How can i fine the convolution of a linear system with given input

I have an adc with linear transfer function h(n)in time domain , and input to this is x(n), a sampled sine wave ,output of adc should be linear convolution of h(n) and x(n).when I convert output into frequency domain using fft, i am getting the amplitude 4 times higher then the input, whereas Gain of ADC is 1.Anyone can please help in this regard

[John D'Errico]

Show what you have done? How can anyone know what you did wrong otherwise?

[Dr Bhawana Garg]

Thanks for replying john.here is the code in which first i have simulated multifrequency signal then applied a window to it and took the FFT. Then simulated an ideal ADC and applied the signal to that adc and calculated the ouput.Finally calculated FFT of the output signal and compared with the FFT of input. Amplitudes at peaks should be almost same at both sides, which is not coming

% simulation of multifrequency signal fs=10000; % sampling frequency N=2048; % Number of samples k=1/fs; % Frequency Resolution f0=fs/N; f=(0:1:N-1)*f0; %Map the frequency to frequency bin amp_ip=[1.7,1.14]; freq_ip=[1000,1600]; phase_ip=[0,pi/8]; i=1; x1= amp_ip(i)*sin(2*pi*freq_ip(i)*(0:1:N-1)/fs +phase_ip(i)); i=2; x2= amp_ip(i)*sin(2*pi*freq_ip(i)*(0:1:N-1)/fs +phase_ip(i)); x=x1+x2;%+x3+x4; figure(1); plot(f,x); hold on;

%Convert into Frequency domain xf=(fft(x))/N; %compute the amplitude spectrum amp_xf=abs(xf); freq_bin=(0:1:N/2)*f0; amp_xf_ss(1)=amp_xf(1); amp_xf_ss(2:N/2+1)=2*amp_xf(2:N/2+1); % Get the single sided spectrum %subplot(2,1,2); plot(freq_bin,amp_xf_ss(1:N/2+1)); hold on;

figure(2); title('\fontname{Arial}FFT of Input signal','Fontsize',14,'Fontweight','Bold'); xlabel('\fontname{Arial} Frequency','Fontsize',12,'Fontweight','Bold'); ylabel('\fontname{Arial}Amplitude','Fontsize',12,'Fontweight','Bold');

% Generate different windows % Length of window is considered equal to number of samples

figure(3)

n=1:1:N;
x_rect=x(n).*rectwin(N)';  % Rectangular Window

plot(n,x_rect); title('\fontname{Arial}Rectangular Window','Fontsize',14,'Fontweight','Bold'); xlabel('\fontname{Arial} Frequency','Fontsize',12,'Fontweight','Bold'); ylabel('\fontname{Arial}Amplitude','Fontsize',12,'Fontweight','Bold'); hold on %FFT analysis of windowed signal amp_ip_rect_ss(1)=amp_ip_rect(1); amp_ip_rect_ss(2:N/2+1)=2*amp_ip_rect(2:N/2+1); % Get the single sided spectrum phase_ip_rect_ss=phase(amp_ip_rect1(1:N/2+1));

%estimation of peaks and their corresponding locations rough=amp_ip_rect_ss; [peak_rc,locs_rc,freq_rc]=PEAK(amp_ip_rect_ss,f); f0_ss=1/((N/2+1)*k);

%SImulation of Ideal ADC

nob=5; level=2^nob;

v_ref=5.12; lsb=v_ref/level; % lsb is least significant bit A=((level/2))*lsb;%max. value of amplitude L=(level/2)-1; Vmin(1,level)=0;

Vc(1,level)=0; Vmax(1,level)=0; CODE(1,level)=0; CODE_noise=0; qe_idl(1,level)=0;

figure(5); z=1; rough1=0; set(gcf, 'color', [1 1 1]) for j= -L-1:1:L+1%biplolar ADC (-128 to +127)

             k=j+L+1;           %(k=0 to 255)
             z=k+1;             %(z=1 to 256)
             Vmin(z)=(j-0.5)*lsb;    % min value at each code
             Vc(z)=(j)*lsb;           %mid value at each code
             Vmax(z)= (j+0.5)*lsb;   % max value at each code
             CODE(z)=k;             %equivalent digital output code

     for i=Vmin(z):.001:Vmax(z)
        %    subplot(2,1,1);
             stairs(i,k);
             hold on;
             %grid on;
                  for  p=k:.1:k+1
                         plot(Vmax(z),p);

                  end    
           end                 
end
amp_ip_rect_ss=rough;

%Output of ADC for the applied input signal rectangular window CODE_rect=0;

for i=1:1:N for j=1:1:level-1 if (x_rect(i)>=Vmin(j) && x_rect(i)<=Vmin(j+1)) CODE_rect(i)=j-1; end end

   end
CODE_OUT=conv(x_rect,Vc);% output of ADC

CODE_rect=CODE_rect.*lsb;

figure(6);
P=length(CODE_OUT);
xf_rect=abs(fft(CODE_OUT))/P;   %compute the amplitude spectrum

% Convert into single sided spectrum f11_rect=(0:1:P)*fs/P; xf1_rect(1)=xf_rect(1); %Single sided amplitude of output signal xf1_rect(2:P/2+1)=2*xf_rect(2:P/2+1); % Get the single sided spectrum %subplot(2,1,2); plot(f11_rect,xf_rect(1:P+1)); hold on;

rough=xf1_rect;

[pks_OAR,pks_OLR,pks_OFR]=PEAK(xf1_rect,f11_rect);

xf1_rect=rough;

Answer 1

[Kamal Hussain]

here i have written a code for linear convolution using tabular method.

%linear convolution using tabular method

x=[1 2 3 4];

y=[1 2 3 4];

shift=0;

lin_conv=[zeros(1,length(x)+length(y)-1)];

for i=1:length(y)

    shiftedd=shiftFTN(x,length(x),length(y),shift); 

    lin_conv=lin_conv + y(i).*shiftedd

    shift=shift+1;

end

%i have used a self made function shiftFTN to shift the sequence to the right by 1.

function [Y]=shiftFTN(A,len_A,len_B,shift)

Y=zeros(1,len_A+len_B -1);

Y(shift+1:end)=[A(1:end),zeros(1,length(Y)-(shift+len_A))];

[shah khan]

great effort