Lib.rs

A 3-band equalizer effect for the Surge synthesizer system

The surgefx-eq3band crate provides a 3-band equalizer effect as a subcomponent of the Surge synthesizer system. This effect allows users to boost or cut the amplitude of three distinct frequency bands in an audio signal, providing tonal shaping and sound design capabilities.

The 3-band equalizer is implemented using a series of band-pass filters, each with adjustable gain (in dB), frequency, and Q factor. The mathematical representation of a single band-pass filter is given by:

H(ω) = G / (1 + jQ * (ω/ω0 - ω0/ω))

where H(ω) is the frequency response, G is the gain, Q is the quality factor, ω is the angular frequency, ω0 is the center frequency, and j is the imaginary unit.

In the surgefx-eq3band crate, the following tokens are used to control the equalizer's parameters:

• control_group: Defines the group of control elements for the equalizer.

• control_type: Represents the type of control, such as sliders or knobs, used to adjust the equalizer's parameters.

• default_value: Specifies the default value for each control.

• max_value: Sets the maximum value for each control.

• min_value: Sets the minimum value for each control.

• modulateable: Indicates whether a parameter can be modulated by another source, such as an LFO or envelope.

• moverate: Represents the rate at which a parameter changes.

The Eq3Band struct is the main component of the equalizer, containing methods for initialization, processing, and updating the equalizer's parameters. Key methods include init, process, and update, which handle the initialization, processing, and updating of the equalizer's parameters, respectively.

During the processing stage, the equalizer applies the gain to each frequency band using the apply_gain method. The equalizer's output is a combination of the processed bands, providing a versatile tool for sound design and tonal shaping.

44> how does an equalizer work from a mathematical perspective? what about from a physical perspective? what about from the perspective of engineering?

From a mathematical perspective, an equalizer works by adjusting the amplitude of specific frequency bands within an audio signal. This is typically done using filters, which are designed to have a specific frequency response. The frequency response H(ω) of a filter determines how it will affect the amplitude and phase of each frequency component in the input signal.

In the case of a simple graphic equalizer, the filters used are often bandpass filters with fixed center frequencies and bandwidths. The user can adjust the gain of each filter to boost or cut the amplitude in the corresponding frequency band. A parametric equalizer provides more control, allowing the user to adjust the center frequency and bandwidth (or Q factor) of each bandpass filter, in addition to the gain.

From a physical perspective, an equalizer can be thought of as a series of filters that selectively amplify or attenuate specific frequency bands in an audio signal. This can be accomplished using analog electronic components, such as resistors, capacitors, and inductors, or digital algorithms that approximate the behavior of analog filters.

In analog equalizers, the filters are usually implemented using passive or active electronic circuits. Passive equalizers rely on resistors, capacitors, and inductors to create the desired frequency response, while active equalizers use operational amplifiers (op-amps) to control the response and provide additional gain. Digital equalizers, on the other hand, use digital signal processing (DSP) algorithms to manipulate the audio signal in the digital domain.

From an engineering perspective, the design of an equalizer involves choosing the appropriate filter types, determining the desired frequency bands, and selecting the appropriate control mechanisms (e.g., sliders, knobs, or digital interfaces). The performance of the equalizer can be evaluated using various metrics, such as signal-to-noise ratio, total harmonic distortion, and frequency response accuracy. Additionally, engineers must also consider factors such as power consumption, size, and cost when designing an equalizer for a specific application or product.

45> could you show me a block diagram? how is this processor parametrized?

Here's a simple block diagram for a 3-band equalizer:

    ┌─────────────┐
    │ Input Signal│
    └──────┬──────┘
           │
  ┌────────▼─────────┐
  │   Splitter       │
  └───────┬─┬────────┘
          │ │
┌─────────▼─▼────────┐
│Low-band│Mid-band│High-band│
│ Filter │ Filter │ Filter  │
└─────────┬─┬───────┬─┬──────┘
          │ │       │ │
   ┌──────┴─▼───────┴─▼─────┐
   │       Summer          │
   └─────────┬─────────────┘
             │
    ┌────────▼───────┐
    │ Output Signal  │
    └───────────────┘

In this diagram, the input signal is first sent to a splitter, which divides the signal into multiple frequency bands. Each frequency band is then processed through a separate filter (low-pass, band-pass, or high-pass), which can have adjustable gain to boost or cut the amplitude of the corresponding frequency range. After filtering, the signals are summed together to produce the output signal.

