Oversample and Predistort by harrde - Revision history

Harrde: /* Explanation */

2007-12-07T23:07:49Z

Explanation

← Older revision		Revision as of 16:07, 7 December 2007
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	===Explanation===		===Explanation===
			The five graphs show a signal at important times as it passes through this system; which is similar to a signal being stored on a CD and then played back. The first graph shows the original signal and the data gathered from sampling. The next graph shows the sampled data plus the interpolation points found through 4 times oversampling. The third graph is a depiction of the transfer function of the D/A converter. This transfer function distorts the output signal as seen in the fourth graph. This is why we pass the signal through a digital filter to predistort it so that at the output of our system it will not be distorted. The filter's transfer function is simply the reciprocal of the D/A converter's transfer function.

Harrde at 22:46, 7 December 2007

2007-12-07T22:46:48Z

← Older revision		Revision as of 15:46, 7 December 2007
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	==Solution==		==Solution==
	MATLAB script and results:		MATLAB script and results:
			<pre>
			f = 10; % Sampling freq.
			T = 1/f; % Sampling period
			N = 10; % Number of sampling points
			t=0:T:(N-1)*T;
			x=sin(2pit)+cos(2pi2*t); % Signal that is sampled
			t_original = 0:.01:1;
			x_original = sin(2pit_original)+cos(2pi2*t_original);

			OSample = 4; % How many times to oversampling

			figure(1);
			clf
			plot(t_original,x_original,'r'); %Original signal sampled
			hold on
			stem(t,x)
			xlabel('Time(s)');
			ylabel('x(t)');
			title('Orignal Data and Sampled Points')
			hold
			legend('Original Data','Sampled Points')

			figure(2);
			N1 = N*OSample;
			X = fft(x);
			X1 = (N1+N)/N*[X(1:N/2),zeros(1,N1),X(N/2+1:N)]; %This is the interpolation transfer function
			x1 = ifft(X1);
			t1=0:N/(N+N1)T:(N-1/(N1+N))T;
			plot(t1,x1,'bo') %Sampled data with interpolation points
			title('Sampled Data After Interpolation');
			ylabel('x(t)');
			xlabel('Time(s)');

			%Now we will work on predistortion filter
			f = linspace(-1/T,1/T,length(X1));
			P = sin(pifT)./(pi*f); %Transfer function of A/D distortion
			figure(3)
			plot(f,P) % A/D distortion transfer function
			title('A/D Distortion Transfer Function');
			ylabel('P(f)');
			xlabel('f(Hz)');

			Out_unfiltered = X1.*P;
			out_unfiltered = ifft(Out_unfiltered);

			Out = X1.(1./P).P;
			out = ifft(Out);

			figure(4)
			clf
			plot(f./10,real(out_unfiltered)) %This is the output with out filter/predistortion
			title('Unfiltered Output');
			ylabel('x(t)');
			xlabel('time(s)');

			figure(5)
			clf
			plot(f./10,real(out)) %This is the output with the filter
			title('Filtered/Predistorted Output');
			ylabel('x(t)');
			xlabel('time(s)');
			</pre>

			[[Image:DH15_1.jpg]]
			[[Image:DH15_2.jpg]]
			[[Image:DH15_3.jpg]]
			[[Image:DH15_4.jpg]]
			[[Image:DH15_5.jpg]]

			===Explanation===

Harrde: New page: Back to my page ==Problem Statement== Make a MATLAB script to do four times oversampling and filter so as to eliminate as much as possible the effect of the D/A converter ...

2007-12-07T07:40:26Z

New page: Back to my page ==Problem Statement== Make a MATLAB script to do four times oversampling and filter so as to eliminate as much as possible the effect of the D/A converter ...

New page

[[User:Harrde|Back to my page]]

==Problem Statement==
Make a MATLAB script to do four times oversampling and filter so as to eliminate as much as possible the effect of the D/A converter that follows the interpolating filter.

==Solution==
MATLAB script and results: