# Is low pass filter more commonly used than high pass filter?

I have heard my teacher saying** that low pass filter is more commonly used than high pass filter because in high pass filter, frequency increases with gain and thus noise also increases and thus it distorts the output. In case of low pass filter, frequency decreases with gain and thus noise decreases and thus output is less distorted.

I was skeptical about this explanation as I thought that low pass filter is used as much as high pass filter according to needs and there is no such thing that 'this' filter is more often than used than 'that'. I thought of doing a bit of research and I found that there are two types of noise- whiter noise and pink noise. White noise increases linearly with frequency and pink noise is inversely proportional to frequency. Generally, white noise is more dominant than pink noise and it is said that pink noise is still not exhibited for frequency as low as $10^{-6}$ Hz. So, I am assuming that white noise is exhibited and for higher frequency, white noise is dominant and thus distort the output. I found this forum of help and it says how to eliminate noise in low pass filter. So, my question is - Is low pass filter more often used than high pass filter? Is there any reason for this or is a false claim?

**My teacher said this statement during we were doing circuit analysis using simulink. He said to always use integrator instead of differentiator because in the laplace transform of differentiation is $sX(s)-x(0)$ whereas the laplace transform of integration is $\frac{X(s)}s - x(0)$ where $s=j\omega$. So, in differentiator, frequency increase and so is noise(act as high pass filter) and in integrator, frequency decreases and so is noise(act as low pass filter). So, eventually he made the statement of using low pass filter than high pass filter.

• you have your definition of filters backward. ... for high pass filter, gain increases with frequency.. not frequency increases with gain .... even though it seems to be the same when you say it. ... the gain is dependent on frequency, not the other way around. ... same thing with the low-pass ... gain decreases with frequency – jsotola Dec 22 '17 at 6:20
• Also, most filters do not talk about gain but the opposite: loss. Only when the input signal in the passband becomes larger when it has reached the output can we say that a filter has gain. – Bimpelrekkie Dec 22 '17 at 6:59
• Differentiators are noisier than integrators, is a fact. Whether or not you misinterpreted the teacher's subsequent comments, we have no way of knowing. – Chu Dec 22 '17 at 8:28

## 2 Answers

So, my question is - Is low pass filter more often used than high pass filter? Is there any reason for this or is a false claim?

It's neither a true claim, nor a false one. It is irrelevant to the understanding of filters. It is also poorly posed, what exactly do you count as a filter?

It might be possible somehow to count all filters used in the world, and come up with two numbers, and decide which was biggest. And when you'd done that exercise, you'd still understand no more about filters.

A filter is used when you need the energy in part of the spectrum to be reduced for some reason. Often that part is down at low frequency, where DC offsets, 1/f noise, drifts, mains hum are unwanted. Often that part is up at high frequency, where broadband noise, aliasing signals, radio reception on unshielded wires are unwanted. As an engineer, you will be called to design and deploy many of each type.

Shadow, as far as the last part of your contribution is concerned (differentiator vs, integrator) your teacher is right. There are some circuits (so called "universal or state-variable" filters and oscillator circuits) which are derived from a second-order differential equation.

A direct hardware realization of this equation would be based on differentiating circuits. This is possible, of course, but we would have to accept all the disadvantages connected with high-pass blocks (differentiators).

However, another and better realization is possible. For this purpose we can transfer the diff. equation into an integral equation (twofold integration of the whole equation). Each hardware realization now consists of low-pass (integrating) stages only, which have much better noise properties.

Examples: Filter/oscillator circuits carrying the names of the corresponding inventors like

(1) "KHN - Kerwin, Newcomb, Huelsman"; (2) "Tow-Thomas"; (3) "Fleischer-Tow"; (4) "Akerberg-Mosberg".