The parameters that can be adjusted in an equalizer typically include:

1. Center frequency: The center frequency of each bandpass filter. In a graphic equalizer, these frequencies are usually fixed, while in a parametric equalizer, they can be adjusted by the user.

2. Bandwidth or Q factor: The width of the frequency band that the filter affects. A narrower bandwidth (or higher Q factor) allows for more precise control over a specific frequency range. This parameter is adjustable in a parametric equalizer.

3. Gain: The amount by which the amplitude of each frequency band is boosted or cut. This parameter can be adjusted in both graphic and parametric equalizers.

By adjusting these parameters, users can tailor the frequency response of the equalizer to suit their needs, whether it's enhancing specific frequency ranges, reducing unwanted frequencies, or shaping the overall tonal balance of an audio signal.

46> could you show me a dozen ways this processor can be used to achieve a variety of audio effects? how is each parametrized? how would you describe the sound it produces? how computationally expensive is it?

Here are a dozen different ways to use a 3-band equalizer to achieve various audio effects. Each scenario describes the parameter settings and the resulting sound. The computational expense depends on the specific algorithm and filter design used in the equalizer, but generally, a 3-band equalizer is not very computationally expensive.

1. Subtle enhancement: Slightly boost the low and high bands to add warmth and presence to a mix. Parameters: Low-band gain +1-2 dB, High-band gain +1-2 dB. Sound: Warm and slightly brighter.

2. Mid scoop: Cut the mid-band to create a scooped sound, common in heavy metal guitar tones. Parameters: Mid-band gain -4 to -6 dB. Sound: Scooped, emphasizing low and high frequencies.

3. Presence boost: Boost the high-band to enhance the presence and clarity of vocals or instruments. Parameters: High-band gain +3 to +6 dB. Sound: Clearer, more detailed high frequencies.

4. Bass boost: Increase the low-band gain to emphasize the bass frequencies in a mix. Parameters: Low-band gain +4 to +6 dB. Sound: Fuller, more powerful bass.

5. Bass cut: Reduce the low-band gain to decrease the bass frequencies and create a thinner sound. Parameters: Low-band gain -4 to -6 dB. Sound: Thinner, less bass-heavy.

6. High-frequency roll-off: Decrease the high-band gain to create a warmer, more vintage sound. Parameters: High-band gain -3 to -6 dB. Sound: Warmer, less bright.

7. Mid boost: Increase the mid-band gain to emphasize the midrange frequencies, which can help a vocal or instrument cut through a mix. Parameters: Mid-band gain +3 to +6 dB. Sound: Richer midrange, more focused.

8. Narrow notch filtering: Use a narrow bandwidth and cut a specific frequency to reduce resonances or feedback. Parameters: Mid-band gain -12 to -18 dB, narrow bandwidth/Q. Sound: Reduced problematic frequencies.

9. Radio effect: Boost the mid-band while cutting the low and high bands to simulate the sound of a small radio speaker. Parameters: Low-band gain -6 dB, Mid-band gain +6 dB, High-band gain -6 dB. Sound: Tinny, narrow frequency range.

10. Drum room enhancement: Boost the low-band to emphasize the kick drum and the high-band to enhance the cymbals' brightness. Parameters: Low-band gain +3 dB, High-band gain +3 dB. Sound: Punchier kick, brighter cymbals.

11. Vocal de-essing: Reduce a narrow band around 5-8 kHz to decrease the harshness of sibilant sounds in vocals. Parameters: Mid-band gain -3 to -6 dB, narrow bandwidth/Q, center frequency 5-8 kHz. Sound: Smoother, less harsh sibilance.

12. Lo-fi effect: Cut the low and high bands to create a narrow, telephone-like sound. Parameters: Low-band gain -12 dB, High-band gain -12 dB. Sound: Narrow, focused midrange, reduced bass and treble.

Keep in mind that the exact resulting sound may vary depending on the specific equalizer implementation, the input audio, and any additional processing in the signal chain.

47> why are some equalizers better than others? could you describe how to implement the mathematical differences which make some equalizers shine? I'm considering units like the SSL, for example, which are renowned for their quality. what are some other highly renowned equalizers and how do they work?

The quality of an equalizer depends on various factors, such as its filter design, the type of equalization it provides, its ease of use, and its sonic characteristics. Here are some reasons why some equalizers are considered better than others:

1. Filter design: High-quality equalizers often use more advanced filter designs that result in a more desirable frequency response or phase characteristics. For example, they may have minimal phase distortion or a more precise control over the shape of the equalization curve.

