fm modulation without using fmmod

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tariq almalki 2017-1-4

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https://ww2.mathworks.cn/matlabcentral/answers/318969-fm-modulation-without-using-fmmod

评论： nima nabavi 2020-8-28

asho.png

how do I write this in matlab ! < I have been running FM modulation using fmmod , everything went great but i have been asked to do it using as shown in the picture ! can you help ?

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Answer 1

John BG 2017-1-5

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https://ww2.mathworks.cn/matlabcentral/answers/318969-fm-modulation-without-using-fmmod#answer_249427

编辑：Walter Roberson 2017-1-7

在 MATLAB Online 中打开

fm_mod1.zip

Tariq

If you open fmmod.m the key lines are

    t = (0:1/Fs:((size(x,1)-1)/Fs))';
    t = t(:,ones(1,size(x,2)));
int_x = cumsum(x)/Fs;
y = cos(2*pi*Fc*t + 2*pi*freqdev*int_x + ini_phase);

so xfm would be

int_x = cumsum(x)/Fs;
xfm = cos(2*pi*Fc*t).*cos(2*pi*freqdev*int_x)-sin(2*pi*Fc*t).*sin(2*pi*freqdev*int_x)   
xi=cos(2*pi*freqdev*int_x)
xq=sin(2*pi*freqdev*int_x)

the fmmod example available from MATLAB help are:

fs = 1000; 
fc = 200;  
t = (0:1/fs:0.2)';
x = sin(2*pi*30*t)+2*sin(2*pi*60*t);
fDev = 50;
y = fmmod(x,fc,fs,fDev);
z = fmdemod(y,fc,fs,fDev); % Demodulate both channels.
figure(1);plot(t,x,'c',t,z,'b--');xlabel('Time (s)');ylabel('Amplitude');
legend('Original Signal','Demodulated Signal');grid on

applying the key lines directly

int_x = cumsum(x)/fs;
xfm = cos(2*pi*fc*t).*cos(2*pi*fDev*int_x)-sin(2*pi*fc*t).*sin(2*pi*fDev*int_x)   ;
xi=cos(2*pi*fDev*int_x);
xq=sin(2*pi*fDev*int_x) ;

IMPORTANT COMMENT:

I Q decomposition only applies a single frequencies.
FM signals have variable BW, unless working with digital FM, for instance FSK, there is not a unique way to define I Q.,
One may consider breaking down the largest BW down into smaller bands, fixed sub-bands, but even then, the nature of the FM signal will render void many of such defined sub-bands.
I suggest you avoid defining I Q components for a generic FM signal unless clearly detailing how you obtain them: the way you have xi and xq are not really In phase and Quadrature components.

in demodulation the key lines of fmdemod.m are

t = (0:1/Fs:((size(y,1)-1)/Fs))';
t = t(:,ones(1,size(y,2)));
yq = hilbert(y).*exp(-j*2*pi*Fc*t-ini_phase);
z = (1/(2*pi*freqdev))*[zeros(1,size(yq,2)); diff(unwrap(angle(yq)))*Fs];

so

   t2 = (0:1/fs:((size(xfm,1)-1)/fs))';
    t2 = t2(:,ones(1,size(xfm,2)));
    xfmq = hilbert(xfm).*exp(-j*2*pi*fc*t2);
    z = (1/(2*pi*fDev))*[zeros(1,size(xfmq,2)); diff(unwrap(angle(xfmq)))*fs];
figure(2);plot(t,x,'c',t2,z,'b--');xlabel('time ');ylabel('amplitude');
legend('Original Signal','Demodulated Signal');grid on

the example lines put all together are:

fs = 1000;
fc = 200;
t = (0:1/fs:0.2)';
x = sin(2*pi*30*t)+2*sin(2*pi*60*t);
fDev = 50;
int_x = cumsum(x)/fs;
xfm = cos(2*pi*fc*t).*cos(2*pi*fDev*int_x)-sin(2*pi*fc*t).*sin(2*pi*fDev*int_x)   ;
xi=cos(2*pi*fDev*int_x);
xq=sin(2*pi*fDev*int_x) ;
t2 = (0:1/fs:((size(xfm,1)-1)/fs))';
t2 = t2(:,ones(1,size(xfm,2)));
xfmq = hilbert(xfm).*exp(-j*2*pi*fc*t2);
z = (1/(2*pi*fDev))*[zeros(1,size(xfmq,2)); diff(unwrap(angle(xfmq)))*fs];
figure(2);plot(t,x,'c',t2,z,'b--');xlabel('time ');ylabel('amplitude');
legend('Original Signal','Demodulated Signal');grid on

the resulting graph is as expected the same of the MATLAB example

.

you can also use SIMULINK

.

let me know if you would like this basic example, attached to my answer (fm_mod1.slx compressed into fm_mod1.zip this forum does not allow attaching Simulink files), to be developed a bit more, or you only want MATLAB code.

.

if you find these lines useful would you please mark my answer as Accepted Answer?

To any other reader, if you find this answer of any help please click on the thumbs-up vote link,

thanks in advance for time and attention

John BG

<mailto:jgb2012@sky.com jgb2012@sky.com>

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Walter Roberson 2017-1-9

University of Virginia http://www.virginia.edu/informationpolicy/copyright/faq.html

Is it illegal for me to share copyrighted stuff even if I don't charge for it?

