How does a low-pass filter affect sound?
What is a Low-Pass Filter?
A low-pass filter (LPF) is an electronic circuit or signal processing filter that allows low-frequency signals to pass through while attenuating or blocking higher frequency signals (see How Do LPFs Work?). The cutoff frequency of a low-pass filter determines the upper limit of frequencies that are allowed to pass – frequencies above the cutoff are attenuated. For example, a low-pass filter with a cutoff frequency of 1 kHz would allow frequencies below 1 kHz to pass unfiltered, while frequencies above 1 kHz would be reduced in amplitude.
Low-pass filters are commonly used in audio applications to reduce unwanted high frequency noise like tape hiss or digitally induced noise. By attenuating frequencies above the audible range, a low-pass filter can help clean up an audio signal by removing these high frequency components while allowing the desired lower frequencies to pass through unaffected.
How Sound Frequencies Work
Sound is produced by vibrations. The rate at which something vibrates determines the frequency of a sound wave. Frequency refers to the number of vibrations per second, measured in Hertz (Hz). Low-frequency sounds have a small number of vibrations per second, while high-frequency sounds have many vibrations per second.
The normal human hearing range is approximately 20 Hz to 20,000 Hz, according to pcmag.com. This means humans can typically hear frequencies between 20 vibrations per second on the low end, to 20,000 vibrations per second on the high end. High frequencies like those used in speech and music tend to be in the 2,000-5,000 Hz range. Lower frequencies under 250 Hz tend to be felt more than heard.
A low-pass filter allows lower frequencies to pass through while blocking higher frequencies. This has the effect of removing the high-frequency components and keeping the lower frequencies that are more felt than heard. The cutoff frequency determines where the filter starts blocking higher frequencies.
Why Use a Low-Pass Filter?
Low-pass filters are commonly used in audio production and sound design for several key reasons:
First, they can help reduce high-frequency hiss and noise in recordings and samples. Frequencies above the cutoff point set by the filter are attenuated, cleaning up any unwanted artifacts or distortion in the high end (source). This allows the important mid and low frequencies to come through more clearly.
Second, low-pass filters smooth out harsh, bright, or grating tones. By filtering out extreme highs, the sound becomes warmer, darker, and less fatiguing on the ears. This can help things sit better in a mix or make certain sounds less abrasive (source).
Finally, low-pass filters are an easy way to focus attention on the bass and low-end of a track. Letting more low frequencies through while attenuating mids and highs makes the bottom-end more pronounced. This technique can help reinforce the groove and rhythmic foundation of dance music and hip-hop (source).
Types of Low-Pass Filters
There are two main types of low-pass filters: passive and active. Passive filters use only resistors, capacitors and inductors to filter the signal. They do not require an external power source. Active filters use active components like transistors and op amps in addition to resistors and capacitors, and require an external power source.
Low-pass filters can also be categorized as analog or digital. Analog low-pass filters operate on continuous analog signals. They provide a smooth frequency response. Common types of analog low-pass filters include Butterworth, Chebyshev, and Bessel filters. Digital filters operate on sampled digital signals using computer algorithms. They can achieve very precise filter characteristics but have a stair-step frequency response.
Some common types of low-pass filters include:
- RC filter – Uses a resistor and capacitor to form a simple single-pole low-pass filter
- RL filter – Uses a resistor and inductor to create a low-pass filter
- Butterworth filter – Maximally flat frequency response with no ripples
- Chebyshev filter – Can have a sharper cutoff than Butterworth but with ripple in the passband
- Bessel filter – Provides a linear phase response and minimizes signal distortion
The choice of low-pass filter depends on the characteristics needed for the particular application, such as sharpness of cutoff, phase linearity, and component availability.
How Low-Pass Filters Work
Low-pass filters work by attenuating frequencies above the cutoff frequency, allowing lower frequencies to pass through the filter unchanged. They use a combination of capacitors and resistors or inductors to create a frequency-dependent response.
The filter circuitry creates a voltage divider that reduces the amplitude of the incoming signal based on its frequency. Higher frequencies are more easily diverted through the resistor or inductor in the filter, while lower frequencies are passed through the capacitor more readily. This selectively attenuates the higher frequencies.
As the frequency increases beyond the cutoff frequency (also known as the -3dB point), the attenuation increases sharply, creating a rolloff slope. The slope depends on the number of poles in the filter circuit, with each additional pole increasing the slope by -20dB per decade. Standard first-order filters have a -20dB/decade rolloff.
The cutoff frequency is determined by the values chosen for the resistor and capacitor. Adjusting these values changes the frequency response, shifting the cutoff point and rolloff slope as needed for the application.
Overall, the low-pass filter circuitry forms a high-impedance path to ground for high frequencies, attenuating them through the resistive branch, while allowing lower frequencies to readily pass through the capacitor with minimal resistance.
