Nosheen
Member level 1
sampling of bandpass signal
Simply I have taken a four channel Amplitude Modulated Signal for my test purpose.
The broadcast range of AM is from 535KHz-1700KHz..(for now i have just chosen four random carriers at which the signal is being modulated).
Infact i m going to sample this modulated signal at a rate such that the very first channel(or carrier) reduces to zero frequency and I could easily apply a Low Pass Filter to extract it.
If this thing gets solved once, then I can easily extract the other three channels as well by the concept of BANDPASS SAMPLING THEOREM...
I m attaching my code which will clarify the problem
-----------------------------------------------
fm=100; wm=100*2*pi;
Fc1=1000; wc1=1000*2*pi;
Fs1=4000; ws1=4000*2*pi;
Fc2=1600; wc2=1600*2*pi;
Fs2=6400; ws2=6400*2*pi;
Fc3=400; wc3=400*2*pi;
Fs3=1600; ws3=1600*2*pi;
Fc4=2600; wc4=2600*2*pi;
Fs4=10400; ws4=10400*2*pi;
t=[1:200]/Fs2;
vc=1;
m=1;
Vam1=vc*(sin(wc1*t)+0.5*m*cos((wc1-wm)*t)-0.5*m*cos((wc1+wm)*t));
Vam2=vc*(sin(wc2*t)+0.5*m*cos((wc2-wm)*t)-0.5*m*cos((wc2+wm)*t));
Vam3=vc*(sin(wc3*t)+0.5*m*cos((wc3-wm)*t)-0.5*m*cos((wc3+wm)*t));
Vam4=vc*(sin(wc4*t)+0.5*m*cos((wc4-wm)*t)-0.5*m*cos((wc4+wm)*t));
Vam=Vam1+Vam2+Vam3+Vam4;
figure
plot(Vam)
z=fft(Vam);
z=abs(z(1
length(z)/2)+1));
frq=[0:lenfigure
plot(frq,z)
grid
----------------------------------------------------
The last portion of the code is just to check whether i can sample my signal to reduce down the Carrier by Decimation or not...This approach might not b correct(i suppose)...
The basic clue is to play with the proper Sampling Rate(Sampling Frequency) so that the carriers reduce to lower frequency range(i.e the audible freq range) for the extraction of AM modulated channel...
Kindly help me out in Sampling the above Composite signal consisting of four carriers so that i can be abe to extract any channel required...
infact i need to digitize this modulated signal which is only done through sampling.
its all about bandpass sampling and we are preferably doing IMPULSE TRAIN SAMPLING..(Time domain sampling and its fourier spectrum in frequency domain)
The idea is that first of all a discrete impulse train of period 1/Ts(Ts=sampling period depending upon the sampling frequency of the required channel)is created which is then multiplied with the time domain envelope(modulated signal).this multiplication results in sampling of the required channel at the period Ts..this process is carried out in time domain.
Alternatively, if an impulse train is created such that each impulses are been spaced at the sampling frequency(Fs) are convolved with the freq domain spectrum of the required modulated channel, it will result in spectral replications of that particular channel at frequencies integer multiples of Fs i.e 0fS,1fS,2fS,3fS,....(Bandpass sampling theorem)
As is known to us that the matlab has a finite memory and it can only accomodate a time limited sequence, so one can generate the impulse train by limiting the impulses(discrete time) to some finite period of time.
now if we initially take only one carrier(channel) and sample it by the method i have already smentioned above, then in freq domain, the spectral replications of that signal can be observed, one whose signal also appears at zero freq(carrier)...now if this has been achieved then we can simply extract our required channel just by using a LOW PASS FILTER...
-->have u observed that by this technique our channel automatically drops down to low frequencies and we need not to downsample it, which might lose our original data waveform to some extent.
If this technique really worked right for one channel extraction, then definetly it will be correctly applicable for the extraction of other channels as well, but since the other channels lie on higher frequencies, we ultimately need to raise the Fs(as bandwidth increases)...
i m going to send u some of my attempts on it, but kindly help me out plz as I am not much strong in MATLAB...
if still there r any queries abt my problem, kindly speak it out,,i'll try to be more specific about my problem
thanxs in advance..
