# Notch Filter: 19 Facts You Should Know

## Notch Filter Definition

Before discussing in detail about notch-filter, let us find out the definition of it. A notch-filter can be defined as a band stop that has a very narrow frequency bandwidth. Great depth, high-quality factor, and sharpness in band-reject characterize a notch-filter. There are several kinds of notch-filters which we will discuss later.

## Notch Filter Equation

Some of the important equations of notch-filter are given below.

• The HF cut-off of the LPF: fL = 1 / ( 2 * RLP * CLP * π)
• The LF cut-off of the HPF: fH = 1 / ( 2 * RHP * CHP * π)
• The quality factor of the notch filter:  Q = fr / Band Width

## Working of notch filter

A notch-filter has the same working principle as of band-reject filter. It allows all other frequency components of the signal and blocks the specified narrow bandwidth. For a passive design, the resistive, capacitive and inductive reactance play the part of controlling the frequency.

## Notch filter graph | Notch filter phase response

The following is the notch-filter graph.

## Notch Filter Q

Q of a notch-filter is a very important parameter. Q or Quality Factor of a Notch-filter is given by the following equation: Centre Frequency/Bandwidth. Q is the measurement of the selectivity of the filter.

The center frequency is the Notch Frequency, and it is the center frequency of the passband.

## Notch filter applications | Use of notch filter

There are several applications of different kinds of notch-filters. Let us discuss some of them.

• Communication Systems: Notch-Filters is one of the important pieces of equipment for a communication system. There is a high probability that the message signals get interfered with by harmonic noises in long-term communication. Notch-filters eliminate the noise.
• Audio Engineering: One of the basic components of audio engineering is a notch-filter. Eliminating noise, spikes are some of the tasks performed by a notch-filter.
• Medical Engineering: Notch-filters have been used in Medical Engineering. Reading of EEG is impossible without a notch-filter.
• Digital Signal Processing: Notch-filters have applications in Digital Signal Processing. A notch-filter is important when there is a need for mixing up signal or condition of elimination of certain frequency component.
• Digital Image Processing: Notch-filters help to eliminate noises from digital images.
• Optical Applications: Notch-filters have applications in optical applications. Blocking off a certain wavelength of light is done by specific optical notch-filters.

## Notch filter EEG

EEG or Electroencephalogram is a very important process in medical sciences. Several filters are used to display the output data produced by the machine. Without the filters, it is quite impossible to read the values.

There are three kinds of filters used in an EEG reading. They are – high pass filter, low pass filter, and notch-filter. High pass filter filters out high-frequency components, whereas low pass filters do the same for common frequency components. The notch-filters filter out a certain given range of frequency.

Especially the supplied frequency of the AC interferes with the EEG readings. Notch-filter removes such interference. For North America, the supply frequency is 60 Hz, so a 60 Hz notch-filter is used. In India and other countries where the supply frequency is 50 Hz, a 50 Hz notch-filter is used.

## Optimum notch filter in image processing

There is certain kind of periodic noises in digital images. The noises are repetitive and unwanted. They create certain patterns and affect the picture badly. One of the solutions to the problem is an optimum notch-filter.

At first, the noise frequency is determined, then the notch-filter produces the repetitive noise, and the output with lesser noise is produced.

## Notch filter transfer function

The following expression gives the transfer function of a notch-filter –

Here, wz refers to the Zero-Circular Frequency, whereas wp refers to the pole-circular frequency. Finally, q means the Quality Factor of the notch-filter.

## How to use a notch filter ?

When there is a need to reject a certain narrow band of frequency, a notch-filter is used. A notch-filter is placed after any source from which the signal needs to be eliminated. In most cases, the filter is set as the very last component of any circuit.

## Difference between notch filter and band stop filter

A notch-filter is one type of bandstop filter. The only difference between a band stop filter and a notch-filter is that a notch-filter has a narrower bandwidth than a normal bandstop filter.

## Bandpass vs Notch filter

There are some differences between the bandpass filter and the notch-filter. Let us elaborate on them.

## Anti notch filter

Notch-filters reject the very narrow bandwidth of signals and allow other components of that signal. The same but opposite task is performed by bandpass filters. The bandpass filters allow passing a certain band of frequency and block different parts of the movement.