Cutoff Frequency
The cutoff frequency is the frequency at which the filter’s output power has dropped to half (-3 dB) of the input power. For a low-pass filter, frequencies above the cutoff frequency are attenuated, while frequencies below it pass through largely unchanged.
For audio applications, the cutoff frequency determines the highest frequency that will be allowed to pass through the filter. Sounds with frequencies above the cutoff will be muted or dampened by the filter. This removes unwanted high frequency noise or bright tones, resulting in a smoother, darker sound.
Some low-pass filters have a fixed cutoff frequency, while others allow it to be adjusted. An adjustable cutoff is useful for tailoring the effect to the source audio. For example, setting a lower cutoff frequency will remove more high frequencies and create a deeper, mellower effect on the sound.
The cutoff frequency depends on the filter’s circuit components. For example, an RC filter’s cutoff can be calculated using the resistor (R) and capacitor (C) values. The specific formula varies by filter type and order.
Filter Slope
The filter slope refers to how steeply the filter cuts off frequencies above the cutoff point. A gradual slope will allow some higher frequencies to pass through, while a steep slope will sharply eliminate frequencies above the cutoff. The slope is measured in decibels per octave (dB/oct). A filter with a slope of 12dB/oct will attenuate frequencies by 12dB for each octave above the cutoff frequency.
A steeper slope means the filter cuts off frequencies more abruptly. This results in a more noticeable change in sound timbre as frequencies are removed. A more gradual slope creates a more subtle filtering effect. For audio applications like reducing harsh treble, a gentler slope around 6-12dB/oct is often preferred to avoid drastic tonal shifts.
According to this source, extremely steep slopes over 24dB/oct essentially act like a brickwall cutoff. This harsh filtering tends to sound unnatural, but can be useful in applications like eliminating mains hum.
Applications of Low-Pass Filters
Low-pass filters have many practical uses, especially in audio applications. Here are some of the main ways low-pass filters are applied:
Music Production – Low-pass filters are commonly used in music production and mixing to eliminate unwanted high frequencies that can cause harshness or masking effects in a mix. For example, low-passing high-hats can help them sit better in a mix by reducing their high-end sizzle. Low-passing is also used on bass sounds to eliminate muddiness.
Noise Reduction – Low-pass filters can help clean up noisy audio recordings by filtering out high-frequency noise. Things like tape hiss, digital clipping artifacts, or background noise can be reduced by applying a low-pass filter to isolate just the lower fundamental frequencies of the audio.
Audio Effects – Creative use of low-pass filters can produce audio effects like muffled or ‘underwater’ sounds. Electronic musicians use low-pass filters creatively to subtly evolve sounds over time. Low-pass filters are also the basis for ‘wah-wah’ effects by modulating the cutoff frequency.
Low-Pass vs High-Pass
The main difference between a low-pass filter and a high-pass filter is the frequencies they allow to pass through. As the names suggest:
- A low-pass filter allows lower frequencies to pass through while attenuating higher frequencies.
- A high-pass filter does the opposite – it allows higher frequencies to pass through while attenuating lower frequencies.
The cutoff frequency determines where each filter starts attenuating frequencies. In a low-pass filter, frequencies below the cutoff are allowed to pass through unaffected while frequencies above the cutoff are attenuated. In a high-pass filter, frequencies above the cutoff pass through while frequencies below the cutoff are attenuated.
For example, a low-pass filter with a cutoff of 1 kHz would allow frequencies below 1 kHz to pass through unfiltered, while frequencies above 1 kHz would be attenuated. A high-pass filter with a 1 kHz cutoff would do the opposite – frequencies above 1 kHz would pass through, while those below 1 kHz would be attenuated.
So in summary, low-pass filters pass low frequencies while attenuating high frequencies, and high-pass filters pass high frequencies while attenuating low ones. The cutoff frequency determines where each filter starts attenuating the frequencies. See this article for a more in-depth comparison.
Example of Low-Pass Filtering
A good example to demonstrate the audible effects of a low-pass filter is to compare an audio clip before and after applying the filter. This audio clip from Reddit user u/Swift_Dream provides a clear illustration:
Before the low-pass filter is applied, the full frequency spectrum of the clip is audible. The highs, mids, and lows are all present. The clip has a bright, crisp quality.
After enabling the low-pass filter set to a cutoff frequency of 500 Hz, the higher frequencies are attenuated. The sound becomes duller, darker, and muffled. The highs and upper mids are filtered out, leaving only the lower mids and bass frequencies. The clip loses its sense of clarity and detail.
The low-pass filter removes the “sparkle” from the original clip. Comparing the two makes the effect very obvious. The unfiltered version has a full, broadband sound while the filtered version is more narrow and muted.
This demonstrates how a low-pass filter alters the tonal quality of a signal by cutting out the high frequencies. The listener perceives a darker, bass-heavy sound once the filter is applied.