MATLAB Answers

Matched filter

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vsee
vsee on 1 Apr 2011
Commented: MUKESH KUMAR on 3 Jun 2020
How can I write a mtached filter in Matlab? I have the filter design and signal processing tool boxes.

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Answers (5)

Honglei Chen
Honglei Chen on 1 Apr 2011
If you have a signal, x, then the matched filter's coefficients is given by time reverse of x, i.e., x(end:-1:1). If your signal is complex, you also need to to use complex conjugate. You can then use it just as an FIR filter. For example,
>> x = ones(10,1);
>> b = x(end:-1:1);
>> y = filter(b,1,x);

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Nuzat Alam
Nuzat Alam on 3 Apr 2013
Hii i was wondering what is the impulse response of matched filter here?I think it is related to b. Do you think if i want to select a specific sample number for b, i also need to change the length of input signal x?
Mustahsan Ali Khan Khanzada Rajput
How to apply matched filter if the signal is complex?
Honglei Chen
Honglei Chen on 12 Jan 2017
It's the same, use the filter function. The only difference is when you come up with the filtering coefficient, you need to add a conjugate, like
b = conj(x(end:-1:1))
HTH

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Andrew Newell
Andrew Newell on 1 Apr 2011
Check out MATLAB Simulations for Radar Systems Design from the File Exchange.

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Bhaskar
Bhaskar on 15 Apr 2011
To elaborate on Honglei's answer. If the signal you are trying to design a matched filter for, is x, then --
>> b = x(end-1:1);
>> y = filter(b,1,x);
You should already have x.

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mmm ssss
mmm ssss on 9 Jan 2012
how can implement the same filter on image ?
how i should represent x.

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Mathuranathan Viswanathan
Mathuranathan Viswanathan on 13 Apr 2013
Hi You can try the model given here
Regards Mathuranathan

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Nicole Bienert
Nicole Bienert on 7 Jan 2020
The built in xcorr function can be used - you just need to normalize by fs and square the output. See below for an ideallized example:
%Purpose: Demonstrate how to match filter correctly
BW=3.84e6;
fs = 50*BW; %sample rate
T= 1/fs; %sample period
fc = 330e6; %center freq
chirpLen=0.075; %chirp length
A=3; %amplitude of voltage signal (normally unknown)
Ar=2; %amplitude of reference voltage signal (normally unknown)
%create the signal withought noise and zero padded on either side (zero
%padding not necessary because xcorr does that, I'm just demonstrating that
%signals don't need to be the same length.)
sig=[zeros(1,ceil(chirpLen*fs)),A*chirp(t,0,t(end),BW),zeros(1,ceil(chirpLen*fs))];
%create the reference chirp
ref_chirp=Ar*chirp(t,0,t(end),BW);
t=[0:T:(length(ref_chirp)-1)*T];
%normalize reference chirp: The reference chirp needs to have energy of 1
%so that it doesn't bias the output of the match filter. A filter shouldn't
%be applying gain to the signal or changing the units. The signal is in
%volts, so we divide by the square root of the energy to normalize it.
%If you know the signal's amplitude (for CW or FMCW):
energy=Ar^2/2*chirpLen;
%If you don't know the signal's amplitude, integrate to find energy (if it is noiseless):
%energy=trapz(t,ref_chirp.^2)
ref_chirp=ref_chirp/sqrt(energy);
% perform match filtering
[R,lags] = xcorr(sig,ref_chirp); %signals don't need to be the same length
%R is the sum of each data sample as the signals are shifted past
%eachother, so to make the numerical integration correct, you need to
%multiply by dx which is T in this case. Then to get the filtered voltage
%signal in units of energy, you need to square it.
R=(abs(R*T)).^2; %absolute value only necessary if signals are complex
% take only positive side
R = R(lags>=0);
lags=lags(lags>=0);
[matchFiltPeak,index]=max(R);
figure()
plot(lags*T,R)
xlim([index-250 index+250]*T)
display(['Energy in signal was: ',num2str(A.^2/2*chirpLen)])
display(['which is the same as the peak of the match filter: ',num2str(matchFiltPeak)])

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Anastasia Kov
Anastasia Kov on 27 Apr 2020
I faced the same code error as Andreas talking about.
I guess, the issue is here:
ref_chirp=Ar*chirp(t,0,t(end),BW);
t=[0:T:(length(ref_chirp)-1)*T];
"ref_chirp" referes to "t" and vise versa.
There must be some additional definition for "ref_chirp" or "t", isn't it?
Anastasia Kov
Anastasia Kov on 27 Apr 2020
As well as I do not understand this line:
R=(abs(R*T)).^2; %absolute value only necessary if signals are complex
It will not work unfortunately, R is not defined.
Could somebody help please?
Would be very usefull to have this code working.
Thank you!

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