Signal Filtering (Part 1) —— The "Noise Sieve" in the Electronic World and Basic Principles

Imagine wearing headphones listening to your favorite song, only to be annoyed by the "zizi" sound of electric current and the "buzzing" of the outside world; or a doctor checking an electrocardiogram, where the curves on the screen are covered by messy ripples, making it impossible to see the heartbeat pattern clearly — these disturbing "noises" have a unified name in the electronic world: noise. And signal filtering technology is like a precise "sound sieve", which accurately sifts out the "voice of truth" we need from the complex electronic noise, making useful signals clearly visible.

Ⅰ. The Nature of Noise: Ubiquitous Information Interference

In the world of signal processing, noise is not simply "unwanted sound" but a general term for all useless electronic disturbances—it is everywhere like air, permeating from inside circuits to the external environment without any gaps. These "electronic interrupters" mainly come from four aspects:

Thermal noise: Electrons in a conductor are never peaceful and law-abiding; they undergo irregular thermal motion with temperature, just like a group of naughty children running around in a crowd, becoming more restless as it gets hotter. It is proportional to the absolute temperature. Even at low temperatures of tens of degrees below zero, electrons will still shake slightly, generating weak noise.

Shot noise: Electric charges themselves are "discrete," just like raindrops hitting a window—they are not a continuous stream of water but random impacts of individual water droplets. This statistical fluctuation of charges causes small fluctuations in signals. For example, when a photoelectric sensor receives light, shot noise is generated due to the randomness of photon impacts.

Flicker noise: Noise caused by "unstable states" on the surface of semiconductors, characterized by greater noise at lower frequencies, also known as 1/f noise. It is like the "rustling sound" of an old radio and is particularly noticeable in low-frequency signals (such as slowly changing temperature signals).

Environmental interference: This is the most common "external intruder" — the 50Hz power frequency interference from household wires, radio waves from mobile phone calls, electromagnetic radiation from factory equipment, and even lightning in thunderstorms can all "mess up" the signals. For example, in a hospital, when an ECG monitor is close to high-power equipment, messy ripples will appear on the screen, which is caused by environmental interference.

In daily scenarios, the impact of noise can be seen everywhere: when a smart bracelet detects heart rate, arm shaking will generate low-frequency noise, causing the heart rate value to fluctuate up and down; when industrial pressure sensors work in the workshop, the high-frequency electromagnetic noise from the operation of motors will cause random fluctuations in pressure readings. If such noise is not handled, it will make the data lose its reference value and even mislead decision-making.

II. Basic Principle of Filtering: Intelligent Selection in the Frequency Domain

The essence of filtering is a "frequency selection competition" — based on the "frequency characteristics" of signals and noise, it selectively allows useful signals to pass through while blocking noise outside. The core mathematical tool behind this is the Fourier transform, which is like a "signal disassembler" that can break down the time-domain signals we see (such as a fluctuating curve) into a combination of "sine wave notes" of different frequencies.

For example, temperature signals are "slow-paced players" with very low frequencies (usually below 1Hz), while electromagnetic interference are "fast-paced players" with frequencies as high as tens or hundreds of hertz. Filtering is to select the "slow-paced" temperature signals and block the "fast-paced" interference. The four common types of filters are like four "sieves" with different functions:

The comparison chart of the frequency responses of the four types of filters is as follows:

   low-pass filter            High-pass filter            band-pass filter             Band-stop filter   

The electrocardiograph in a hospital is a typical application of the "filter combination": the low-pass filter blocks high-frequency interference from muscle tremors, the high-pass filter eliminates baseline drift caused by the patient's breathing, and the band-stop filter accurately cuts off 50Hz power frequency interference — only with these three measures working together can the real curve of the heartbeat be clearly displayed, helping doctors diagnose the condition. In industrial scenarios, pressure sensors use RC low-pass filter circuits to simply and efficiently filter out high-frequency electromagnetic noise generated by motor operation, making pressure readings more stable.

III. Detailed Explanation of Classic Filter Circuits

Different scenarios have different requirements for filtering. Engineers have designed three classic filtering circuits, which are like three "sieves with different styles," each having its own area of expertise:

1. Butterworth filter: "A perfectionist pursuing stability"

Core features: The signal amplitude within the passband is "absolutely flat," just like a smooth road with no undulations.

Second-order circuit transfer function: H(s) = ω_c² / (s² + √2 ω_c s + ω_c²) (where ω_c is the cutoff angular frequency)

Application scenarios: Measurement systems requiring precise amplitude, such as industrial pressure sensors and laboratory precision instruments. In chemical production, tiny amplitude changes in pressure signals may indicate changes in reaction status, and the Butterworth filter can accurately retain these changes without introducing additional distortion; it is also commonly used for low-pass filtering in audio equipment to make music playback smoother.

2. Chebyshev filter: "A practical expert in efficient blocking"

Core characteristics: Extremely steep roll-off特性 – the transition interval from "allowing passage" to "completely blocking" is extremely narrow, just like a steep hillside that can be crossed in one go. However, the cost is that there is slight ripple in the passband, similar to small undulations on a road surface.

Typical parameters: Allows ±0.5dB ripple within the passband; under the same order, the stopband rejection effect far exceeds that of Butterworth.

Applicable scenarios: Scenarios that require strong blocking of specific noises, such as filtering interference signals from adjacent frequency bands in radio frequency communication equipment; for sensors near industrial frequency converters, Chebyshev filters can efficiently suppress the wide-frequency noise generated by frequency converters.

3. Bessel filter: "The guardian of waveforms"

Core features: It has a perfect linear phase response, just like a smooth conveyor belt, allowing the signal waveform to pass "intact" without distortion.

Application scenarios: Fields with high requirements for waveform integrity such as digital communication and image processing. For example, in high-definition video transmission, Bessel filters can ensure the phase synchronization of image pixels, avoiding blurry images and ghosting; in medical ultrasound equipment, they can make the outline of ultrasound images of organs clear without stretching or deformation.

The Technical Foundation and People's Livelihood Value of Basic Filtering

From simple RC low-pass circuits to sophisticated Butterworth filter networks, classic filtering technologies, rooted in solid theories, have built the "first line of defense against noise" in the electronic world. They may not be as intelligent and flexible as digital filtering, but with the advantages of stability, reliability, and controllable costs, they have permeated every field related to our lives, such as medical care, industry, and consumer electronics. It is these seemingly basic "frequency screening" logics that enable the weak signals captured by sensors to remain true, and allow data to be stripped of value from messy noise, becoming the prerequisite for all subsequent signal processing. In today's era of rapid development of intelligent technology, classic filtering technologies remain an irreplaceable technical cornerstone. With the simple logic of "removing the dross and retaining the essence", they safeguard the original signal authenticity of electronic systems, laying a solid foundation for people's livelihood security and industrial upgrading.