Ⅰ. Filter Definition
In electronics, a filter (signal processing) is a kind of devices or process that removes some unwanted components or features from a signal. Filtering is a class of signal processing, the defining feature of filters being the complete or partial suppression of some aspect of the signal. Most often, this means removing some frequencies or frequency bands. However, filters do not exclusively act in the frequency domain; especially in the field of image processing many other targets for filtering exist. As is known to all, electronic filters remove unwanted frequency components from the applied signal, enhance wanted ones, or both.
Introduction to Signal Filtering
Catalog
Ⅱ. Type of Filters and Functions
2.1 Type of Filters
Filters have different effects on signals of different frequencies. According to this fact, the basic filter types can be classified into four categories: low-pass, high-pass, band-pass, and band-stop. Each of them has a specific application in DSP. One of the objectives may involve digital filters design in applications. Generally, the filter is designed based on the specifications primarily for the passband, stopband, and transition band of the filter frequency response. The filter passband is the frequency range with the amplitude gain of the filter response being approximately unity. The filter stopband refers to the frequency range over which the filter magnitude response is attenuated to eliminate the input signal whose frequency components are within that range. The transition band means the frequency range between the passband and the stopband.
Figure 1. Filtering Out the Noise (signal processing)
Because there are many different standards of classifying filters and these overlap in many different ways, there is no clearly distinctive classification. Filters may be:
- non-linear or linear
- analog or digital
- time-variant or time-invariant , also known as shift invariance.
- discrete-time (sampled) or continuous-time
- passive or active type of continuous-time filter
- infinite impulse response (IIR) or finite impulse response (FIR) type
2.2 Filtering Functions
- Separate useful signals from noise to improve signal immunity and signal-to-noise ratio.
- Filter out unwanted frequency to improve signal analysis accuracy.
- Separate single frequency from complex frequenc
Figure 2. Electronic Filter
Ⅲ. Filter Technologies
Filters can be built in a number of different technologies. Before that, it is necessary to know some basics of it deeply.
- Center frequency
The main parameters of the filter: the center frequency of the filter's pass-band f 0, generally f 0 = (f 1 + f 2) / 2, f 1 and f 2 are boundary frequencies of band-pass or band-stop filter, which decreased by 1dB or 3dB. In addition, narrowband filters often use the smallest point of insertion loss as the center frequency to calculate the pass-band bandwidth.
- Cutoff frequency
It refers to the right frequency point of the pass-band of the low-pass filter and the left frequency point of the pass-band of the high-pass filter, and it is usually defined by relative loss points, 1dB or 3dB. The relative reference for the relative loss is: the low-pass is based on the insertion loss at DC, and the high-pass is based on the insertion loss at a high-pass frequency at which no parasitic stop-band occurs.
- Pass-band bandwidth
The bandwidth of the filter is simply the difference between the upper and lower cutoff frequencies, while passband bandwidth is the difference between the upper and lower cutoff frequencies of, for example, a band-pass filter, a communication channel, or a signal spectrum.
- Insertion loss
It refers to the loss of the original signal in the circuit due to the introduction of the filter. And it is characterized by the loss at the center or the cutoff frequency. If it is the full-band interpolation loss, it must be emphasized.
Note: When adding a filter at the input end, the impedance of the filter should be mismatched with the impedance of the power supply. The more severe the mismatch, the more ideal the attenuation is, and the better the insertion loss characteristics. That is, if the internal resistance of the noise source is low impedance, the input impedance of the EMI filter connected to it should be high (such as a series inductor with a large amount of inductance); if the internal resistance of the noise source is high impedance, the input impedance of the EMI filter should be low (such as a large parallel capacitor). Due to the imbalance of the line impedance, the two components will convert to each other during transmission, and the situation becomes complicated.
- Ripple
It refers to the peak-to-peak value of the insertion loss that fluctuates on the basis of the average loss curve with the frequency in the 1dB or 3dB bandwidth (cutoff frequency).
- Pass-band riplpe
The amount of change in insertion loss in the pass-band with frequency. For example, in a 1dB bandwidth, it is 1dB.
- Pass-band standing wave ratio (VSWR)
An important indicator for measuring whether the signal in the filter pass-band is properly transferred. Ideal VSWR is 1: 1, when mismatched, VSWR> 1. For an actual filter, bandwidth satisfies VSWR <1.5: 1, which is generally less than 3dB, and the proportion when at 3dB is related to the filter order and insertion loss.
