Questions tagged [matched-filter]

Matched filter is obtained by correlating a known signal, or template, with an unknown signal to detect the presence of the template in the unknown signal.

Filter by
Sorted by
Tagged with
30
votes
6answers
49k views

Understanding the Matched Filter

I have a question about matched filtering. Does the matched filter maximise the SNR at the moment of decision only? As far as I understand, if you put, say, NRZ through a matched filter, the SNR ...
12
votes
1answer
3k views

Optimum matched filter without ISI

Given a filter used to shape the digital signal, $p(x)$, and given that we do not want the filter combination to cause any ISI, what "matched" filter, $q(x)$ will maximise the SNR? Matched filters ...
7
votes
1answer
1k views

Location of Matched Filter

In a digital communication receiver, matched filter(SRRC filter) is used. In different literatures, the location of the matched filter is mentioned in two different places. One is just after the ADC ...
7
votes
1answer
209 views

How to Tell How Likely a Signal Is Present in Another One (Variance Unknown)?

I know this is probably a simple question, but I haven't been able to find a satisfactory answer anywhere... Say you have a time series signal of finite length N. Call it $y[n]$. It looks like a ...
7
votes
1answer
2k views

Match Filter in Time-Frequency domain instead of just Time domain. Redundant, or better?

Assume you have a signal, and within it, some pulses are present. A pulse is a simple tone. You know the pulses' duration and shape. (Let us assume that a pulse is made of a couple of cycles, and then ...
4
votes
3answers
377 views

Calculating penalty to SNR for non-matched filter

If a matched filter is optimal for detecting a known pulse in an AWGN channel, any other filter must have a degraded SNR. Given a discrete pulse shape and an arbitrary non-matched filter, is it ...
4
votes
1answer
2k views

How do you calculate the gain of a matched filter?

I know that you can calculate the gain of a low-pass filter by summing the filter coefficients. I don't know how to calculate the gain of an arbitrary matched filter. For instance, I have created a ...
4
votes
3answers
2k views

Does oversampling improve processing gain?

I am used to Time-Bandwidth product describing the processing gain or improvement in SNR for a spread spectrum signal using a matched filter. One could view the bandwidth $B$ as the sample rate (...
4
votes
2answers
3k views

Finding a signal inside a time series using MATLAB's $\tt xcorr()$

I would like to find the exact replica of signal A in time series B. I am working with the simple toy example below, in which A is located starting at the 4th position in B. I thought that using <...
4
votes
1answer
1k views

Whitened Matched Filter

I am seeking for an advice on whitened matched filtering technique. I have looked into the literature and I do understand its the purpose and how to select the filter in order to achieve the desired ...
4
votes
2answers
972 views

Create Matched Filter Reference Signal when Scaling Unknown

I am working on a problem which raised what should be a simple question, but I'm stuck on it. The objective is to detect a shifted and scaled version of a known signal in the presence of Additive ...
4
votes
2answers
677 views

How to calculate the phase shift AND time delay of non-periodic signals

Say I have two non-periodic signals, $f_1(t)$ and $f_2(t)$, with Fourier transforms $F_1(\omega)$ and $F_2(\omega)$. Basically, I need to line up $f_1(t)$ and $f_2(t)$ as close as possible, and I am ...
4
votes
0answers
146 views

Discrete-time model of 2-user CDMA system, recovered information at receiver using polarity detection?

I have discrete-time model of 2-user CDMA system with: $b_1=-1, b_2=+1, \alpha_1, \alpha_2, s_1, s_2$ and $n$ white noise. What are the recovered infromation bits for user 1 and user 2 respectively ...
3
votes
3answers
757 views

Matched filter loss due to frequency offset

I'm working with a pulsed radar signal which uses linear chirp pulses. I perform pulse compression by applying a matched filter of the simulated chirp waveform and recording the location and power of ...
3
votes
1answer
199 views

Why do we really split pulse shaping between the transmitter and the receiver?

EDIT: There was a small error in my code when plotting the Squared RC. Below is the correct frequency response, and clearly RC² doesn't fulfill Nyquist's criterion. ---------------------------------- ...
3
votes
3answers
3k views

Pulse Compression(Chirp) SNR Gain

I've created both single tone signal and a LFM chirp signal with same pulse duration and cross correlated both of them with their own(matched filter). Peak points of both results were same as expected ...
3
votes
2answers
78 views

Besides computational costs, is filtering, decimating, then filtering different from just filtering?

