Ee443 communications 1 - lab 2 - loren schwappach

CTU: EE 443 – Communications 1: Lab 2: MATLAB Project – Coherent Detection 1

Colorado Technical University EE 443 – Communication 1

Lab 2: MATLAB Project – Coherent Detection September 2010

Loren K. Schwappach

ABSTRACT: This lab report was completed as a course requirement to obtain full course credit in EE443, Communication 1 at Colorado Technical University. Given a message and a carrier signal, this lab report uses MATLAB to demonstrate the process of coherent detection of a message signal from a modulated signal. All of the code mentioned in this lab report was saved as a MATLAB m-file for convenience, quick reproduction, and troubleshooting of the code. All of the code below can also be found at the end of the report as an attachment, as well as all figures.

If you have any questions or concerns in regards to this laboratory assignment, this laboratory report, the process used in designing the indicated circuitry, or the final conclusions and recommendations derived, please send an email to [email protected]. All computer drawn figures and pictures used in this report are of original and authentic content.

I. INTRODUCTION

MATLAB is a powerful program and is useful in the

visualization of mathematics, physics, and applied

engineering. In this lab exercise MATLAB will be used to

demonstrate modulation and coherent detection. Given the

following:

(1)

(2)

Use MATLAB to investigate the effects of an

oscillator’s synchronization with the carrier signal in the

coherent detection process.

Coherent detection is a process used to recover DSB-

SC signals by first multiplying the signal by a local oscillator

signal with the same frequency and phase as the original

carrier signal and low pass filtering the result.

II. PROCEDURE / RESULTS

To demonstrate all of the signals and local oscillator

synchronization effects, the MATLAB code provided at the

conclusion of this report was utilized, and can be saved as an

m-file. Furthermore, all of the images in this section can be

found at the end of this report in an easier to read format.

First the message signal (1) above and the cosine

signal (2) above were created and graphed in MATLAB, as

illustrated by figures 1 and 2.

Figure 1: m(t) = 5cos(2pi*36t)+2sin(2pi*180t).

Figure 2: c(t) = 10cos(2pi*1500t).

Next the message and carrier signals were multiplied

together resulting in the modulated DSB-SC signal c(t) as

illustrated in the time and frequency domains by figures 3,4,

and 5 below.

mailto:[email protected]


Figure 3: DSB-SC Modulated Signal s(t) in the time

domain.

Figure 4: DSB-SC Modulated Signal S(f) in the frequency

spectrum (2-sided spectrum).

Figure 5: DSB-SC Modulated Signal S(f) in the frequency

spectrum (positive spectrum).

You can see by figures 5 and 6 that DSB-SC

modulation results in shifting the message signal both above

(Upper SB) and below (Lower SB) the carrier signal while

suppressing the carrier signal as required by DSB-SC

modulation.

Next, the DSB-SC signal is multiplied by a local

oscillator synchronized both in phase and frequency of the

original carrier signal c(t) this results in the demodulated

output signal as shown by figures 6, 7, and 8.

Figure 6: DSB-SC Demodulated Signal v(t) in the time

domain.

Figure 7: DSB-SC demodulated Signal V(f) in the

frequency spectrum (2-sided spectrum).

Figure 8: DSB-SC Demodulated Signal Y(f) in the

frequency spectrum (positive spectrum).


You can now see the shape of the original message

signal m(t) as the maximum positive amplitude, and minimum

negative amplitude of v(t) in figure 6. Figures 7 and 8

illustrate that demodulated result puts the message signal m(t)

back to its original frequency position. The original signal can

now be recovered using a LP filter to eliminate the high

frequency components.

Next to verify the effects of an out of synchronization

local oscillator, the local oscillator is first moved out of

frequency with the carrier frequency (by .01% and 2%), next

the local oscillator is moved out of phase with the carrier

phase (by 45º , 90º, and 180º). The results are shown by

figures 9-23 below.

Figure 9: DSB-SC (.01% Out of Sync LO) Demodulated

Signal v(t) in the time domain.

Figure 10: DSB-SC (.01% Out of Sync LO) demodulated

Signal V(f) in the frequency spectrum (2-sided spectrum).

Figure 11: DSB-SC (.01% Out of Sync LO) Demodulated

Signal Y(f) in the frequency spectrum (positive spectrum).

Figure 12: DSB-SC (2% Out of Sync LO) Demodulated


Figure 13: DSB-SC (2% Out of Sync LO) demodulated



Figure 14: DSB-SC (2% Out of Sync LO) Demodulated

Signal V(f) in the frequency spectrum (positive spectrum).