- Return loss
The decibels (dB) of the ratio of the port's signal input power to the reflected power, and it is also equal to | 20Log10ρ |, where ρ is the voltage reflection coefficient. In addition, when the input power is completely absorbed by the port, the return loss value is infinite.
- Stop band rejection
It is a major index to measure the performance of filter selection. The higher the index, the better the suppression of out-of-band interference signals. There are usually two formulations: one is how much dB is required to suppress a given out-of-band frequency fs, and the calculation method is the attenuation fs=As-IL; another is to propose a characterizing filter whose amplitude-frequency response is close to the ideal rectangle index of degree-rectangular coefficient (KxdB> 1), KxdB = BWxdB / BW3dB, (x can be 40dB, 30dB, 20dB, etc.). The more the filter order, the higher the rectangularity, in other words, the closer the K is to the ideal value 1, the more difficult it is to make an ideal filter.
- Delay (Td)
It refers to the time required for the signal to cross the filter. The value is the derivative of the diagonal frequency of the transmission phase function.
- In-band phase linearity
This indicator characterizes the phase distortion introduced by the filter on the transmission signal in the pass-band. The filter designed according to the linear phase response function, which has good phase linearity, but its frequency selectivity is very poor. It is only used to pulse or phase-modulate signal transmission system applications.
- Order (stage)
For high-pass and low-pass filters, the order is the sum of all capacitors and inductors in the filter circuit. For a band-pass filter, the order is the total number of parallel resonators; for a band-stop filter, the order is the total number of series and parallel resonators.
- Absolute bandwidth / relative bandwidth
This indicator is usually used for band-pass filters, which characterize the frequency range of signals that can pass through the filter, and reflects the frequency selection of the filter. Relative bandwidth is the percentage of absolute bandwidth to center frequency.
- Standing wave
It indicates the impedance matching between the filter port and the required system, and also it indicates how much of the input signal failed to enter the filter and was reflected back to the input.
- Loss
It represents the energy lost after the signal passes through the filter, that is, the energy consumed by the filter.
- Pass-band flatness
The absolute value of the difference between the maximum loss and the minimum loss in the pass-band of the filter, which characterizes the difference in energy consumption of filters for different frequency signals.
- Out-of-band rejection
It is the "attenuation" outside the pass-band frequency range of the filter, which characterizes the filter's ability to select unnecessary frequency signals.
- Absolute group delay
The time it taken for a signal to pass from the input port to the output port within the pass-band of the filter.
- Group delay fluctuation
The difference between the maximum and minimum absolute group delay in the pass-band of the filter, which characterizes the dispersion characteristics of a filter.
- Power capacity
It refers to the maximum power of the pass-band signal that can be input to the filter.
- Phase consistency
The difference in the phase of the transmitted signal between different filters of the same index in the same batch, which characterizes the differences (consistency) between batch filters.
- Amplitude consistency
The difference of transmission signal loss between different filters with the same index in the same batch, which represents the differences (consistency) between batch filters.
Figure 3. Low-Pass Electrical Filter
Ⅳ. Main Characteristic Indexes of Filtering
- Characteristic frequency
① The pass-band cutoff frequency fp = wp / (2p) is the frequency of the boundary point between the passband and the transition band, at which the signal gain decreases to the specified lower limit.
② Stop-band cut-off frequency fr = wr / (2p) is the frequency of the boundary point between the stopband and the transition band, at which the signal attenuation (reciprocal of the gain) decreases to the specified lower limit.
③ The corner frequency fc = wc / (2p) is the frequency when the signal power is attenuated to 1/2 (about 3dB). In many cases, fc is often used as the pass-band or stop-band cutoff frequency.
④ Natural frequency f0 = w0 / (2p), when there is no loss in the circuit, it refers to the resonance frequency of the filter, and complex circuits often have multiple natural frequencies.
- Gain and attenuation
The gain of the filter in the pass-band is not constant.
① For the low-pass filter pass-band gain Kp, for the ordinary filters, it refers to the gain at w = 0; for the high-pass, it refers to the gain at w → ∞; for the band pass, it refers to the gain at the center frequency.
② For the band-stop filter, the stop-band attenuation should be given, and the attenuation is defined as the inverse of the gain.
③ The change amount of the pass-band gain △ Kp, refers to the maximum change amount of the gain at each point in the pass-band. If △ Kp is in dB, it means the variation of the gain dB value.
- Damping coefficient and quality factor
The damping coefficient is a characterization of a filter’s damping effect on a signal with an angular frequency at w0, and is an indicator of energy loss in the filter.
