# Reducing noise that grows with frequency

I have a project in university where my professor gave us the following problem:

There is a transducer generating an AC signal with amplitude of 7.5mV and a frequency range from 50Hz to 150Hz.

This signal is subject to a noise of the following pattern:

The noise with frequency from 0 to 50Hz has -0.1dB of intensity (compared with the signal)

The noise with frequency of 60Hz has 1dB of intensity (this is due to the fact that power supply in my country works at 60Hz)

The noise with frequency from 50Hz upwards has a growth of 0.3dB/decade in intensity.

He asked us to remove this noise. He told us to discuss, use the internet, and try to find good solutions. I have a solution here, but honestly I don't know if it is good enough or if it is something a professional would do. Here is my approach.

• The first thing I do is using a band-stop filter to stop every signal from around 60Hz. I will be losing some of the original signal but a lot of the noise will be lost as well.
• Then I will apply a band-pass filter to collect all the signal that goes from 50Hz to 150Hz.
• The next thing I do is to apply a low pass filter that will start filtering at about 75Hz of frequency (I am thinking of a Bode's chart here).

Is this a good solution?

I am not sure because it seems that I will be losing a lot of the original signal with frequency around 150Hz, for example, due to the low pass filter.

Is there a better way to remove this noise?

• He didn't say the nature of the noise, just saying that this wasn't important.

• We are supposed to remove this noise only using electronic circuits. Capacitors, inductors, operational amplifiers, diodes, etc.

• How flat must the signal-passband be? in other words, are you allowed to reduce the signal over the 50-150Hz region? – analogsystemsrf Apr 17 at 12:55
• A possible method (used widely). en.wikipedia.org/wiki/Noise_shaping – Peter Smith Apr 17 at 12:58
• Generally, if a prof gives an assignment and says "use the internet" they probably don't mean "find a forum and ask someone who knows". Do some research, and flesh out your question with what you've found already – Scott Seidman Apr 17 at 13:10
• Mr. Scott Seidman: This is not an exam nor an assignment, and I am not asking for an answer (the professor even said that there is no "correct" answer). I am a student, and I am learning, so I thought that I would be appropriate to discuss with professionals about how it is done "in real life". I am sorry if it appears that I am trying to get an ready answer or cheat, I must have poorly expressed myself. I just wanted to make this clear before continuing the debate. Anyone care to explain the downvote? – Vitor C Goergen Apr 17 at 13:36
• As described, this situation is a kobayashi maru. it's unsolveable. In the "real" world, we do not try to resolve an unsolveable problem with a circuit. That is wasted time and money. Instead, we try to alter the situation so that it is solveable. For example, one might look for a sensor with a higher sensitivity, higher output signal - to overcome the noise. – scorpdaddy Apr 17 at 14:28

Communication Theory tells us the optimum SNR is when the signal BW is maximized and Noise BW is minimized with a "Matched Filter"

• This means the filter passes with the matching spectrum and while blocking the spectrum of noise with the same shape filters as each spectrum with some consideration to phase requirements.

• Here is a situation where the noise is co-channel or shares common bandwidth and is slightly greater than the signal.

• There are methods suggested here to reduce this interference.
• We cannot assume the sensor or noise source have been isolated properly due to;
• unbalanced impedance, poor shielding, grounding, supply filtering, cable isolation or excessive Common Mode noise coupling induced by some yet to be defined source.
• assuming we cannot improve this, we must consider the rate of change of the sensor signal which has been defined as 7.5mV and a frequency range from 50Hz to 150Hz.
• if both the amplitude and frequency must be preserved, there must be a limit on how fast it can change due to the sensor bandwidth must be limited or at least specified.
• the 1st step is to analyze the spectrum of signals and noise to define a baseline for computing the ideal SNR by averaging then sweeping the sensor frequency and/or voltage.
• one possibility is only the frequency of the sensor is important.
• then a PLL with a defined LPF BW to reject phase frequency errors to control the VCO can be used.
• or a PLL with a voltage-controlled bandpass filter, BPF with some BW defined e.g. 10 Hz or 1Hz or 0.1 Hz
• I have used this method with a wider BW to lock onto a signal then a very narrow BW to track it for Doppler techniques from VLF halfway around the globe with a whip antenna where the SNR was -40dB. The only phase shift was during sunrise and sunset.
• the other is to examine the noise spectrum for coherence, dominant frequencies or random, stochastic or a repetitive pulse and with random noise such as a nearby auto ignition noise and cancel out any repetitive noise.
• Is the signal repetitive over a number of cycles, N , such that we do not lose any information in a short interval? then a computed autocorrelation filter could work. ( This was used for Voyager space communication at extremely low bit rates and far distances)

I hope this gives you some concepts for solutions.

This is not something that can be solved with filters alone. Your SNR is negative at 60 Hz and for everything above 108 Hz, and it's only at most +0.1 dB below that. The only way to extract the signal in that case is to have a lot of a priori knowledge about the signal itself that allows you to distinguish it from the noise. For example, if you know that the signal is a steady tone whose frequency changes slowly (and the noise is not), you can use autoregression or autocorrelation to find the signal buried in the noise.

But if there's nothing definite you can say about the noise, then the situation is hopeless. The noise could very well be mimicking the signal.