# why is noise always a high frequency signal ? what then is frequency of a noise?

while designing signal conditioning circuits for sensors , we design low pass filters to remove high frequency noise. why can't noise be a low frequency signal or what will its frequency be ?

• We filter out all but the frequencies of interest; those we can not filter out otherwise we have no signal, thus any noise in there will stay there. – PlasmaHH Jan 21 '16 at 10:58

"Signal conditioning circuits for sensors" generally use op-amps and internal op-amp voltage noise tends to have a frequency response like this: - As can be seen, the bigger noises are at the lower frequencies. So why concentrate on the high frequency stuff?

Let's say the average (ball park) voltage noise between 0.1 Hz and 1 Hz is about 60 nV per root-hertz. The total noise that this will produce across that bandwidth is: -

$\sqrt{1 - 0.1} \times 60nV$ = 57 nV.

What about between 1 Hz and 10 Hz - we could use 30 nV per root-hertz as the figure and we would calculate the noise as 90 nV. Between 10 Hz and 100 Hz (10 nV per root-hertz) the noise would be about 95 nV.

As you can see, for a decade change in frequency the actual noise power (over that bandwidth) gets bigger as frequency rises.

Now let's say that the sensor has a frequency response of interest up to 10kHz - how much noise exists in the range 10 kHz to 100 kHz i.e. how much noise could we get rid of (because we don't use or need that part of the spectrum)?

the spectral noise density looks to me about 3 nV per root-hertz from the graph so total noise produced by this op-amp in the frequency range 10 kHz to 100 kHz is: -

$\sqrt{100k - 10k} \times 60nV$ = 900 nV.

This is why we mainly concentrate on removing high frequency noise.

Another very good reason might be to avoid aliasing when feeding the (amplified or not) sensor output into an analogue to digital converter. Noise above the Nyquist sampling rate (if not significantly reduced) will be folded down into the converted base-band. if you don't understand this you can maybe imagine a sinewave under-sampled like this: - Imagine the red signal is noise above the Nyquist sampling rate. When sampled it can appear to be a sinewave (blue) that is of a much lower frequency. This is aliasing.

• thank you sir, so what i understood is that even if a sensor output has low frequency noise ,the total noise in that range is less , also we need to capture the signal of our interest ,so we do not concentrate on it. is that right? – prasanna Jan 22 '16 at 4:15
• I assume a zero-noise sensor that has a "signal conditioning circuit" (as per your question). That conditioner I assume to be an op-amp (quite common). I then look at the typical noise introduced by an op-amp (see the graph) and explain why Low frequency noise might appear to be a problem but sometimes isn't. I then explain why the op-amp output is often filtered to remove the high frequency noise. The answer I have given addresses the question: "why can't noise be a low frequency signal or what will its frequency be ?". – Andy aka Jan 22 '16 at 9:08

Noise is an unwanted signal, period.

Typical sources of natural noise tend to be broadband, that is all frequencies from DC to very high indeed.

The electrical noise produced by resistors, Johnson noise, has a flat frequency spectrum from DC to very high. Flat spectrum means equal power per Hz of bandwidth.

Consider listening to a flat noise signal. Looking at the noise power above and below (say) a mid A of 440Hz. There are only 440 1Hz bandwidths below it, but 10000 to 20000 (depending on how old you are and where your hearing cuts off) above it, so the noise signal sounds dominated by the high frequency hiss.

The noise produced by opamps however tends to be flat above some low frequency, usually in the audio band, most amps are flat above the 1kHz wher noise is typically specified, but then increases towards DC, due to what's called flicker noise. This is a big problem for DC instrumentation. High quality opamps intended for DC use will also have noise specs in the 0.1Hz to 10Hz range, and these numbers tend to dwarf the 1kHz numbers.

For DC signals and low frequency signals, eliminating the noise above their bandwidth can result in orders of magnitude reduction in noise voltage. Which is why it's done.

Other sources of unwanted signals can be narrow band. Your neighbour's garage door opener for instance can be removed by an RF filter. Mains hum can cause big problems in signal conditioning as the freqeuncy is so low, and can often be in the bandwidth of the signal. This then needs a reduction in the hum pickup, as filtering will do no good.

"why can't noise be a low frequency signal or what will its frequency be" Who says it can't ?? I can be any frequency so including low frequencies. For example Pink noise has more power at low frequencies !

It depends on the device what kind of noise it produces. If the signals you want from a sensor are low frequency only, then you could filter out the higher frequency components and get a "cleaner", nicer looking signal. Taking out the high frequencies is similar to "averaging", you take the average of many measurements to get a more accurate reading.