You can see from figures 9-14 that a small error in

frequency synchronization can (2% error (LO=1.47 kHz)) can

completely eliminate signal recovery. However message

recover can still occur with a very small error in frequency

(<= .01% error (LO=1.49985 kHz).

Several additional LO frequencies were tested by

changing the LO error and it was determined that anything

greater than .01% error would eliminate recovery of the

message signal.

Thus, frequency synchronization is extremely

important for coherent detection and should be limited to very

small % error =<.01%.

Next the effects of phase synchronization are

examined and the results are shown by figures 15-23 below.

Figure 15: DSB-SC (45º Out of Phase LO) Demodulated


Figure 16: DSB-SC (45º Out of Phase LO) demodulated


.
















From figures 15-23 above, it is observed that an

increase in the LO phase compared to the carrier phase will

gradually attenuate the signal (0º to <90º), until the signal is

fully attenuated (90 º). There after the signal will be inverted

(>90º to 180º), attenuate the inverted signal (>180º to 270º),

and un-invert and increase to max amplitude (270º to 360º).

Thus the maximum frequency deviation that will

permit signal recovery by the local oscillator is an increase or

decrease in phase of the local oscillator by 90 degrees (fully

attenuated).

The final and bonus part of this lab was to apply a

MATLAB command that could filter the DSB-SC

demodulated output. This is the final step of the coherent

detection process. This was achieved using the “butter”

function to create a low pass third order Butterworth filter

transfer function at 500 Hz, and the “lsim” function to apply

the transfer function to the demodulated time domain output.

The results are shown by figures 24-26 below.


Figure 24: DSB-SC Filtered Demodulated Signal v(t) in the

time domain.

Figure 25: DSB-SC Filtered demodulated Signal V(f) in

the frequency spectrum (2-sided spectrum).

Figure 26: DSB-SC Filtered Demodulated Signal V(f) in

the frequency spectrum (positive spectrum).

Figure 24 demonstrates successfully that coherent

detection can indeed be used for the recovery of a message

signal from a DSB-SC modulated signal. Comparing figure

24 to Figure 1, the v(t) is indeed the message signal m(t) with

an increased magnitude. For example: 34Vpp versus 8Vpp.

For the final part of this lab, the process of coherent

detection and filtering is investigated using MATLAB’s

Simulink tool set. This was accomplished for a sinusoidal

input and a square wave input respectively.

For the input sinusoidal wave two sinusoidal inputs

were added summed resulting in the sinusoidal input used

previously in MATLAB (1). This sinusoidal input was then

modulated (multiplied) by the carrier input previously used in

MATLAB (2). The resultant DSB-SC modulated wave s(t) is

then demodulated (multiplied) by a local oscillator

synchronous in frequency and phase with the original carrier

frequency c(t)’. The final demodulated output is then filtered

to remove the unwanted harmonics restoring our original

message signal m(t).

All of these processes are illustrated in the time and

frequency domain using Simulink.

Figure 27: Simulink investigation of coherent detection

and filtering (sinusoidal input), Overall view.



and filtering (sinusoidal input), zoomed for input view.

Figure 29:Simulink investigation of coherent detection and

filtering (sinusoidal input), zoomed for filtering view.


Figure 30: m1(t) = 5cos(2pi*38t).

Figure 31: m1(t) = 2sin(2pi*180t).

Figure 32: m(t) = 5cos(2pi*36t)+2sin(2pi*180t). Notice the

Simulink resultant wave is the same as the result from

MATLAB.

Figure 33: Modulated DSB-SC wave s(t). Notice result

matches MATLAB plot. m(t)*c(t)=s(t).

Figure 34: Demodulated wave v(t). Notice Result matches

MATLAB plot. s(t)*c(t)’ = v(t). The 1st process of

coherent detection is complete. Still need to remove

unwanted harmonics.

Figure 35: Filtered demodulated wave v(t). Notice

resultant wave looks like our original message m(t). This

was accomplished using a 1st order LP Butterworth at

200Hz. The final process of coherent detection is now

complete.



resultant wave looks somewhat like our original message

m(t). This was accomplished using a 1st order LP

Butterworth at 500Hz. Notice the output still contains

several undesired harmonics, the 200Hz LP produced

cleaner results. The final process of coherent detection is

now complete.


resultant wave looks very much like our original message

m(t). This was accomplished using a 5th order LP

Butterworth at 200Hz. This appears to be the best filter

selection. The final process of coherent detection is now

complete.

Figure 38: M(f) frequency spectrum. Notice there are no

harmonics.

Figure 39: Modulated DSB-SC signal S(f) frequency

spectrum.