## Notch filter characteristics

Some of the attributes of a notch-filter –

• Narrow bandwidth
• High Q value
• Great depth

## Notch filter high q

Twin T notch-filters can provide a very good amount of depth, almost infinite. If an LM102 voltage follower is added to the network, the Q of the circuit gets a skyrocketing growth from 0.3 to 50. That is how a high Q is achieved.

## Gain of notch filter

The gain of a notch-filter can be calculated using the following equation.

## Notch filter coefficients

Notch-filter coefficients are referred to as the coefficients of the transfer functions.

Here, wz refers to the Zero-Circular Frequency, whereas wp refers to the pole-circular frequency. Finally, q means the Quality Factor of the notch-filter.

## Transfer function of notch filter in s domain

The following expression gives the transfer function of a notch-filter –

## Active notch filter

An active notch-filter is a combinational circuit of two separate circuits. For example, connecting a low pass filter and a high pass filter in a parallel connection and adding an op-amp for amplifying purposes will work as an active notch-filter.

## Inverse notch filter

Inverse notch-filter is a special type of Notch-filter that has an infinite impulse response. Inverse notch-filters are very useful in medical image processing where there is a need to eliminate narrowband signals. Inverse notch-filters do the job efficiently.

## Cavity notch filter

Notch-filters are a special type of Cavity filter. Cavity filters allow a certain narrow band of frequency. So, we can say that the working is the same as notch-filters. That is why often cavity filters and-notch-filters are termed cavity notch-filters.

Adjustable notch-filters are also tunable notch-filters. One can adjust the frequency as per the need. Some of the Adjustable notch-filters are very important in audio engineering.

Adjustable q notch-filters can change the Q value of the notch-filter. Therefore, the Q is a very important parameter of the filter.

The adjustable Q value is needed for the audio engineering department.

## Bandpass notch filter | Notch band pass filter

Notch-filters are a special type of bandpass filter. Bandpass filters allow a certain band of frequency to pass. In bandpass filters, theoretically, any range of rounds can be given by the required design. But, in bandpass filters, the band’s scope is typically narrower than the usual ones.

## Notch filter VST

VST is a filter envelope plugin. An envelope provides several edges to a filter. VST notch-filters offer many advantages like mixing up audios very finely, etc.

## FM Notch filter

FM notch-filters or Frequency Modulation notch-filters are some of the important instruments for Software-Defined Radios. Even these filters made the Software-defined Radios popular. It also helps in radio communications.

## Tunable fm notch filter

Tunable FM notch-filters are special kind of notch-filters which can adjust the center frequency as per the need of the applications. No need to say again that the FM filters need the tunable filters because several frequency bands need to be blocked from a signal in FM.

## RF Notch filter

RF or Radio-Frequency Notch-filters are used to reject only one frequency from a given band of frequency. Generally, RF notch-filters have a Q. Basic RF filters are designed from low-pass filters to achieve high efficiency. However, converting them into a notch-filter is a tough process and needs a high level of caution and efficiency.

## Tunable notch filter RF

Just like other tunable notch-filters, the tunable rf notch filter can adjust the frequency band as per the need.

## 60 Hz Notch filter EEG

EEG or Electro-Encephalograph Machines has an inbuilt 60 Hz notch-filter. The high pass filters and low pass filters are fixed at their highest and lowest calibrations.

## 60hz Notch filter IC

There is a readymade filter IC available to minimize the circuit. It includes one low pass and one high pass filter, and one op-amp for summing up the outputs of both the filters. The most popular 60hz notch-filter IC from Texas Instruments is UAF42.

## 50 Hz notch filter

A 50 Hz notch-filter can reject a 50 Hz signal by keeping the power of the movement almost intact. A 50 Hz notch-filter is needed when the 50 Hz band is necessary to be accurately rejected.

## 50 Hz notch filter circuit

A 50 hz circuit can be designed using the same frequency of a 60 hz notch-filter as given previously. Some typical values for creating a 50 Hz filter are given below. C= 47 nano-farad, Resistance R1, R2 = 10 kilo-ohm, R3, R4 = 68 kilo-ohm.

## switched capacitor notch filter

A switched capacitor notch-filter is another advanced topology. This topology provides high precision, high Q value. This topology has several applications.

## HF notch filter

HF Notch-Filter stands for High-Frequency Notch-Filters. Notch-filters of 50-60 Hz cannot give a good depth value or a high Q. High-frequency notch-filters (which rejects or allows a high-frequency component) are more realistic, provides a desired bandwidth and depth.

