Why there is a modulation in case of frequency offset?

Question

Alex 2013-3-17

0
链接

此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/67520-why-there-is-a-modulation-in-case-of-frequency-offset

There is modulation in a last graph of a signal (figure 1). At programm there is no such kind of modulation (there is only transfer of a signal on the carrier frequency). Why? Where a mistake?

Image: http://picturepush.com/public/12436413

MATLAB code:

% ++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
% +++++++++++++++++++++ Doppler Shift ++++++++++++++++++++++++++++++++++++
% ++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
%%Initialization
clear all; close all; clc; format longE;
% ~~~~~~~~~~~~~~~~~~~ Begin of the Programm ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
% Initial parameters of the Signal
f=100; %Frequency of the signal (sin), [Hz];
Fc=1e3; %Carrier frequency, [Hz];
Fd=30*f; %Sampling frequencym, [Hz];
A=1; %Amplitude
%%~~~~~~~~~~~~~~~~~~Initializing Doppler Shift~~~~~~~~~~~~~~~~~~~~~~~~~~
c=3e8; %Speed of light, [m/a];
%````````````````````````````````Speeds: ```````````````````````````````
        Fdoppler=10; %Maximal Doppler Shift, [Hz]
        Speed=(Fdoppler*c)/(Fc+f); %Necessary speed in [m/s] for receiving necessary shift.
        speeedfordisp=(Fdoppler*3.6*c)/(Fc+f); %Necessary speed in [m/s] for receiving necessary shift.
        fprintf('\n\n\n\nAt the set parameters for receiving shift on %d Hz\nspeed is necessary: \n \t -- [m/s]:\t %.3f;\n \t -- [km/h]:\t %3f.\n\n', Fdoppler, Speed, speeedfordisp);
%``````````````````````````````````````````````
%New wave frequency (after Doppler Effect):
    betta=Speed/c;
           alpha=0;
           f_dopl=((Speed*(Fc+f))/c)*cosd(alpha);
%%~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
%~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
%~~~~~~~ Passing a signal throught the channel with a Doppler Effect ~~~~~
%~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
%Parametrs of the signal
    t=(0:1/Fd:1);
    N = length(t);
    NFFT = 16000;
    FrequencyAxe=Fd*linspace(0,1,NFFT); %Frequency Axe;
%Initializing the signal
    Signal=A*sin(2*pi*f.*t);
%Modulating the signal:
    SignalModulated=Signal.*exp(1i*2*pi*(Fc).*t);
%Add Doppler Effect:
    Spectr = fft(SignalModulated); %Conver to the Frequency Domain
    SignalModulated_D=ifft(circshift(Spectr, [0 f_dopl])); %Add shift
%Demodulation the signal
    SignalDemodulated=SignalModulated_D.*exp(-1i*2*pi*(Fc).*t);
%`````````````````````````````````````````````````````````````````````````
%```````````````````````` END OF PROGRAMM'S PART `````````````````````````
%`````````````````````````````````````````````````````````````````````````
%~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
%~~~~~~~~~~~~~~~~~ Calculating a spectr of the signals ~~~~~~~~~~~~~~~~~~~
%~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
%Spectr of the initial signal:
    SpectrInitialSignal=(1/NFFT).*fft(Signal, NFFT); Plot_SpectrInitialSignal=abs(SpectrInitialSignal(1:NFFT));
%Spectr of the modulated signal:
    SpectrModulatedSignal=(1/NFFT).*fft(SignalModulated, NFFT); Plot_SpectrModulatedSignal=abs(SpectrModulatedSignal(1:NFFT));
%Spectr of the modulated signal with a Doppler Effect:
    SpectrModulatedSignal_D=(1/NFFT).*fft(SignalModulated_D, NFFT); Plot_SpectrModulatedSignal_D=abs(SpectrModulatedSignal_D(1:NFFT));
%Spectr of the demodulated signal (with a Doppler Effect):
    SpectrDemodulatedSignal=(1/NFFT).*fft(SignalDemodulated, NFFT); Plot_SpectrDemodulatedSignal=abs(SpectrDemodulatedSignal(1:NFFT));
%`````````````````````````````````````````````````````````````````````````
%```````````````````````` END OF PROGRAMM'S PART `````````````````````````
%`````````````````````````````````````````````````````````````````````````
%~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
%~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ Plot ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
%~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