Figure 40: Demodulated (unfiltered) signal V(f). Notice

the original message is back with several higher frequency

harmonics above 1.5 kHz. We can obtain a scaled

amplitude m(t) by filtering out these high frequency

harmonics.


Figure 41: Demodulated (filtered) signal V(f). Used a 1

st

order LP Butterworth at 200Hz. Notice the harmonics are

now being attenuated.


st

order LP Butterworth at 500Hz. Notice the harmonics are

not as attenuated as they were in figure 41. Thus Figure

41 provided a better cutoff frequency for the LP filter.

Figure 43: Demodulated (filtered) signal V(f). Used a 5th

order LP Butterworth at 200Hz. Notice the harmonics

extremely attenuated now, providing a very clean copy of

our original message signal. The final stage of coherent

detection is complete.

Next coherent detection and filtering were verified

using a square wave input. For the square wave input a pulse

wave of 5 amplitude, 50% duty cycle, and a period of 20ms

was used. Thereafter the same process used for the sinusoidal

wave was used. However, the final filters required

modification to allow enough LF component sinusoidal waves

(Approx 10*frequency of square wave) in for producing the

output square wave. This is because the input square wave is

actually made up of several sinusoidal harmonics, and without

these harmonics.


and filtering (square wave input), Overall view.



and filtering (square wave input), zoomed for input view.


and filtering (square wave input), zoomed for filtering

view.


Figure 47: m(t) – square wave in time domain.

Figure 48: DSB-SC modulated wave, s(t).

Figure 49: Unfiltered demodulated wave, v(t).

Figure 50: Filtered demodulated wave, v(t). Filtered using

a 1st order Butterworth LP at 50 Hz. Notice we have lost

the square wave’s shape by filtering at too low of a

frequency. Need to increase the LP cutoff to retrieve the

harmonics required by our square wave (A good number

is 10*the highest frequency).


a 1st order Butterworth LP at 500 Hz. Notice we have

retrieved the square wave’s shape by filtering at 500Hz but

the order of our Butterworth is still to low. We need a

higher order filter to provide a cleaner square wave

output.



a 3rd order Butterworth LP at 500 Hz. Notice we have

retrieved the square wave’s shape and cleaned out the high

frequency noise. This is the best of the three filter designs

used. The process of coherent detection is now complete.

Figure 53: M(f) frequency spectrum. Notice the square

wave is made up of several components, thus a good low

pass filter must take these components into account. This

is why the best design used a 3rd

order Butterworth at 500

Hz.

Figure 54: Modulated DSB-SC signal S(f) frequency

spectrum.

Figure 55: Demodulated (unfiltered) wave, v(t).

Figure 56: Demodulated (filtered) wave, V(f). Used a 1

st

order LP Butterworth at 50Hz, too low to correctly

reproduce square wave.


st

order LP Butterworth at 500Hz, the square wave shape is

now there but high frequency harmonics are still creating

a problem.


Figure 58: Demodulated (filtered) wave, V(f). Used a 3rd

order LP Butterworth at 500Hz, the square wave shape is

now there and the high frequency harmonic noise has been

eliminated. This is the best of the three filter designs used.

The process of coherent detection is now complete.

III. CONCLUSIONS

MATLAB is a great utility for representing complex

concepts visually and can easily be manipulated to show

signals in various formats. This lab project was successful in

demonstrating MATLABs powerful features in a quick and

easy method, and demonstrating how MATLAB can be used

for analyzing complex processes like coherent detection and

filtering visually.

This lab illustrated that for coherent detection to

work, the local oscillator needs to be in synchronization with

the carrier in both phase and frequency. For coherent

detection the maximum frequency deviation from the carrier

had to be less than .01% of the carrier and less than +-90

degrees in phase with the carrier as shown through MATLAB.

Finally, the importance of low pass filtering was

explored, and from it the importance of using good nth order

filters at a frequency capable of retrieving the original

message. The sinusoidal filter proved was easy to design

since only the max frequency needed consideration. The

square wave filter design however required further analysis,

and it was observed that a cutoff frequency of 10 times the

square waves frequency was needed.

This was a great lab and thoroughly explored the

concepts of coherent detection.

REFERENCES

[1] Haykin, S., “Analog and Digital Communications 2nd

Edition” John Wiley & Sons, Haboken, NJ, 2007.


Figure 59: m(t) = 5cos(2pi*36t)+2sin(2pi*180t).

Figure 60: c(t) = 10cos(2pi*1500t).


Figure 61: DSB-SC Modulated Signal s(t) in the time domain.

Figure 62: DSB-SC Modulated Signal S(f) in the frequency spectrum (2-sided spectrum).