The reciprocal of the damping coefficient is called quality factor, and is an important indicator of the frequency selection characteristics of the valence band-pass and band-stop filters, Q = w0 / △ w, where △ w in the formula is the 3dB bandwidth of the band-pass or band-stop filter, w0 is the center frequency, and in many cases the center frequency is equal to the natural frequency.
- Sensitivity
The filtering circuit is composed of many components, and changes of parameter values of each component will affect the performance of the filter. The sensitivity of a certain performance index y of the filter to the change of a certain component parameter x is recorded as Sxy, which is defined as: Sxy = (dy / y) / (dx / x).
This sensitivity is not the same concept with the sensitivity of measuring instruments or circuit systems. The smaller the sensitivity, the stronger the fault tolerance of the circuit, and the higher the stability.
- Group delay function
When the filter's amplitude-frequency characteristics meet the design requirements, in order to ensure that the output signal distortion does not exceed the allowable range, certain requirements should be put forward for its phase-frequency characteristic ∮(w). In filter design, the closer the group delay function d∮ (w) / dw is to a constant, the smaller the signal phase distortion.
Ⅴ. Filter Classifications Analysis
5.1 Passive Filter & Active Filter
- Passive filter
A passive filter is composed of passive components only. It is based on the principle that the reactance of the capacitive and inductive components changes with frequency. The advantages of this type of filter are: simple circuit, causal power supply, and high reliability. Also there are disadvantages: the signal in the pass-band has energy loss, the load effect is relatively obvious, and electromagnetic induction is easy to cause when using inductive components. When the inductance is large, the size and weight of the filter are relatively large, which is not applicable in the low frequency range.
The passive filter circuit has a simple structure and is easy to design, but its pass-band magnification and cut-off frequency change with the load, so it is not suitable for occasions with large signal processing requirements. Passive filter circuits are usually used in power circuits, such as filtering after DC power rectification, or LC (inductance, capacitor) circuit filtering when high current loads are used.
- Active filter
Active filters are composed of passive components and active devices. The advantages of this type of filter are that the signal in the pass-band has no energy loss, even be amplified; the load effect is not obvious, and the mutual influence is small when multi-levels are connected. The simple method of cascading is easy to form high-order filter, and the device is small, lightweight, and does not require magnetic shielding. Their disadvantages are that the pass-band range is limited by the bandwidth of the active device and requires a DC power supply; the reliability is not as high as that of a passive filter, and it is not suitable for high voltage, high frequency, and high power applications.
The load of the active filter circuit does not affect the filtering characteristics, so it is often used in places with superior signal processing requirements. Active filter circuit is generally composed of an RC network and integrated operational amplifier, so it can only be used under the condition of suitable DC power supply, and it can also be amplified. However, the composition and design of the circuit are also more complicated. Active filter circuits are not suitable for high voltage and high current applications.
5.2 Digital Filter & Analog Filters
5.2.1 Terminology
A digital filter is an algorithm or device consisting of a digital multiplier, an adder, and a delay unit. The function of the digital filter is to perform arithmetic processing on the digital code of the input discrete signal to achieve the purpose of changing the signal spectrum. Digital filters can be made by computer software or large-scale integrated digital hardware.
There are active and passive analog filters. Active filters mainly consist of op amps, op amps, resistors, and capacitors. They have problems such as voltage drift, temperature drift, and noise, while digital filters do not get these problems, so they can achieve high stability and accuracy.
5.2.2 Differences between Digital filter & Analog filters
Digital filters are used for discrete systems, analog filters are used in continuous-time systems, and they can also be used in discrete-time systems, such as SC (switched capacitor) filters.
From the point of view of implementation, analog filters are generally built with analog devices such as capacitors and inductors. Digital filters can be implemented by software or digital chips. It is troublesome to replace the capacitor and inductor when the technique parameters of the analog filter are changed. If there is a need for replacement, it is necessary to modify the coefficients (such as when implemented in software).
From the technical view, for example, it is very difficult for analog filters to reach -60dB, and digital filters can easily reach this.
The biggest difference between analog and digital filters is that the digital filter on the Fs/2 frequency is flipped, that is, symmetrical, while analog filters are not. Therefore, a large number of interpolation filters are selected in the DAC, and the image frequency is placed at a far frequency point, and then the analog filter regarded as a sound meter is used to filter out the image frequency in the radio frequency band.
The expression of analog filters is different from digital filters: analog filters are represented by H (S), and digital filters are represented by H (Z). Analog filter is based on the approximation of amplitude-frequency characteristics, while digital filters can achieve phase matching.