%Intializing of label variables:
    TimeAxe='Time, [s]';
    FreqAxe='Frequency, [Hz]';
%   TESTING PART (All plots are separated from each other)
      figure(1)
      %~~ SIGNALS ~~
          %Plot the initial signal:
              subplot(4,2,1);
                  plot(t, Signal);
              xlabel(TimeAxe);
              title('Initial signal');
          %Plot the modulated signal
              subplot(4,2,3);
                  plot(t,SignalModulated);
              xlabel(TimeAxe);
              title('Modulated signal');
          %Plot the modulated signal with a Doppler Effect
              subplot(4,2,5);
                  plot(t,SignalModulated_D);
              xlabel(TimeAxe);
              title('Modulated signal with a Doppler Effect');
          %Plot the demodulated signal with a Doppler Effect
              subplot(4,2,7);
                  plot(t,SignalDemodulated);
              xlabel(TimeAxe);
              title('Demodulated signal');
      %`````````````
      %~~ SPECTRS ~~       
          %Plot the SPECTR of the initial signal
              subplot(4,2,2);
                  plot(FrequencyAxe,Plot_SpectrInitialSignal);
              xlabel(FreqAxe);
              title('Spectr of the initial signal');
          %Plot the SPECTR of the modulated signal:
              subplot(4,2,4);
                  plot(FrequencyAxe,Plot_SpectrModulatedSignal);
              xlabel(FreqAxe);
              title('Spectr of the modulated signal');
          %Plot SPECTR of the modulated signal with Doppler Effect
              subplot(4,2,6);
                  plot(FrequencyAxe,Plot_SpectrModulatedSignal_D);
              xlabel(FreqAxe);
              title('SPECTR of the modulated signal \bf with Doppler Effect');
          %Plot SPECTR of the demodulated signal:
              subplot(4,2,8);
                  plot(FrequencyAxe,Plot_SpectrDemodulatedSignal);
              xlabel(FreqAxe);
              title('Spectr of the demodulated signal');
      %`````````````
      %GRAPHICS
      %~~ Signals ~~
      figure(2);
      %Plot the initial signal and demodulated signal:
      subplot(2,1,1);
      hold on;
          %Plot the initial signal:
           plot(t,Signal,'m');
          %Plot the recieved signal:
           plot(t,SignalDemodulated, 'r');
      hold off;
      xlabel(TimeAxe);
      legend('Initial signal','Demodulated signal');
      title('Initial signal and demodulated signal');
      %Plot the modulated signal and the modulated signal with the Doppler Effect:
      subplot(2,1,2);
      hold on;
          %Plot the modulated signal:
           plot(t,SignalModulated, 'm');
          %Plot the modulated signal with a Doppler Effect:
           plot(t,SignalModulated_D, 'r');
      xlabel(TimeAxe);
      legend('Modulated signal','Modulated signal \bfwith Doppler Effect');
      title('Modulated signal with/without Doppler Effect');
  %~~ SPECTRS ~~
  figure(3);
      hold on;
          %Plot the SPECTR of initial signal
           plot(FrequencyAxe,Plot_SpectrInitialSignal, 'm');
          %Plot the SPECTR of the recieved signal
           plot(FrequencyAxe,Plot_SpectrDemodulatedSignal, 'r');
      hold off;
      xlabel(TimeAxe);
      legend('Spectr of the initial signal','Spectr of the demodulated signal');
      title('Spectrs of the initial signal and demodulated signal');

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Answer 1

Youssef Khmou 2013-3-17

0
链接

此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/67520-why-there-is-a-modulation-in-case-of-frequency-offset#answer_78952

编辑：Youssef Khmou 2013-3-17

在 MATLAB Online 中打开

hi Alex,

Your question is acceptable, you expect to visualize the Demodulated signal as the original, but the Doppler shift acts also as modulation, try this small example :

Fs=20;
f=5;
t=0:1/Fs:5;
y=sin(2*pi*t*f);
FF=fft(y);
FF2=circshift(FF,[0 10]);
y2=ifft(FF2);
subplot(1,2,1), plot(t,y), 
title(' Original Signal');
subplot(122), plot(t,y2);
title(' Recovered Signal after shifting the Spectrum +> with 10 steps');