Figure 63: DSB-SC Modulated Signal S(f) in the frequency spectrum (positive spectrum).

Figure 64: DSB-SC Demodulated Signal v(t) in the time domain.


Figure 65: DSB-SC demodulated Signal V(f) in the frequency spectrum (2-sided spectrum).

Figure 66: DSB-SC Demodulated Signal Y(f) in the frequency spectrum (positive spectrum).


Figure 67: DSB-SC (.01% Out of Sync LO) Demodulated Signal v(t) in the time domain.

Figure 68: DSB-SC (.01% Out of Sync LO) demodulated Signal V(f) in the frequency spectrum (2-sided spectrum).


Figure 69: DSB-SC (.01% Out of Sync LO) Demodulated Signal Y(f) in the frequency spectrum (positive spectrum).

Figure 70: DSB-SC (2% Out of Sync LO) Demodulated Signal v(t) in the time domain.


Figure 71: DSB-SC (2% Out of Sync LO) demodulated Signal V(f) in the frequency spectrum (2-sided spectrum).

Figure 72: DSB-SC (2% Out of Sync LO) Demodulated Signal V(f) in the frequency spectrum (positive spectrum).


Figure 73: DSB-SC (45º Out of Phase LO) Demodulated Signal v(t) in the time domain.

Figure 74: DSB-SC (45º Out of Phase LO) demodulated Signal V(f) in the frequency spectrum (2-sided spectrum).

.


Figure 75: DSB-SC (45º Out of Phase LO) Demodulated Signal V(f) in the frequency spectrum (positive spectrum).



Figure 82: Simulink investigation of coherent detection and filtering (sinusoidal input), Overall view.


Figure 83: Simulink investigation of coherent detection and filtering (sinusoidal input), zoomed for input view.


Figure 84:Simulink investigation of coherent detection and filtering (sinusoidal input), zoomed for filtering view.


Figure 85: m1(t) = 5cos(2pi*38t).

Figure 86: m1(t) = 2sin(2pi*180t).


Figure 87: m(t) = 5cos(2pi*36t)+2sin(2pi*180t). Notice the Simulink resultant wave is the same as the result from

MATLAB.

Figure 88: Modulated DSB-SC wave s(t). Notice result matches MATLAB plot. m(t)*c(t)=s(t).


Figure 89: Demodulated wave v(t). Notice Result matches MATLAB plot. s(t)*c(t)’ = v(t). The 1

st process of coherent

detection is complete. Still need to remove unwanted harmonics.

Figure 90: Filtered demodulated wave v(t). Notice resultant wave looks like our original message m(t). This was

accomplished using a 1st order LP Butterworth at 200Hz. The final process of coherent detection is now complete.


Figure 91: Filtered demodulated wave v(t). Notice resultant wave looks somewhat like our original message m(t). This

was accomplished using a 1st order LP Butterworth at 500Hz. Notice the output still contains several undesired

harmonics, the 200Hz LP produced cleaner results. The final process of coherent detection is now complete.


Figure 92: Filtered demodulated wave v(t). Notice resultant wave looks very much like our original message m(t). This

was accomplished using a 5th order LP Butterworth at 200Hz. This appears to be the best filter selection. The final

process of coherent detection is now complete.

Figure 93: M(f) frequency spectrum. Notice there are no harmonics.


Figure 94: Modulated DSB-SC signal S(f) frequency spectrum.

Figure 95: Demodulated (unfiltered) signal V(f). Notice the original message is back with several higher frequency

harmonics above 1.5 kHz. We can obtain a scaled amplitude m(t) by filtering out these high frequency harmonics.



st order LP Butterworth at 200Hz. Notice the harmonics are now

being attenuated.


st order LP Butterworth at 500Hz. Notice the harmonics are not

as attenuated as they were in figure 41. Thus Figure 41 provided a better cutoff frequency for the LP filter.


Figure 98: Demodulated (filtered) signal V(f). Used a 5th order LP Butterworth at 200Hz. Notice the harmonics

extremely attenuated now, providing a very clean copy of our original message signal. The final stage of coherent

detection is complete.


Figure 99: Simulink investigation of coherent detection and filtering (square wave input), Overall view.


Figure 100: Simulink investigation of coherent detection and filtering (square wave input), zoomed for input view.


Figure 101: Simulink investigation of coherent detection and filtering (square wave input), zoomed for filtering view.


Figure 102: m(t) – square wave in time domain.

Figure 103: DSB-SC modulated wave, s(t).


Figure 104: Unfiltered demodulated wave, v(t).

