Frequency Filters Explained: EEG & EMG Applications

Bio signals are characterized by voltage and current, with frequency (0.01-200 Hz) and amplitude (microvolts to millivolts) being the most important properties. These signals are very weak and easily affected by environmental interference. Three major bio signals are studied: ECG (heart performance, 0.01-200 Hz, 10-500 μV) uses chest electrodes to measure cardiac cycles via PQRST complex; EEG (brain activity, 0.1-200 Hz, 2-200 μV) uses helmet-shaped electrodes with ~64 electrodes to measure brain states like sleep stages; EMG (muscle activity, 10-2000 Hz, 10-1000 μV) uses needle or surface electrodes to measure muscle contraction. All require controlled environments due to signal weakness.

Electromyography (EMG) is a technique for evaluating and recording the electrical activities produced by skeletal muscles, measuring the sum of motor unit action potentials as bipolar signals with amplitudes ranging from 0 to 10 mV and frequencies between 6 to 500 Hz, with three main types including surface EMG (non-invasive, electrodes on skin), high-density EMG (multiple closely spaced electrodes for spatial analysis), and needle EMG (invasive, single motor unit recording); while Electroencephalography (EEG) is a non-invasive neurophysiological technique that records electrical activities of the brain through electrodes placed on the scalp, detecting brain waves categorized into frequency bands (Alpha 8-13 Hz for relaxed wakefulness, Beta 14-30 Hz for alert cognitive activity, Theta 4-7 Hz for light sleep/creativity, Delta 0.5-4 Hz for deep sleep, and Gamma 30-100 Hz for heightened cognitive processing), with applications in diagnosing neurological disorders like epilepsy and sleep disorders, monitoring brain functions, and enabling brain-computer interfaces.

EEG (electroencephalogram) measures brain electrical activity to diagnose neurological conditions like epilepsy, seizures, strokes, encephalitis, and degenerative diseases such as Alzheimer's, while EMG (electromyography) assesses nerve and muscle function through nerve conduction studies and needle examinations to detect nerve damage from conditions like carpal tunnel syndrome and diabetes; both procedures require specialized two-year college training and strong interpersonal skills to help neurologists diagnose patients effectively.

Electroencephalography (EEG) is a diagnostic procedure that measures electrical activity in the brain using electrodes placed on the scalp, while Electromyography (EMG) measures electrical activity produced by skeletal muscles; both are essential neurophysiological tests used to diagnose neurological conditions, assess muscle function, and study brain and muscle disorders.

Electrophysiological signals are electrical potentials generated by biological tissues that can be measured and analyzed for diagnostic and research purposes. ECG (electrocardiogram) measures heart electrical activity through P, QRS, and T waves, with limb leads providing frontal plane views and chest leads (V1-V6) providing horizontal plane views. EMG (electromyogram) captures muscle electrical signals, typically around 3mV at 1kHz, useful for rehabilitation and motor skill assessment. EEG (electroencephalogram) records brain wave activity for conditions like epilepsy and dyslexia. Signal conditioning circuits are essential for acquiring these bio-potentials, requiring proper electrode placement, impedance reduction, and appropriate frequency response filtering to isolate the desired signals from environmental noise.

Signal-to-noise ratio (SNR) quantifies measurement quality as the ratio of signal average to noise standard deviation (linear definition) or in decibels (logarithmic). Higher SNR means tighter clustering around the mean value. Four functional parts comprise typical optical experiments: laser source, experiment design, detector (converting optical to electronic signals), and signal analysis chain. Noise sources include 1/f pink noise near DC, white noise floor (typically detector shot noise representing best-case performance), and spikes at 50/60 Hz power lines or radio frequencies. Averaging acts as low-pass filtering around DC, reducing high-frequency noise contributions.

The signal-to-noise ratio measures how much desired audio signal exists compared to unwanted noise. Early audio equipment from the 1960s-70s had significant 60Hz or 50Hz hum from electrical lines, which made it difficult to hear music clearly. Hifi standards emerged to eliminate this noise.

Raw signals from muscle and nerve recordings contain three common noise sources: (1) Inherent noise, which originates within electrical equipment and can be reduced by using high-quality electronic components; (2) Ambient noise, which comes from electromagnetic radiation sources including electrical equipment, light bulbs, and fluorescent lamps, with the dominant source being 50 or 60 Hz radiation from power supplies; (3) Motion artifacts, which generate unwanted signals due to electrode-skin contact (impedance) or wire movement, typically occurring in the 0-20 Hz frequency range.

The Signal-to-Noise Ratio (SNR) is a unitless quantity that characterizes the relative strength of a desired signal compared to background noise, defined as the ratio of signal power to noise power (S/N) or the ratio of RMS signal voltage to RMS noise voltage. SNR can be expressed in decibels (dB) using the formulas: SNR(dB) = 10 × log₁₀(S/N) for power ratios or SNR(dB) = 20 × log₁₀(V_s/V_n) for voltage ratios, where the power SNR equals the square of the voltage SNR. Common reference points include 0 dB (equal signal and noise power), 3 dB (signal power is twice the noise power), and -3 dB (signal power is half the noise power).