[/b]
Simply I have taken a four channel Amplitude Modulated Signal for my test purpose.
The broadcast range of AM is from 535KHz-1700KHz..(for now i have just chosen four random carriers at which the signal is being modulated).
Infact i m going to sample this modulated signal at a rate such that the very first channel(or carrier) reduces to zero frequency and I could easily apply a Low Pass Filter to extract it.
If this thing gets solved once, then I can easily extract the other three channels as well by the concept of BANDPASS SAMPLING THEOREM...
I m attaching my code which will clarify the problem
-----------------------------------------------
fm=100; wm=100*2*pi;
Fc1=1000; wc1=1000*2*pi;
Fs1=4000; ws1=4000*2*pi;
Fc2=1600; wc2=1600*2*pi;
Fs2=6400; ws2=6400*2*pi;
Fc3=400; wc3=400*2*pi;
Fs3=1600; ws3=1600*2*pi;
Fc4=2600; wc4=2600*2*pi;
Fs4=10400; ws4=10400*2*pi;
t=[1:200]/Fs2;
vc=1;
m=1;
Vam1=vc*(sin(wc1*t)+0.5*m*cos((wc1-wm)*t)-0.5*m*cos((wc1+wm)*t));
Vam2=vc*(sin(wc2*t)+0.5*m*cos((wc2-wm)*t)-0.5*m*cos((wc2+wm)*t));
Vam3=vc*(sin(wc3*t)+0.5*m*cos((wc3-wm)*t)-0.5*m*cos((wc3+wm)*t));
Vam4=vc*(sin(wc4*t)+0.5*m*cos((wc4-wm)*t)-0.5*m*cos((wc4+wm)*t));
Vam=Vam1+Vam2+Vam3+Vam4;
figure
plot(Vam)
z=fft(Vam);
z=abs(z(1
length(z)/2)+1)); frq=[0:lenfigure
plot(frq,z)
grid
----------------------------------------------------
The last portion of the code is just to check whether i can sample my signal to reduce down the Carrier by Decimation or not...This approach might not b correct(i suppose)...
The basic clue is to play with the proper Sampling Rate(Sampling Frequency) so that the carriers reduce to lower frequency range(i.e the audible freq range) for the extraction of AM modulated channel...
Kindly help me out in Sampling the above Composite signal consisting of four carriers so that i can be abe to extract any channel required...
infact i need to digitize this modulated signal which is only done through sampling.
its all about bandpass sampling and we are preferably doing IMPULSE TRAIN SAMPLING..(Time domain sampling and its fourier spectrum in frequency domain)
The idea is that first of all a discrete impulse train of period 1/Ts(Ts=sampling period depending upon the sampling frequency of the required channel)is created which is then multiplied with the time domain envelope(modulated signal).this multiplication results in sampling of the required channel at the period Ts..this process is carried out in time domain.
Alternatively, if an impulse train is created such that each impulses are been spaced at the sampling frequency(Fs) are convolved with the freq domain spectrum of the required modulated channel, it will result in spectral replications of that particular channel at frequencies integer multiples of Fs i.e 0fS,1fS,2fS,3fS,....(Bandpass sampling theorem)
As is known to us that the matlab has a finite memory and it can only accomodate a time limited sequence, so one can generate the impulse train by limiting the impulses(discrete time) to some finite period of time.
now if we initially take only one carrier(channel) and sample it by the method i have already smentioned above, then in freq domain, the spectral replications of that signal can be observed, one whose signal also appears at zero freq(carrier)...now if this has been achieved then we can simply extract our required channel just by using a LOW PASS FILTER...
-->have u observed that by this technique our channel automatically drops down to low frequencies and we need not to downsample it, which might lose our original data waveform to some extent.
If this technique really worked right for one channel extraction, then definetly it will be correctly applicable for the extraction of other channels as well, but since the other channels lie on higher frequencies, we ultimately need to raise the Fs(as bandwidth increases)...
i m going to send u some of my attempts on it, but kindly help me out plz as I am not much strong in MATLAB...
if still there r any queries abt my problem, kindly speak it out,,i'll try to be more specific about my problem
thanxs in advance..
[/b]