Figure 105: Filtered demodulated wave, v(t). Filtered using a 1

st order Butterworth LP at 50 Hz. Notice we have lost the

square wave’s shape by filtering at too low of a frequency. Need to increase the LP cutoff to retrieve the harmonics

required by our square wave (A good number is 10*the highest frequency).


Figure 106: Filtered demodulated wave, v(t). Filtered using a 1st order Butterworth LP at 500 Hz. Notice we have

retrieved the square wave’s shape by filtering at 500Hz but the order of our Butterworth is still to low. We need a higher

order filter to provide a cleaner square wave output.

Figure 107: Filtered demodulated wave, v(t). Filtered using a 3rd order Butterworth LP at 500 Hz. Notice we have

retrieved the square wave’s shape and cleaned out the high frequency noise. This is the best of the three filter designs

used. The process of coherent detection is now complete.


Figure 108: M(f) frequency spectrum. Notice the square wave is made up of several components, thus a good low pass

filter must take these components into account. This is why the best design used a 3rd

order Butterworth at 500 Hz.

Figure 109: Modulated DSB-SC signal S(f) frequency spectrum.


Figure 110: Demodulated (unfiltered) wave, v(t).


st order LP Butterworth at 50Hz, too low to correctly reproduce

square wave.



st order LP Butterworth at 500Hz, the square wave shape is now

there but high frequency harmonics are still creating a problem.

Figure 113: Demodulated (filtered) wave, V(f). Used a 3rd order LP Butterworth at 500Hz, the square wave shape is now

there and the high frequency harmonic noise has been eliminated. This is the best of the three filter designs used. The

process of coherent detection is now complete.


%---------------------------

% MATLAB CODE

%---------------------------

function Lab2 = Comm1Lab2() %Function name for calling in MATLAB % Colorado Technical University % EE 443 - Communications I % Lab 2 - MATLAB Project - Coherent Detection % By Loren K. Schwappach % Uses centeredFFT() for obtaining a two-sided spectrum

%---------------------------

% Generating Carrier, Message and Modulated wave fc = 1500; ac = 10; cPhi = 0; fm1 = 36; %frequency of the first sinusodial wave am1 = 5; %amplitude of the first sinusodial wave fm2 = 180; %frequency of the second sinusodial wave am2 = 2; %amplitude of the second sinusodial wave fs = 10*fc; %sampling frequency ts = 1/fs; %sampling interval t = 0:ts:1-ts; %time vector m = (am1*cos(2*pi*fm1*t) + am2*cos(2*pi*fm2*t)); %composite message wave c = ac*cos(2*pi*fc*t + cPhi); %carrier wave st = m.*c;

% Plot of Message in Time Domain timePlot = figure; %gives graph window a name and keeps it available plot (t(1:500),m(1:500)); %plots sinusodial wave in time domain title('Message - Time domain'); xlabel('Time (s)'); %adds xlabel to graph ylabel('Amplitude'); %adds ylabel to graph grid; %turns on grid axis([0,27.5e-3,-8,8]); %defines axis [x(min),x(max),y(min),y(max)]

% Plot of Carrier in Time Domain timePlot = figure; %gives graph window a name and keeps it available plot (t(1:200),c(1:200)); %plots sinusodial wave in time domain title('Carrier - Time domain'); xlabel('Time (s)'); %adds xlabel to graph ylabel('Amplitude'); %adds ylabel to graph grid; %turns on grid axis([2e-3,6e-3,-10,10]); %defines axis [x(min),x(max),y(min),y(max)]

% Plot of Modulated Wave in Time Domain timePlot = figure; %gives graph window a name and keeps it available plot (t(1:500),st(1:500)); %plots sinusodial wave in time domain title('DBS-SC Modulated Signal - Time domain'); xlabel('Time (s)'); %adds xlabel to graph ylabel('Amplitude'); %adds ylabel to graph grid; %turns on grid axis([6.5e-3,21e-3,-80,80]); %defines axis [x(min),x(max),y(min),y(max)]

% Plot of Modulated Wave in Frequency Domain [Sf,SfRange] = centeredFFT(st,fs); %Uses centeredFFT function freqPlot = figure; %gives graph window a name and keeps it available stem(SfRange,Sf); %Creates stem graph for magnitude spectrum


title('DBS-SC Modulated - 2 Sided Spectrum') xlabel('Freq (Hz)'); %adds xlabel to graph ylabel('Amplitude'); %adds ylabel to graph grid; %turns on grid axis([-2000,2000,-1,13]); %defines axis [x(min),x(max),y(min),y(max)]