SNR stands for Signal to Noise Ratio, which is present in every cable. In layman's terms, the signal is transferred to your modem via cable, but this cable absorbs electromagnetic interference on its way from the cabinet to your modem. This absorbed interference is termed as 'noise' in networking language. The four prime factors causing this noise are: (1) Other cables passing close to your cable, especially electric cables; (2) All connectors or joints in the line, especially if deteriorated; (3) If your cable passes close to motors or transformers; (4) If your cable passes close to radio transmission systems.

RC circuits exhibit fundamental frequency-dependent behavior based on capacitor reactance. At low frequencies, capacitors block current (high impedance); at high frequencies, they act as shorts (low impedance). This enables RC circuits to function as filters. The complex voltage gain for a series RC circuit is (jωRC)/(1 + jωRC), yielding magnitude |V2/V1| = ωRC / √(1 + (ωRC)²). When output measures across the resistor, it acts as a high pass filter (attenuating low frequencies, passing high frequencies). When output measures across the capacitor, it acts as a low pass filter (passing low frequencies, blocking high frequencies). The break frequency occurs at ω_break = 1/(RC), where magnitude equals 1/√2. These principles form the foundation of passive filter design.

Electronic filters remove unwanted frequency components from signals. Two main types exist: low-pass filters allow low frequencies while blocking high frequencies, and high-pass filters do the opposite. The pass-band represents frequencies that pass through, while the stop-band represents blocked frequencies. RC filters use resistors and capacitors as frequency-dependent voltage dividers. Unlike resistors, capacitors have impedance Z = -j/(ωC) that changes with frequency, enabling selective signal processing. At DC (f=0), capacitors act as open circuits; at high frequencies, they act as short circuits. This frequency-dependent behavior enables the fundamental operation of passive filters.

RC filters are passive circuits using resistors and capacitors to selectively pass or block frequencies. Low-pass filters connect input to resistor, then capacitor to ground, passing low frequencies while blocking high ones. High-pass filters reverse this topology, passing high frequencies while blocking low ones. The cutoff frequency is f_c = 1/(2πRC), derived from the RC time constant (τ = RC) representing charging/discharging time. Capacitors block DC but allow AC, with behavior depending on voltage integral across phases. Low-pass filters work because low frequencies fill capacitors quickly, overflowing to output; high frequencies don't fill capacitors, flowing to ground. High-pass filters block low frequencies that fill capacitors, allowing high frequencies to reach output through the resistor.

Analog circuit design is essential because everything in the real world operates on analog principles - sensors, microphones, cameras, and temperature sensors all produce analog signals. Analog circuit designers perform three core functions: amplifying weak signals, filtering noise, and performing ADC/DAC conversions. Network theory serves as the fundamental language of electronics, similar to programming languages in computer science. Without understanding network fundamentals, circuit design becomes guesswork. A circuit is a combination of electrical components connected in a closed path with power supply and ground, enabling current flow through every element. A network is any combination of electrical components, whether the path is closed or open. Every circuit is a network, but not every network is a circuit - a network becomes a circuit only when it has a complete closed path with power rails. In VLSI design, chips before power routing act like networks (no closed path), while powered chips become complete circuits. Resistance opposes current flow, similar to friction opposing motion. It protects components by limiting current. The formula R = ρL/A shows resistance depends on resistivity, length, and cross-sectional area. Ohm's Law (V = IR) governs voltage drop across resistive elements. In IC layouts, metal wires have inherent parasitic resistance causing voltage drops along interconnects. Longer wires increase resistance and delay (RC time constant), while wider wires decrease resistance but consume more layout area. Via count affects interconnect resistance - more vias provide better conductivity. The RC time constant (τ = RC) determines how quickly capacitors charge or discharge through resistors. Higher resistance means longer time constants, meaning slower charging/discharging and greater delay. Capacitors store energy in electric fields between conducting plates separated by dielectrics, with stored energy given by E = ½CV². They resist sudden voltage changes by drawing or supplying current. MOSFETs have inherent parasitic capacitances (gate-to-body, gate-to-source, gate-to-drain) that affect high-frequency performance. As frequency increases, these capacitances cause reactance to rise, reducing amplifier gain.

Passive RC filters use resistors and capacitors for low-frequency signal processing. Resistors offer wide value ranges and low cost, while capacitors provide compact form factors. Unlike resistors with constant impedance, capacitors exhibit frequency-dependent behavior where impedance decreases with increasing frequency. This property enables filter functionality. Basic RC filters include high-pass and low-pass configurations: placing the capacitor after the resistor creates a low-pass filter that shunts high frequencies, while placing it in-line creates a high-pass filter allowing only high frequencies to pass. Both share the same corner frequency calculated from component values but exhibit slow transitions with approximately -20 dB attenuation per decade.