# kindly help me in sampling this bandpass signal...

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#### 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

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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

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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

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#### mondunno bandpass sampling am signal

hi

seems like u're trying hard for this. study Digital and Analog communication by K. Sam Shanmugam. your doubt would be clear.

there is a very good topic on bandpass sampling. its enough for this problem...
before that you need to know what to expect from the results u've got... ur points are right. but just that when the first channel is brought to 0 frequence(it means the DC level in the signal is the amplitude of that frequency, and you wont find the monotone(sine) as such(its what you're expecting)).

mon

#### comsian

##### Newbie level 4 sampling of cos signal

hello mon, i m Nosheen
can u please help us drop down the very first carrier to zero freq with its upper side band in the positive freq range and the LSB at negative axis...

i simply want the freq shifted spectrum of my original bandpass signal...

can u please do this 4me,i'll be highly grategul...

#### mondunno bandpass signal

hello

u try it out. first important point is u must resample the Vam at different rates(which means there must be common sampling frequency to all signals, better its a multiple of other carrier frequencies), dont keep so many different sampling frequency, just keep 1 sampling freq as mentioned here.

next resampling must be done at carrier frequency rate, so that the carrier gets shifted to 0 freq.

remember to low pass filter this resampled samples. finally
try it out
mon

#### ednan bandpass signal cosine

Hello...

plz help me in up/down sampling...

i have a simple cos signal of any frequency...i want to do first down sampling by 2...and then do up sampling...in MATLAB...plz help me..if any one of u do work on it...
Thanx

#### dsPIC24F

##### Member level 3 sampling of bandpass signals

Have you tried MTLAB demos?
Though people said they are all junk.
To me, it worth a try.

#### ednan which demo i try for this...?

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