% Plot of Modulated Wave in Frequency Domain - Close Up freqPlot = figure; %gives graph window a name and keeps it available stem(SfRange,Sf); %Creates stem graph for magnitude spectrum title('DBS-SC Modulated - Pos Spectrum Closeup') xlabel('Freq (Hz)'); %adds xlabel to graph ylabel('Amplitude'); %adds ylabel to graph grid; %turns on grid axis([1200,1800,-1,13]); %defines axis [x(min),x(max),y(min),y(max)]

% ---------------------------------------------

% In Phase & Freq Demod Segment % Plot of Demodulated Wave in Time Domain cPhib = cPhi; %In phase with carrier fcb = fc; %In frequency with carrier r = cos(2*pi*fcb*t+cPhib).*st; %Multiplies LO with s(t) timePlot = figure; %gives graph window a name and keeps it available plot (t(1:500),r(1:500)); %plots sinusodial wave in time domain title('DBS-SC Demodulated Signal - Time domain'); xlabel('Time (s)'); %adds xlabel to graph ylabel('Amplitude'); %adds ylabel to graph grid; %turns on grid axis([0,27.5e-3,-80,80]); %defines axis [x(min),x(max),y(min),y(max)]

% Plot of Demodulated Wave in Frequency Domain [Rf,RfRange] = centeredFFT(r,fs); %Uses centeredFFT function freqPlot = figure; %gives graph window a name and keeps it available stem(RfRange,Rf); %Creates stem graph for magnitude spectrum title('DBS-SC DeModulated - 2 Sided Spectrum') xlabel('Freq (Hz)'); %adds xlabel to graph ylabel('Amplitude'); %adds ylabel to graph grid; %turns on grid axis([-500,500,-1,13]); %defines axis [x(min),x(max),y(min),y(max)]

% Plot of Demodulated Wave in Frequency Domain - Close Up freqPlot = figure; %gives graph window a name and keeps it available stem(RfRange,Rf); %Creates stem graph for magnitude spectrum title('DBS-SC DeModulated - Pos Spectrum Closeup') xlabel('Freq (Hz)'); %adds xlabel to graph ylabel('Amplitude'); %adds ylabel to graph grid; %turns on grid axis([0,200,-1,13]); %defines axis [x(min),x(max),y(min),y(max)]

% ---------------------------------------------

% Out of Freq Demod Segment % Plot of Out of Freq Demodulated Wave in Time Domain FreqOffset = .9999; % .01% error cPhib = cPhi; %In phase with carrier fcb = fc*FreqOffset; %Out of frequency with carrier r = cos(2*pi*fcb*t+cPhib).*st; timePlot = figure; %gives graph window a name and keeps it available plot (t(1:500),r(1:500)); %plots sinusodial wave in time domain


title('DBS-SC (Out of Freq) Demodulated Signal - Time domain'); xlabel('Time (s)'); %adds xlabel to graph ylabel('Amplitude'); %adds ylabel to graph grid; %turns on grid axis([0,27.5e-3,-80,80]); %defines axis [x(min),x(max),y(min),y(max)]

% Plot of Out of Freq Demodulated Wave in Frequency Domain [Rf,RfRange] = centeredFFT(r,fs); %Uses centeredFFT function freqPlot = figure; %gives graph window a name and keeps it available stem(RfRange,Rf); %Creates stem graph for magnitude spectrum title('DBS-SC (Out of Freq) DeModulated - 2 Sided Spectrum') xlabel('Freq (Hz)'); %adds xlabel to graph ylabel('Amplitude'); %adds ylabel to graph grid; %turns on grid axis([-500,500,-1,13]); %defines axis [x(min),x(max),y(min),y(max)]

% Plot of Out of Freq Demodulated Wave in Frequency Domain - Close Up freqPlot = figure; %gives graph window a name and keeps it available stem(RfRange,Rf); %Creates stem graph for magnitude spectrum title('DBS-SC (Out of Freq) DeModulated - Pos Spectrum Closeup') xlabel('Freq (Hz)'); %adds xlabel to graph ylabel('Amplitude'); %adds ylabel to graph grid; %turns on grid axis([0,200,-1,13]); %defines axis [x(min),x(max),y(min),y(max)]

%---------------------------

% Out of Freq Demod Segment % Plot of Out of Freq Demodulated Wave in Time Domain FreqOffset = .98; cPhib = cPhi; %In phase with carrier fcb = fc*FreqOffset; %Out of frequency with carrier r = cos(2*pi*fcb*t+cPhib).*st; timePlot = figure; %gives graph window a name and keeps it available plot (t(1:500),r(1:500)); %plots sinusodial wave in time domain title('DBS-SC (Out of Freq) Demodulated Signal - Time domain'); xlabel('Time (s)'); %adds xlabel to graph ylabel('Amplitude'); %adds ylabel to graph grid; %turns on grid axis([0,27.5e-3,-80,80]); %defines axis [x(min),x(max),y(min),y(max)]