Even if you're not making any money from doing it, it is still illegal for you to distribute material without permission from the copyright holder. Whether you are profiting or not, you are still taking money out of the pockets of musicians, actors, writers, etc. by giving away the fruits of their labors for free.

http://www.templetons.com/brad/copymyths.html

2) "If I don't charge for it, it's not a violation."

False. Whether you charge can affect the damages awarded in court, but that's main difference under the law. It's still a violation if you give it away -- and there can still be serious damages if you hurt the commercial value of the property. There is a USA exception for personal copying of music, which is not a violation, though courts seem to have said that doesn't include widescale anonymous personal copying as Napster. If the work has no commercial value, the violation is mostly technical and is unlikely to result in legal action. Fair use determinations (see below) do sometimes depend on the involvement of money.

Walter Roberson 2017-1-10

编辑：Walter Roberson 2017-1-10

John BG,

Is it your position that:

A) This matter is outside of all intellectual property law? Or

B) This matter is outside of intellectual property law related to the relevant jurisdiction? Or

C) That this topic is generally covered by some intellectual property law in the relevant jurisdiction, but the relevant law specifically indicates that the matter is outside the jurisdiction of the law? Or

D) That the topic falls within some intellectual property law within the relevant jurisdiction, but that the law specifically lists this matter as an exemption for which the law does not apply? Or

E) That the topic falls within some intellectual property law within the relevant jurisdiction, but the law declares that the penalty for this matter shall be 0? ("Zero-rating") ? Or

F) That the topic falls within some intellectual property law within the relevant jurisdiction, but the relevant law specifically declares this kind of usage to be "acceptable" anyhow? Or

G) That the topic falls within some intellectual property law within the relevant jurisdiction, but the relevant law specifically gives some guidelines on "acceptable" uses and your consultation with people who deal with copyright law is that this falls within those acceptable uses? Or

H) That the topic falls within some intellectual property law within the relevant jurisdiction, but the relevant law specifically gives some guidelines on "acceptable" uses and your personal interpretation, having read the law yourself, but without reference to backing sources, is that this falls within those acceptable uses? Or

I) That the topic falls within some intellectual property law within the relevant jurisdiction, but the relevant law specifically gives some guidelines on "acceptable" uses and your personal interpretation, not having read the law yourself, and without reference to backing sources, is that this falls within those acceptable uses? Or

J) That court cases within the relevant jurisdiction have nullified the wording of the relevant intellectual property law for this matter? Or

K) That intellectual property law does fully apply, but the Mathworks license agreement relinquishes the relevant legal rights? Or

L) That intellectual property law does fully apply, but the terms of use of this Answers facility relinquishes the relevant legal rights? Or

M) That intellectual property law does fully apply, but the Mathworks has granted you personally an exemption? Or

N) You heard it on the Interwebz, so it must be true?

As I have already cited three sources, I expect that you will cite sources to back your position.

Walter Roberson 2017-1-28

Jan, with regards to deleting incorrect answers:

Someone could hypothetically give a whole lot of bad or weak answers, so just looking at total number of answers alone would not be the way of finding out how much someone's answers should be trusted. A potential mitigation in a situation where the user can only see number of answered questions would be if the moderators deleted bad or weak answers, so that users only saw the count of answers that had been deemed somehow acceptable. But we do not do that kind of pruning; instead we comment on the weak answers or post better answers (if we have time and happen to notice.)

Adam: fraction of answers accepted is also tricky. Different volunteers tend to concentrate on different implicit communities, and the different implicit communities have different dynamics about what they tend to Accept.

The professional and research communities tend to recognize quality answers and take the time to Accept those, more likely to have seen similar situations and more likely to be aware of the benefits of feedback in improving the outcomes for everyone.

The undergraduate student community often does not bother to Accept answers, not being accustomed to such systems or the benefits of explicitly accepting solutions towards improving overall quality. Instead, undergraduate students tend towards accepting blocks of code that solve homework assignments, rather than towards answers that discuss concepts and point to documentation (thus encouraging the student to learn how to write the code, compared to having the code handed to them with no learning required on their part.)

The different volunteers have different expertices, and sometimes those are called upon differently by different communities. For example the people asking about GPU or more advanced parallel processing tend to be more towards the professional side, whereas the people asking about Neural Networks tend to be students. When combined with the different tendencies of different communities to formally Accept answers, this can lead to different volunteers having different acceptance ratios even though they might be equally skilled.

The mechanism that is in place to counter-weight some of these difficulties is that the community is permitted to vote for answers, thus allowing knowledgeable people to add weight to good answers.

How, then do we put all of these factors together to arrive at some kind of metric of the value of someone's contributions?

One could make proposals such as "fraction of Answers that are either Accepted or Voted for", but there are difficulties with that as well. For example we have had spammers vote for spam Answers, giving the spammer an apparent 100% ratio...

Atul Dwivedi 2019-3-12

How we can demodulate the fm signal if given carrier is: xc=cos(2*pi*200*t)+cos(2*pi*500*t)?

nima nabavi 2020-8-28

Thank you man. Really thanks.

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