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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.

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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 ...
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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 ...
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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 ...
6
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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 ...
6
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1answer
205 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 ...
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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 ...
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3answers
365 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
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1answer
189 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. ---------------------------------- ...
4
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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 ...
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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 (...
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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 <...
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2answers
918 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 ...
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2answers
74 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 ...
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2answers
635 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 ...
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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 ...
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3answers
695 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 ...
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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) ...
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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 ...
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4answers
576 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
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1answer
143 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 ...
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4answers
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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 ...
2
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1answer
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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 ...
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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 ...
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1answer
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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: $SSD = \sum {\left(F - I\right)^2}$ ...
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0answers
286 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 ...
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1answer
202 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 ...
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0answers
110 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 ...
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2answers
632 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 ...
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2answers
1k 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 ...
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2answers
179 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 ...
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1answer
232 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. ...
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2answers
754 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 ...
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1answer
46 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 ...
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1answer
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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 ...
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1answer
182 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 ...
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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 ...
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1answer
633 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 ...
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2answers
758 views

How MATLAB calculates matched filter gain

Here is a bunch of code from MATLAB documentation: Designing a Basic Monostatic Pulse Radar: ...
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0answers
140 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'...
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0answers
340 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}^{-...
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0answers
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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 (...
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0answers
324 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 ...
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0answers
98 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. ...
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3answers
543 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,...
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3answers
154 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 ...
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2answers
69 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 ...
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2answers
436 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 ...
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1answer
186 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 ...
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1answer
234 views

Matched filter for variable time scaling?

Lets say I have some arbitrary waveform shape I want to look for. We'll use this as an example: If my input is some mildly noisy signal, and I see something like this: I can run that through a ...
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2answers
218 views

Optimum Filter Signal Detection for Non AWGN Channels

I have been reading this question and it confirms that the matched filter is the maximum-likelihood receiver in the presence of additive white Gaussian noise. So in the AWGN channel it maximizes the ...