% Plot of Out of Freq Demodulated Wave in Frequency Domain [Rf,RfRange] = centeredFFT(r,fs); %Uses centeredFFT function freqPlot = figure; %gives graph window a name and keeps it available stem(RfRange,Rf); %Creates stem graph for magnitude spectrum title('DBS-SC (Out of Freq) DeModulated - 2 Sided Spectrum') xlabel('Freq (Hz)'); %adds xlabel to graph ylabel('Amplitude'); %adds ylabel to graph grid; %turns on grid axis([-500,500,-1,13]); %defines axis [x(min),x(max),y(min),y(max)]

% Plot of Out of Freq Demodulated Wave in Frequency Domain - Close Up freqPlot = figure; %gives graph window a name and keeps it available stem(RfRange,Rf); %Creates stem graph for magnitude spectrum title('DBS-SC (Out of Freq) DeModulated - Pos Spectrum Closeup') xlabel('Freq (Hz)'); %adds xlabel to graph ylabel('Amplitude'); %adds ylabel to graph grid; %turns on grid axis([0,200,-1,13]); %defines axis [x(min),x(max),y(min),y(max)]


% ---------------------------------------------

% Out of Phase Demod Segment % Plot of Out of Phase Demodulated Wave in Time Domain PhiOffset = (45)*(pi/180); %1 degree off phase cPhib = cPhi+PhiOffset; %In phase with carrier fcb = fc; %Out of frequency with carrier r = cos(2*pi*fcb*t+cPhib).*st; timePlot = figure; %gives graph window a name and keeps it available plot (t(1:500),r(1:500)); %plots sinusodial wave in time domain title('DBS-SC (Out of Phase) Demodulated Signal - Time domain'); xlabel('Time (s)'); %adds xlabel to graph ylabel('Amplitude'); %adds ylabel to graph grid; %turns on grid axis([0,27.5e-3,-80,80]); %defines axis [x(min),x(max),y(min),y(max)]

% Plot of Out of Phase Demodulated Wave in Frequency Domain [Rf,RfRange] = centeredFFT(r,fs); %Uses centeredFFT function freqPlot = figure; %gives graph window a name and keeps it available stem(RfRange,Rf); %Creates stem graph for magnitude spectrum title('DBS-SC (Out of Phase) DeModulated - 2 Sided Spectrum') xlabel('Freq (Hz)'); %adds xlabel to graph ylabel('Amplitude'); %adds ylabel to graph grid; %turns on grid axis([-500,500,-13,13]); %defines axis [x(min),x(max),y(min),y(max)]

% Plot of Out of Phase Demodulated Wave in Frequency Domain - Close Up freqPlot = figure; %gives graph window a name and keeps it available stem(RfRange,Rf); %Creates stem graph for magnitude spectrum title('DBS-SC (Out of Phase) DeModulated - Pos Spectrum Closeup') xlabel('Freq (Hz)'); %adds xlabel to graph ylabel('Amplitude'); %adds ylabel to graph grid; %turns on grid axis([0,200,-13,13]); %defines axis [x(min),x(max),y(min),y(max)]

% ---------------------------------------------

% Out of Phase Demod Segment % Plot of Out of Phase Demodulated Wave in Time Domain PhiOffset = (90)*(pi/180); %2 degrees off phase cPhib = cPhi+PhiOffset; %In phase with carrier fcb = fc; %Out of frequency with carrier r = cos(2*pi*fcb*t+cPhib).*st; timePlot = figure; %gives graph window a name and keeps it available plot (t(1:500),r(1:500)); %plots sinusodial wave in time domain title('DBS-SC (Out of Phase) Demodulated Signal - Time domain'); xlabel('Time (s)'); %adds xlabel to graph ylabel('Amplitude'); %adds ylabel to graph grid; %turns on grid axis([0,27.5e-3,-80,80]); %defines axis [x(min),x(max),y(min),y(max)]

% Plot of Out of Phase Demodulated Wave in Frequency Domain [Rf,RfRange] = centeredFFT(r,fs); %Uses centeredFFT function freqPlot = figure; %gives graph window a name and keeps it available stem(RfRange,Rf); %Creates stem graph for magnitude spectrum title('DBS-SC (Out of Phase) DeModulated - 2 Sided Spectrum') xlabel('Freq (Hz)'); %adds xlabel to graph ylabel('Amplitude'); %adds ylabel to graph


grid; %turns on grid axis([-500,500,-13,13]); %defines axis [x(min),x(max),y(min),y(max)]