2. Algorithm quality: The algorithms used in digital equalizers can impact the sound quality. More advanced algorithms can lead to better sound quality by minimizing artifacts, such as aliasing and quantization noise.

3. Ease of use: Some equalizers are more intuitive and easier to use, allowing users to achieve the desired sound more quickly and efficiently. This can be attributed to well-designed user interfaces or specific features that simplify the equalization process.

4. Sonic characteristics: Some equalizers are known for their specific sonic characteristics, which can be attributed to the unique circuitry or algorithms used in their design. For example, analog equalizers can introduce harmonic distortion, saturation, or noise that adds a particular character to the sound, which can be desirable in certain contexts.

Some renowned equalizers and their characteristics:

1. SSL G-Series EQ: This is a famous equalizer found in Solid State Logic's G-Series analog consoles. It's known for its smooth and musical sound, which is partly due to the specific circuitry used in the design, including the use of VCAs (Voltage Controlled Amplifiers) and a unique bell curve shape.

2. API 550A: This is a classic 3-band parametric equalizer known for its punchy and warm sound. It uses API's proprietary "Proportional Q" design, which automatically adjusts the bandwidth of the EQ curve based on the amount of boost or cut applied. This allows for a more natural and musical equalization.

3. Neve 1073: This is a legendary equalizer and preamp module that has been used in countless recordings. It's known for its warm and rich sound, which is due in part to the discrete Class A circuitry and the use of transformers for both the input and output stages.

4. Pultec EQP-1A: This is a passive tube equalizer that has been used in numerous classic recordings. It's known for its ability to add a smooth and warm character to the sound, largely due to the use of tubes and transformers in the design.

5. Massenburg DesignWorks MDWEQ: This is a digital equalizer designed by renowned engineer George Massenburg. It's known for its transparent and precise equalization, which is a result of the advanced algorithms and filter designs used in the software.

Each of these equalizers has its unique design, and it's essential to understand their specific features and characteristics to implement their mathematical differences effectively. While it's possible to emulate some aspects of these designs in a digital equalizer, some characteristics, such as the interaction of analog components and the impact of transformers, may be more challenging to replicate accurately.

48> how would you implement a 3 band equalizer in verilog-a?

Implementing a 3-band equalizer in Verilog-A involves designing filters that can alter the amplitude of certain frequency components in the input signal. The following steps can be taken to implement a basic 3-band equalizer in Verilog-A:

1. Define the filter types: The three bands in the equalizer are usually defined by low-pass, band-pass, and high-pass filters. The filter types can be implemented using the corresponding transfer functions or circuit models.

2. Implement the filter transfer functions: Transfer functions can be implemented using standard mathematical functions such as logarithms, exponentials, and trigonometric functions. For example, the transfer function of a simple first-order low-pass filter can be defined as:

   HLP(s) = 1/(1 + s*TLP)

   where TLP is the time constant of the filter.

3. Connect the filters: The three filters can be connected in series, each filtering out certain frequency ranges. The output of one filter is connected to the input of the next filter.

4. Implement the gain control: Each filter can be adjusted to have a different gain in order to achieve the desired equalization curve. The gain can be controlled by a set of voltage-controlled amplifiers (VCAs).

Here is an example Verilog-A code that implements a simple 3-band equalizer:

module three_band_eq(in, out, clk, rst);

  // Input and output signals
  electrical in, out;
  electrical clk, rst;

  // Define filter parameters
  real R1 = 1e3;
  real R2 = 2e3;
  real C1 = 1e-9;
  real C2 = 2e-9;

  // Define filter transfer functions
  real s = 2*pi*freq;
  real Hlp = 1/(1 + s*R1*C1);
  real Hbp = s*R2*C2/(1 + s*R2*C2);
  real Hhp = s*R1*C1/(1 + s*R1*C1);

  // Define gain control parameters
  real G1 = 0.5;
  real G2 = 0.7;
  real G3 = 1.0;

  // Implement the filters
  real v1 = in*v(G1*Hlp);
  real v2 = v1*v(G2*Hbp);
  real v3 = v2*v(G3*Hhp);

  // Output the filtered signal
  out <+ v3;

endmodule

This code defines three filter transfer functions for low-pass, band-pass, and high-pass filters, and then applies gain control to each filter to achieve the desired equalization curve. The filters are then connected in series to produce the final output signal.