Figure 4. EMI Filters Image
Ⅵ. One Question Related to Filter and Going Further
6.1 Question
How to Select EMI Filters?
6.2 Answer
Some people think that the higher the insertion loss of an EMI filter, the better, and the more stages of the filtering network, the better. In fact, this is not the right way to choose a EMI filter. In addition, the more stages of the filtering network, the more expensive, the larger the size and weight. In practice, the best way to select and evaluate an EMI filter is to install it on a device for testing. As is known to all, the performance of a filter depends largely on the load impedance of the device. It cannot be derived from one data of impedance insertion loss. Because it is a complex function of the filtering element impedance and the equipment impedance, and its magnitude and phase change within the frequency range. What's more, different performance levels of conducted radiation control (FCC, VDE) and sensitivity control required by the filter selection test are performed on the device.
Frequently Asked Questions about Filter (Signal Processing) Basics
1. What is filter in digital signal processing?
In signal processing, a filter is a device or process that removes some unwanted components or features from a signal. Filtering is a class of signal processing, the defining feature of filters being the complete or partial suppression of some aspect of the signal.
2. Why do we use filter in digital signal processing?
Digital filters are used for two general purposes:
(1) Separation of signals that have been combined
(2) Restoration of signals that have been distorted in some way. Analog (electronic) filters can be used for these same tasks; however, digital filters can achieve far superior results.
3. What is filter response?
In comparison, filters carried out by convolution are called Finite Impulse Response or FIR filters. As you know, the impulse response is the output of a system when the input is an impulse. In this same manner, the step response is the output when the input is a step (also called an edge, and an edge response).
4. Which filter is present in DSP system?
An ideal bandpass filter and second-order approximations. With DSP software, there are two basic approaches to filter design: finite impulse response (FIR) and infinite impulse response (IIR).
5. What are the functions of filter in signal processing?
In the field of signal processing, a filter is a device or process that, completely or partially, suppresses unwanted components or features from a signal. This usually means removing some frequencies to suppress interfering signals and to reduce background noise.
6. What is filter frequency?
A frequency filter is an electrical circuit that alters the amplitude and sometimes phase of an electrical signal with respect to frequency. ... The frequency separating the attenuation band and the pass is called the cut-off frequency.
7. What is IIR filter in DSP?
The infinite impulse response (IIR) filter is a recursive filter in that the output from the filter is computed by using the current and previous inputs and previous outputs. Because the filter uses previous values of the output, there is feedback of the output in the filter structure.
8. Where FIR filter is used?
The term FIR abbreviation is “Finite Impulse Response” and it is one of two main types of digital filters used in DSP applications. Filters are signal conditioners and function of each filter is, it allows an AC components and blocks DC components. The best example of the filter is a phone line, which acts as a filter.
9. What are the most commonly used active filters?
The most common and easily understood active filter is the Active Low Pass Filter. Its principle of operation and frequency response is exactly the same as those for the previously seen passive filter, the only difference this time is that it uses an op-amp for amplification and gain control.
10. Why IIR filter is unstable?
So, for unstable filters, the impulse response is not absolutely summable. In another way, the impulse response never approaches zero. Again, for IIR filter, h continues to go on with n i.e. never goes to zero. So, IIR filters are supposed to be unstable.
Recommended Reading
Complete Introduction and Classification of Filters and Applications
Principle and Function of the Filter
Common Applications of Filter
Classification of Electronic Filters
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Recently, the market for dielectric filters has developed well. Its main advantages are large power capacity and low insertion loss, but there are two major disadvantages: first, the volume is large, (in centimeters), which occupies a lot of space compared to integrated circuits. Second, it is a discrete device and cannot be integrated with the signal processing circuit, and there is signal processing chip that needs to pass through a non-negligible transmission line. So impedance matching must be performed, therefore, the circuit has a complicated structure and signal attenuation somehow.
If the connection between the filter case and the device case is poor, it is equivalent to a distributed capacitance between them. This will cause the filter to have a large ground impedance at high frequencies, where the distributed capacitance and distributed inductance resonate, the ground impedance tends to infinity.
The most commonly used filters are low-pass and band-pass. Low-pass is widely used in image suppression of the mixer section and harmonic suppression of frequency source. Band-pass is widely used in front-end signal selection of receivers, spurious suppression after transmitter power amplifier, and frequency source dispersion suppression.
If the filter is poorly grounded and the grounding impedance becomes large, some interference signals will pass through the filter. In order to solve this, the insulation paint on the chassis should be scraped off to ensure a good electrical connection between the filter housing and the chassis.