How does matched filter work

Mahalanobis, A. I feel like the other answers don't state succinctly the step by step process of how the matched filter is used on a concrete example, and what it actually consists of, and why it is needed and how it fits into the big picture, without being wordy or mathematical. Also there is a confusion about how the reference signal is known.

Instead, the reference symbol template is known. There is a matched filter consisting of a time reversed template for each symbol each of the M symbols in Hartley's law that can be possibly transmitted, and the matched filter convolves it in the time domain with the input signal, starting at a particular time instant, which will be the beginning of the received symbol.

The symbol is multiplied by the reference symbol and then they are integrated, which results in a convolution. Since the reference symbol is time inverted, the convolution is identical to correlation -- recall:. The time inversion of the reference symbol is indeed the impulse response of the matched filter, because when an impulse is convolved with the time inverse of the symbol template, the impulse response becomes the time inverse of the symbol.

Matched filtering is equivalent to filtering the signal by multiplying the frequency spectrum of the signal with the frequency response of the time inverse of the symbol template i. If the BPSK waveform uses a SRRC filter then the matched filter is also a SRRC filter: the transmitter uses a square root raised cosine filter to perform pulse shaping and the corresponding receiver uses a square root raised cosine filter as a matched filter [3].

Sign up to join this community. The best answers are voted up and rise to the top. Stack Overflow for Teams — Collaborate and share knowledge with a private group. Create a free Team What is Teams? Learn more. Understanding the Matched Filter Ask Question. Asked 8 years, 6 months ago. Active 1 month ago. Viewed 63k times. According to Wikipedia The matched filter is the optimal linear filter for maximizing the signal to noise ratio SNR in the presence of additive stochastic noise This to me implies that it maximises it everywhere, but I don't see how that is possible.

Improve this question. Royi 28k 3 3 gold badges 52 52 silver badges bronze badges. If the noise is additive Gaussian noise, then no filter, whether linear or nonlinear, can give a smaller error probability than the matched filter. Add a comment. Active Oldest Votes. In short, "does the matched filter maximize the SNR only at the sampling instant, or everywhere? Improve this answer. Dilip Sarwate Dilip Sarwate There's a significant portion of a digital communication theory course shoved into one package.

I have a question regarding the graph of the matched filter output. What's the output of that graph I'm trying to hand draw it? Note that except at the sampling instants, the filter output has receiver-induced intersymbol interference ISI in it! So, whatever pleases you Show 3 more comments. Juancho Juancho 4, 17 17 silver badges 18 18 bronze badges. I tried to post it in the comments here but it was too long and not allowed. Thanks for your answer. Jason R Jason R You said that the output of the matched filter not at the decision point make no difference and are irrelevant.

I had figured this out and was wondering why a better filter could not be made, say, one that grabs the energy contained in those portions and includes that at the point of decision. Not sure if that makes sense! Hope it does! My guess is that this can't be done because then the filter wouldn't be linear Alexander Grau Alexander Grau 21 1 1 bronze badge. This is the original paper Mahalanobis, A.

Aaron Aaron 1, 7 7 silver badges 8 8 bronze badges. The sampling stage comes after the eye diagram in the above scenario. Lewis Kelsey Lewis Kelsey 1 1 silver badge 8 8 bronze badges. Maybe you didn't read my answer all the way to the end. It describes how a correlation receiver works and how its output differs from the matched filter output at all times except the sampling instants.

Sign up or log in Sign up using Google. Sign up using Facebook. Sign up using Email and Password. Post as a guest Name. Email Required, but never shown. The Overflow Blog. Does ES6 make JavaScript frameworks obsolete? Podcast Do polyglots have an edge when it comes to mastering programming Featured on Meta. The SNR is based on a desired false-alarm rate of 1e-6 for a noncoherent detector.

Create radiator and collector objects that operate at 10 GHz. Create a free space path for the propagation of the pulse to and from the target. Then, create a receiver and a matched filter for the rectangular waveform. After you create all the objects that define your model, you can propagate the pulse to and from the target. Collect the echo at the receiver, and implement the matched filter to improve the SNR.

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MatchedFilter 'Coefficients' ,wav, Open Live Script. RadarTarget 'Model' , 'Nonfluctuating' , InitialPosition ;. RectangularWaveform 'PulseWidth' ,25e-6, Radiator 'PropagationSpeed' ,c, FreeSpace 'PropagationSpeed' ,c, Collector 'PropagationSpeed' ,c, ReceiverPreamp 'NoiseFigure' ,0, Coefficients -1;.

You have a modified version of this example. Do you want to open this example with your edits? No, overwrite the modified version Yes.