With such inaccurate specification, put an AC coupled amplifier with a huge (but usually unknown) amplification after the device. Bandpass the signal to the desired bandwidth and use a true RMS meter to measure the power at output.
At the amplifier input, replace your bridge with a good quality (non carbon composite) resistor (with the same resistance as your bridge) at room temperature, which will generate about -174 dBm/Hz of noise power.
Since the gain of the unspecified amplifier varies over time, you need to perform the measurement several times a second, so use a relay to switch the amplifier between your bridge and the resistor a few times a second.
At the amplifier output, since you know the thermal noise power generated by the resistor at the desired bandwidth, it is easy to determine the noise output power from your bride at the same bandwidth.
You'll need to provide a LOT more info on exactly what you are trying to do here... Like say, what's the load, what's the application, what type of "noise" you are talking about etc
Dave.
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First you'd have to establish a reference signal, as the waveform being measured is signifigantly different in nature from the source. (It is, in reality, a noise/distortion generator, as far as the original source is concerned) A precision bipolar rectifier, working from the same original source, could serve as a new reference of an intended output signal.
If you subtract the varying amplitude reference from the signal being examined, you may negotiate a minimum output or null condition, the remainung uncancelled output content of which can be examined for harmonic amplitudes, unrelated spurs and combined effective power readings, in comparison to the new reference. Nulling methods are notoriously sensitive to the practical workbench environment and inadvertent procedural or material errors.
Note that the original source must be the voltage at the input rectifier terminals, as it's load may contribute to distortion in the source signal, without actually being responsible for 'generating' the noise.
The whole thing seems a somewhat pointless exercise. It would be interesting to know if there was a constructive reason for it. This might be situation where spice modelling reduces the resources needed to produce a reasonable approximation of answers to these questions.
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