Implementation of Analog Matched Filter
Analog matched filters are widely used in special cases where they have been in practice possible to construct. Examples:


dispersive delay line in chirp pulse compression radar; an acoustic surface wave filter
integrator to detect rectanqular DC pulses (actually a pulse lenght delay line and a subtractor are also needed if we haven't a clock which keep the integrator reset when no pulses are expected to arrive)


For arbitary complex pulses analog matched filters are impractical because the needed tolerances are not manageable.

NOT ASKED, but maybe useful: Detection with correlator is mathematically equivalent with using a matched filter. For example  greenbacks were in first gasoline automates recognized this way in analog domain. A candidate slided over a half transparent greenback image. If there occurred a sudden peak in the total light penetration, the candidate at least had right greenback patterns.

ADD due a comment:

The questioner asked a link to an existing implementation. Unfortunately I have no such weblink. But I can include one version which should be plausible altough hopelessly impractical when compared the equivalent processing in digital domain.

Here's a matched filter for 1 second long rectangular DC pulses. The impulse response of such filter should be also one second long rectangular DC pulse.

That impulse response is possible to generate with an integrator. The length 1s is achieved by subtracting the same input delayed by 1 second. Subtraction and integration are possible to realize with a differential amplifier and integrator which are made of opamps. In the next image they are built both with one opamp:



If the integration time constant is 1s (for ex. R=100kOhm, C=10uF), one volt DC pulse would generate 1 volt high triangle pulse to the output.

To prevent integrator to drift to saturation there are discharging resistors Rd, drawn with dashed line. Having R=100kOhm, I would try Rd = 500kOhm...1MOhm. Discharging time constant 5...10s should not spoil the filtering of 1s pulses and surely wins at least  the drift caused by non-idealities of modern high performance opamps.

1 second linear delay is problematic. If one accepts quite low system bandwidth - say 5kHz - a looped tape recorder can be used. It unfortunately doesn't record DC, but the signal can be shifted upper with mixing:



When the signal has been stored 1s, it's taken out and mixed back to 0Hz. The written mixing method is AM, which is inefficient due the generated lower sideband + carrier. But it's simple technically and the needed carrier frequency (more than 10kHz, say 12kHz) + both sidebands are still well recordable and possible to get separated (=filtered) from the leaked input signal at the output of the modulator.

The lowpass filter at the input of the whole system kills those signals which are out of the 5kHz bandwidth.