Background: I have a variety of BPSK which uses a raised cosine transmitted pulse shape: $$ h(t) = {1 \over 2}\, (1+\cos(\pi t))\, \Pi(t/2) $$ After matched filtering in the receiver, the end result ...
3
votes
1answer
1k views

Radar SNR for a LFM Waveform

How do you estimate the detection SNR for a radar transmitting an LFM (chirp) waveform? I'm looking for an SNR equation that is a function of chirp bandwidth and compressed (or uncompressed) ...
3
votes
1answer
1k views

Image Matching on iOS

Was recommended to migrate this question from SO. I am building an iOS app that, as a key feature, incorporates image matching. The problem is the images I need to recognize are small orienteering ...
2
votes
4answers
622 views

Estimate Delay of a Known Signal Delayed by Sub Sample Resolution

Given a known signal $ x \left( t \right) $ and its delayed version $ y \left(t, \tau \right) = x \left( t - \tau \right) $. Both are sampled by Sampling Frequency $ {F}_{s} $ to generate the signals $...
2
votes
1answer
334 views

Matched filter and cross correlation in digital processing

I am very new to signal processing, and a bit confused with the matched filter. Assume that I have a time series and a specific waveform I need to identify in it. By definition: a matched filter ...
2
votes
1answer
19 views

Plane Settings of the Matched $z$-transform Method

I've come across that the matched $z$-transform maps poles of the $s$-plane design to locations in the $z$-plane. My question is, what is the $s$-plane and what does this mean? I'm aware that the ...
2
votes
1answer
74 views

Is it possible to open up this particular convolution equation?

I have three vectors, $x[n]$, $w[n]$, and $z[n]$. I need to compute: $y[n] = z[n] * \Big(x[n] \cdot w[n] \Big)$. This is easy to do. However, is there a way I can do this by 'opening' up the ...
2
votes
1answer
1k views

normalized sum of squared differences

I want to search for a patch in a region of image, and I will use the normalized sum of squared differences. I know that the sum of the squared differences is: $SSD = \sum {\left(F - I\right)^2}$ ...
2
votes
0answers
310 views

How to eliminate matched filter background?

The question My goal is to detect an unknown frequency $f_1$ with a mixer and a matched filter. My simulation shows (below) that I correctly identify the 50 kHz external signal - but it also ...
2
votes
1answer
224 views

Obtaining phase and magnitude of 2 spectral components after ADC

I am currently implementing a digital filter to obtain the output of a PID controller. The control loop is carried out by applying a 1kHz sine wave at the input of the system and reading the output ...
2
votes
0answers
114 views

Signal rescaling

Please help me out with this one. I think I've been given an impossible task. I'm working on a system that transmits an active signal and looks for strong reflections. The transmitter is actually ...
1
vote
2answers
794 views

Finding Reference Audio Signal in Test Audio Signal and Cropping Accordingly

As seen in the diagram, below I have a reference audio and a test audio. I want to find at what part of the test clip the reference audio be heard. Once, that is found I want to crop the test file ...
1
vote
2answers
2k views

How to interpret output of matched filter with complex input?

I have implemented a matched filter based on the Fourier Transform approach. In the real numbers domain that means that I use as the coefficients of my filter (B) the inverted time-samples of the ...
1
vote
2answers
222 views

Carrier Frequency Offset, Rotating Constellation and Correlator

I have been further reading up on carrier recovery methods and something is not clear to me: It's written that a carrier frequency offset results in a rotating constellation diagram but if you are ...
1
vote
1answer
262 views

Cross-correlation - Why is there a complex part after FFT/IFFT when deleting the mirrored part of the spectrum?

