Having no success using point by point division to derive impulse estimate. What am I doing wrong?

Hello All,

I have been trying to derive the impulse response of a filter by the technique of taking the cross correlation of the input and the output signal of a filter and dividing that by the auto-correlation of the input signal via point-by-point division.

I can derive the impulse response by using the "deconv" function (duh!) but something is not quite working out with the point-by-point division method.

I have attached my code in hopes someone can take a look at this and help me figure out what I am doing wrong here.

I am very new to DSP and I would really appreciate it if someone gave me some tips on how to troubleshoot this.

Thank you.

close all
clear all

%%Read finalPrjInput.txt into x(t)

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figure(1); subplot(2,2,1); 
plot(x);
title('Original Input Signal');
grid;

%%designing the FIR filter

% Filter created using "fir1" function
Fpass1 = 8000;
Fpass2 = 12000;
Fs = 200000;
b = fir1(40,[2*Fpass1/(Fs/2) 2*Fpass2/(Fs/2)],'bandpass');

fvtool(b,1,200000)

%%Test impulse response of the filter
N=128;
impulse=[1,zeros(1,N)]; % Defining an impulse
figure(3); subplot(2,2,1);
plot(impulse);

h=filter(b,1,impulse); % Apply the generated impulse at the filter's input
title('impulse function');
grid;

figure(3); subplot(2,2,2);
plot(h/max(h)); % Plot the normalized impulse response
title('Actual impulse response');
grid;

%%Running signal x(t) through the filter

convOut = conv(b,x) % Filtering signal using "conv"

figure(1); subplot(2,2,3);
plot(convOut);title('Filtered Signal usinig "conv"');
grid;

%%Finding Impulse Response Estimate using Cross-correlation

% The output derived using the "conv" function is cross-correlated
% with the input x
Rxy = xcorr(convOut,x);
figure(4); subplot(3,2,1);
plot(Rxy);title('Rxy using "conv" output');
grid;

% Autocorrelation of the input
Rxx = xcorr(x,x);
figure(4); subplot(3,2,3);
plot(Rxx); title('Autocorrelation of the input x')
grid;

% Using "deconv" here instead of point-by-point division
figure(4); subplot(3,2,4);
[u,l]=deconv(Rxy,Rxx);
plot(u); title('"deconv" with Rxy and Rxx');
grid;

% Flipping the result from the previous step to arrive at
% the impulse response estimation -- successful!
figure(3); subplot(2,2,4);
impulseEst=flipud(u);
plot(impulseEst/max(impulseEst)); title('Impulse Response Estimate');
grid;

% Here is my attempt to find the impulse response estimate using
% point-by-point division
figure(5); subplot(1,1,1)
imp2=Rxy(1:2047) ./ Rxx
plot(imp2); title('Impulse Response Estimate Using Point-by-Point Division');
grid;

Answer 1

[bym]

you are successful using deconv; which is analogous to division in the frequency domain. I suggest you do the division in the frequency domain.