## 1khz notch filter

A one kilo-hertz notch-filter has a basic principle, the same as the previously discussed 50 hz or 60 hz filters. The only difference is that a one khz notch-filter is more realistic and can be designed for real-time applications. The 50-60 Hz filters are capable of giving 40 to 50 dB depth. But as an engineer, one must focus on the depth and the Q value. So, the one khz filter comes into action.

## Notch filter in frequency domain

Notch-filters deal with frequency. The main principle of a notch-filter is to block a certain narrow band of frequency. So we can say the notch-filter works in the frequency domain only.

## 2 meter notch filter

A 2 meter notch-filter is a solution to a very general communication problem called – intermodulation. But the filter suffers a high loss during operation.

## Audio notch filter

A notch-filter is an important instrument for audio engineering. Generally, some unwanted frequency components get mixed up in the original audio. To remove or eliminate such frequency, an audio notch-filter is used.

## Notch filter equalizer

A notch-filter can be used as an equalizer in audio engineering. It can help to find out several unwanted spikes or noise, and also, it can remove those noise and spikes. That is how it helps to make the audio clear.

## Periodic noise reduction using a notch filter

There is certain kind of periodic noises in digital images. The noises are repetitive and unwanted. They create certain patterns and affect the picture badly. One of the solutions to the problem is an optimum notch-filter.

At first, the noise frequency is determined, then the notch-filter produces the repetitive noise, and the output with lesser noise is produced.

## Acoustic notch filter

As mentioned earlier, Notch-filters are important for audio engineering. After the audio is being recorded, different audio or acoustic audio is needed to mix up. There is a probability that any spike gets introduced in the mix-up. An acoustic notch-filter can remove such noise and spikes.

## Variable notch filter

Variable notch-filters are essential for audio engineering. These kinds of notch-filters can change the intended frequency in a certain range.

In audio engineering, several unintended frequencies may present; to remove them, we need notch-filters. Instead of using one filter to omit a single frequency is not a great solution. Variable notch-filters serve our purpose here.

## T Notch filter

T notch filter is a basic notch-filter with a ‘T’ network of RCR components. It is a special design technique.

## Double T Notch filter | Double notch filter

Double T notch-filter or Twin T filter is an updated version of the T network. As the name suggests, here, two T networks are connected to form a notch-filter. One network consists of RCR components. Another is of CRC components.

## Crossover notch filter

Crossover notch-filters can be described as series of notch-filters connected. These filters are designed so, to eliminate the driver resonance from the filter networks.

## Series notch filter

Series notch-filters are used for the elimination of the driver resonance. Series notch-filters are designed using Capacitor, Resistance, and an Inductor. All the components are connected in a series connection, and the driver is connected in parallel with them.

## Parallel notch filter

Parallel notch-filters are specially designed to eliminate significant unwanted peaks from the driver’s response. This filter is similar because all the basic elements are connected in parallel, unlike the series notch-filter.

## High Q notch filter

High Q notch-filters are popular for providing great depth in rejection. Generally, Twin T notch-filters are used to get a high q value and get more depth—the Q value changes from normal 0.3 to 50 for a Twin T filter.

## Sallen key notch filter

Sallen Key is a topology for designing higher-order filter circuits. Using this topology, notch-filters can also be created. The topology is also termed as Voltage Controlled Voltage Source. R.P. Sallen and E.P. Key first started it in the year 1955. Therefore, the topology is named after them.

## Butterworth notch filter

Butterworth filters provide the flattest possible frequency response. So now, if a notch-filter is designed to provide a flat response, then the notch-filter will be called a Butterworth notch-filter.

## AM Notch filter

AM Notch-Filter or Amplitude Modulation Notch-filter is designed to help the measurement of emission of a broadcasting station using a spectrum analyzer. AM Notch-filter is very useful for AM radio communication stations when there are nearby other towers. This is because it can allow only AM band EAS reception while the other strong fields are present.

## Dynamic notch filter

The dynamic filter is a set of algorithms. First, the algorithm finds the noise frequencies. Then, active notch-filters are used to eliminate such spikes of noise.

## Microstrip notch filter

As we can see, there are several filters available in the market for different uses. But Microstrip notch-filters are especially useful for wireless communication systems.

## Analog notch filter

A notch-filter can be classified into the main domain; one is Analog another – Digital. We have previously discussed Digital Notch-filter, like – IIR, FIR, etc. Analog notch-filters are RLC notch-filters, RC notch-filters, T notch-filters, Twin T notch-filters, etc.