I want to detect a special shape in my time series and I apply an matched filter using cross-correlation to increase the SNR. ...
1
vote
2answers
813 views

Fourier transform of a Fourier transform

I generate a Gaussian noise and then I filter it with a passband FIR Kaiser window filter. When I perform the Fourier transform of the output of the filter and plot its magnitude spectrum, it is ...
1
vote
1answer
56 views

Cascading conventional filter with matched filter

The most upvoted answer to this question suggests to use a "conventional" filter in cascade with a matched filter to first remove out of band noise (with conventional filter) and then optimize signal ...
1
vote
1answer
77 views

Perform overlap add with available FFT size smaller than filter coefficients

I would like to process 12 to 20 seconds of incoming audio at a sample rate of 44100. I must process this audio in real time in an STM embedded kit (perhaps also an Android Smartphone). I'm trying to ...
1
vote
1answer
21 views

Is there a hypothetical situation where once can use Wiener filter prior Matched filter to get better result?

Is there a hypothetical situation where once can use Wiener filter prior Matched filter to get better result? Mostly I am looking for an example or a situation where both the filters are required as ...
1
vote
1answer
212 views

Understanding the over sampling factor effects before a Matched Filter?

I am trying to design a matched filter at the receiver side to a half sine pulse shaping function sent by the transmitter of an OQPSK transceiver. I am not sure I understand the effect of varying the ...
1
vote
2answers
1k views

What are the differences between estimation and detection optimal filters (matched and Wiener)?

What is the differences between the two of them? I know that the matched filter is a detection filter because it detect what is the peak of the signal and return the time delay of reflected and ...
1
vote
1answer
659 views

Optimal time for sampling symbol in digital receivers

I'm studying various publications about symbol timing recovery algorithms, Early-late, Mueller and Muller & Gardner. All documents I've read tells that, to minimize ISI : The optimal time for ...
1
vote
2answers
776 views

How MATLAB calculates matched filter gain

Here is a bunch of code from MATLAB documentation: Designing a Basic Monostatic Pulse Radar: ...
1
vote
2answers
88 views

About understanding a Matched Filter

I have some basic doubt in understanding a matched filter (MF). Please note that I have already seen very informative post in this context Understanding the Matched Filter In what follows, I list ...
1
vote
0answers
159 views

Frequency Domain Variant of Pearson's Sample Correlation Coefficient?

Suppose that you need to find (i.e. acquire) $x_1$, a short data packet with a known bit sequence preamble (i.e. a PRBS BPSK), in $x_2$, quantized samples recorded from the output of an ADC. You don'...
1
vote
0answers
356 views

Noise covariance matrix

I am attempting to implement a generalized least squares estimator that uses a noise covariance matrix from measured data. The basic model is as follows $$\hat{c}_{GLS} = \left(\bf{A}^T\bf{\Sigma}^{-...
1
vote
0answers
335 views

Audio - TDOA and $\tt xcorr$, find the 'best' peak

I try to locate a mobile device using multilateration. The mobile device acts as the receiver and in the room I have three speakers. To calculate the position I need the time difference of arrival (...
1
vote
0answers
352 views

Moving signal power normalization

I am using matched filters using GNU Radio to extract from noise a CW Morse signal. The filter actually performs pretty well in various SNR environments. My problem is that the threshold upon I decide ...
1
vote
0answers
101 views

Should I normalize my input vector when using a matched filter?

I am using a matched filter to recognize an audio sample within a noisy input stream by cross correlating my sample with the input array and checking if the maximum crosses over my threshold. ...
0
votes
3answers
652 views

Derivation of the Optimal Matched Filter - Convolution vs. Correlation

On the Wikipedia page for Matched Filters here, there is a matrix algebra derivation for an optimal matched filter. Now, considering the output of an LTI system is found using the convolution operator,...
0
votes
3answers
180 views

“Complex Matched Filter”

What does a complex matched filter mean? . A complex bandpass filter can be formed by multiplying a low pass filter by exp(jwt) getting an analytic filter (one sided in the frequency domain) which is ...
0
votes
2answers
70 views

How to detect a long signal inside an even longer one?

I'm trying to detect a long pattern inside a long recorded audio. In order to do so I am implementing a matched filter in time by performing a FIR filtering using the coefficients of my pattern ...
0
votes
2answers
459 views

matched filtering in GSM

After the estimation of channel impulse response (using the training sequence in burst), to cancel the effect of channel on the received signal, I think, we should convolve the received signal with ...
0
votes
1answer
226 views

Radar video signal and matched filtering

In order to make my question more clear and give more details I'm trying to understand the processing signal procedure in radars,i understood till this moment that a transmitter generates a signal ...