[[User:eric.clay|Eric Clay]]

[[User:tsung-lin.yang|Chuck Yang]]

[[User:elton.zebron|Elton Zebron]]

[[User:Luke.chilson|Luke Chilson]]

[[User:Brandon.price|Brandon Price]]

[[User:Fonggr|Greg Fong]]

===2007-2008 contributors===

[[User:baldwin.britton|Baldwin Britton]]

[[User:Harrde|Denver Harris]]

[[User:Pridma|Mark Priddy]]

[[User:ChrisRas|Chris Rasmussen]]

[[User:RothMi|Michael Roth]]

[[User:Rothsa|Sally Roth]]

===2006-2007 contributors===

[[User:Smitry|Ryan J Smith]]

[[User:Nathan|Nathan Ferch]]

[[User:Andrew|Andrew Lopez]]

[[User:Sherna|Nathan Sherman]]

[[User:Adkich|Chris Adkins]]

===2005-2006 contributors===

[[User:GabrielaV|Gabriela Valdivia]]

[[User:SDiver|Raymond Betz]]

[[User:chrijen|Jenni Christensen]]

[[User:wonoje|Jeffrey Wonoprabowo]]

[[User:wilspa|Paul Wilson]]

[[User:Frohro|Instructor: Rob Frohne]]

===2004-2005 contributors===

[[User:Barnsa|Sam Barnes]]

[[User:Santsh|Shawn Santana]]

[[User:Goeari|Aric Goe]]

[[User:Caswto|Todd Caswell]]

[[User:Andeda|David Anderson]]

[[User:Guenan|Anthony Guenterberg]]

PSK31 Demodulation (Kurt & Michael)

2012-12-14T05:23:04Z

Michael.vonpohle:

PSK31 Demodulation (Kurt & Michael)

2012-12-14T05:22:27Z

Michael.vonpohle: /* Transmitter */

PSK31 Demodulation (Kurt & Michael)

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Michael.vonpohle: /* Receiver */

PSK31 Demodulation (Kurt & Michael)

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Michael.vonpohle:

PSK31 Demodulation (Kurt & Michael)

2012-12-14T05:05:34Z

Michael.vonpohle:

PSK31 Demodulation (Kurt & Michael)

2012-12-14T05:02:35Z

Michael.vonpohle: /* Code Overview */

PSK31 Demodulation (Kurt & Michael)

2012-12-14T04:54:47Z

Michael.vonpohle: /* Results/Problems */

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2012-12-14T04:53:25Z

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PSK31 Demodulation (Kurt & Michael)

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Michael.vonpohle: /* Transmitter */

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Michael.vonpohle: /* Receiver */

PSK31 Demodulation (Kurt & Michael)

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Michael.vonpohle: /* Code */

File:K&M PSK31Signal.png

2012-12-14T04:45:28Z

Michael.vonpohle: Undo revision 10637 by Michael.vonpohle (Talk)

File:K&M PSK31Signal.png

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Michael.vonpohle:

Example

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File:K&M Sync Points.png

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File:K&M Signal Mixed and Filtered.png

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Michael.vonpohle:

File:K&M PSK31Signal.png

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Michael.vonpohle:

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PSK31 Demodulation (Kurt & Michael)

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Michael.vonpohle: Created page with '== THE PROJECT!!! =='

== THE PROJECT!!! ==

User:Michael.vonpohle

2012-12-13T03:58:11Z

Michael.vonpohle: /* Projects/Pages */

== General Information ==

I'm an Electrical Engineering Major and have attended Walla Walla since 2009. I plan to graduate in 2013. This page contains a summary of my contributions to the wiki.

== Projects/Pages ==

[[PSK31 Demodulation (Kurt & Michael)]]

User:Michael.vonpohle

2012-12-13T03:49:19Z

Michael.vonpohle: Created page with '== General Information == I'm an Electrical Engineering Major and have attended Walla Walla since 2009. I plan to graduate in 2013. This page contains a summary of my contribut…'

== General Information ==

I'm an Electrical Engineering Major and have attended Walla Walla since 2009. I plan to graduate in 2013. This page contains a summary of my contributions to the wiki.

== Projects/Pages ==