% ---------------------------------------------

% Out of Phase Demod Segment % Plot of Out of Phase Demodulated Wave in Time Domain PhiOffset = (180)*(pi/180); %3 degrees off phase cPhib = cPhi+PhiOffset; %In phase with carrier fcb = fc; %Out of frequency with carrier r = cos(2*pi*fcb*t+cPhib).*st; timePlot = figure; %gives graph window a name and keeps it available plot (t(1:500),r(1:500)); %plots sinusodial wave in time domain title('DBS-SC (Out of Phase) Demodulated Signal - Time domain'); xlabel('Time (s)'); %adds xlabel to graph ylabel('Amplitude'); %adds ylabel to graph grid; %turns on grid axis([0,27.5e-3,-80,80]); %defines axis [x(min),x(max),y(min),y(max)]

% Plot of Out of Phase Demodulated Wave in Frequency Domain [Rf,RfRange] = centeredFFT(r,fs); %Uses centeredFFT function freqPlot = figure; %gives graph window a name and keeps it available stem(RfRange,Rf); %Creates stem graph for magnitude spectrum title('DBS-SC (Out of Phase) DeModulated - 2 Sided Spectrum') xlabel('Freq (Hz)'); %adds xlabel to graph ylabel('Amplitude'); %adds ylabel to graph grid; %turns on grid axis([-500,500,-13,13]); %defines axis [x(min),x(max),y(min),y(max)]


% ---------------------------------------------

% Filterted In Phase & Freq Demod Segment % Plot of Filtered Demodulated Wave in Time Domain cPhib = cPhi; %In phase with carrier fcb = fc; %In frequency with carrier r = cos(2*pi*fcb*t+cPhib).*st; %Multiplies LO with s(t) [b_num,b_den] = butter(3,2*pi*500,'s'); %3rd order butter xfer fn Filtered_r = lsim(b_num,b_den,r,t); %applies filter to signal timePlot = figure; %gives graph window a name and keeps it available plot (t(1:500),Filtered_r(1:500)); %plots sinusodial wave in time domain title('DBS-SC Filtered Demodulated Signal - Time domain');


xlabel('Time (s)'); %adds xlabel to graph ylabel('Amplitude'); %adds ylabel to graph grid; %turns on grid axis([0+(1.1e-3),27.5e-3+(1.1e-3),-37,35]); %defines axis

[x(min),x(max),y(min),y(max)]

% Plot of Filtered Demodulated Wave in Frequency Domain [Rf,RfRange] = centeredFFT(Filtered_r,fs); %Uses centeredFFT function freqPlot = figure; %gives graph window a name and keeps it available stem(RfRange,Rf); %Creates stem graph for magnitude spectrum title('DBS-SC Filtered DeModulated - 2 Sided Spectrum') xlabel('Freq (Hz)'); %adds xlabel to graph ylabel('Amplitude'); %adds ylabel to graph grid; %turns on grid axis([-500,500,-13,13]); %defines axis [x(min),x(max),y(min),y(max)]

% Plot of Filtered Demodulated Wave in Frequency Domain - Close Up freqPlot = figure; %gives graph window a name and keeps it available stem(RfRange,Rf); %Creates stem graph for magnitude spectrum title('DBS-SC Filtered DeModulated - Pos Spectrum Closeup') xlabel('Freq (Hz)'); %adds xlabel to graph ylabel('Amplitude'); %adds ylabel to graph grid; %turns on grid axis([0,200,-13,13]); %defines axis [x(min),x(max),y(min),y(max)]

% end Comm1Lab2

% ***************************************************************************

% *************************************************************************** % Additional MATLAB m.file for better FFT % *************************************************************************** % *************************************************************************** function [X,freq]=centeredFFT(x,Fs) %this is a custom function that helps in plotting the two-sided spectrum %x is the signal that is to be transformed %Fs is the sampling rate

N=length(x);

%this part of the code generates that frequency axis if mod(N,2)==0 k=-N/2:N/2-1; % N even else k=-(N-1)/2:(N-1)/2; % N odd end T=N/Fs; freq=k/T; %the frequency axis

%takes the fft of the signal, and adjusts the amplitude accordingly X=fft(x)/N; % normalize the data X=fftshift(X); %shifts the fft data so that it is centered

% ***************************************************************************

Ee443 communications 1 - lab 2 - loren schwappach

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Transcript of Ee443 communications 1 - lab 2 - loren schwappach