## RC Notch filter

RC notch-filters are analog notch-filters that are designed with resistors and capacitors. In this kind of filter, manually, we can supply values of r and c.

## IC Notch filter

LC notch-filters are analog notch-filters that are designed with an inductor and capacitor. In this kind of filter, manually, we can supply values of L and c.

## Arduino Notch filter

Several digital filters can be designed using Arduino. Writing appropriate codes will help an engineer to realize even Notch-Filter digitally. The digital filter codes are available on GitHub. Try to modify them to make a notch-filter.

## Coax stub Notch filter

Coax stub notch-filter is a type of notch-filter build within coaxial cables to remove noise and attenuation. ‘T’ coaxial connector will be very useful for designing such a filter. The addition of a second stub will be very helpful to improve the situation. Radio, Television centers use this filter.

Almost in every major city, there is a high possibility that one can receive the radio frequency from the FM radio stations. The FM broadcast notch-filter will provide a 30db attenuation for the FM signals in the range of 88 to 108 MHz.

## GPS Notch filter

GPS notch-filters help to catch the satellite signals. However, the basic rule is that the GPS module will receive a comparatively weaker signal from the satellite. This is because the nearby located towers may interfere with the incoming signal.

The GPS notch-filter will help here to attenuate the signal by – 30 dB. In addition, it will allow the GPS module to receive a fairer band from the satellite.

## Bainter Notch filter

Bainter notch-filter is nothing but a basic notch-filter. A notch-filter consisting of one low pass filter, one high pass filter, and one adder to get the output frequency response can be termed a Bainter Notch-filter.

## Wideband notch filter

If a band-reject filter has a wideband frequency as the operational band, then the filter is technically a wideband filter. If the band-reject filter has a narrow band of frequency, the filter is known as the Notch-filter. So, a Notch-filter cannot be a wideband notch-filter. It is technically impossible.

## Eagle notch filter

A QAM notch-filter is based upon the phase cancellation concept. Eagle Comtronics Inc designs this narrow network. That is why QAM notch-filters are popular as Eagle Notch-Filter.

## Crystal notch filter

Notch-Filters can be designed using crystals also. A crystal has a very high-Quality factor. A crystal notch-filter is useful for creating a notch-filter that has a very narrow band.

## Peak notch filter

It is a digital notch-filter. The filter can resist each channel of an input signal for a certain center frequency and a bandwidth of 3 dB.

## Narrow notch filter | Narrow band Notch filter

Notch-filters reject a very sharp band of frequency, saying a very narrow band of frequency. That is why notch-filters are often termed narrow notch-filters.

## TV channel Notch filter | TV Notch filter | Cable Notch filter

The TV notch-filters help to solve the modulation problem that could occur in the transmission line. The tv notch-filter can make room for the modulated channel once it is installed in the queue. The filter also prevents reverse broadcasting to the coaxial cable. The increasing bandwidth now increased the demand for cable television notch-filters.

## MNE Notch filter

MNE is popular software which provides us platform to build several electronics instrument. For example, we can design certain notch-filters in the MNE platform by writing some specific code.

## Opposite of Notch filter

Notch-filters reject the very narrow bandwidth of signals and allow other components of that signal. The same but opposite task is performed by bandpass filters. The bandpass filters allow passing a certain band of frequency and block different parts of the signal.

## Automatic Notch filter

An automatic notch-filter is something that can change the center frequency as well as the Q value as per the need. Several mechanical systems use these kinds of filters.

## Gaussian Notch filter

A gaussian notch-filter is a digital filter. This filter is used to remove noise from various digital images. The specialty of the filter made it popular and is used in multiple applications as well as in various investigating agencies.

## Notch filter parameters

There are some parameters to measure the accuracy of the notch-filter. One of the important among them is the Q factor or Q (Details given above). Another is the depth of the output. Finally, the bandwidth is also one of the parameters.

## Notch filter impulse response

The following image shows a notch-filter impulse response.

## Second order Notch filter transfer function

The following expression shows the second order notch-filter’s transfer function.

Sudipta Roy

I am an electronics enthusiast and currently devoted towards the field of Electronics and Communications. I have a keen interest in exploring modern technologies such as AI & Machine Learning . My writings are devoted towards providing accurate and updated data to all learners. Helping someone in gaining knowledge gives me immense pleasure. Let's connect through LinkedIn - https://www.linkedin.com/in/sr-sudipta/