Phasor UGen: Comprehensive Guide With Examples

In the realm of audio synthesis and digital signal processing, the Phasor unit generator (UGen) stands as a fundamental building block for creating a variety of effects and sounds. This article delves into the intricacies of the Phasor UGen, exploring its functionality, parameters, and common applications. We'll discuss how to add, test, and benchmark this versatile tool, ensuring you have a solid understanding of its capabilities.

What is a Phasor UGen?

At its core, a Phasor is a linear ramp generator. Imagine a straight line ascending from a starting point to an ending point. This is precisely what a Phasor does: it produces a signal that increases linearly over time, moving from a defined start value to a defined end value. Once it reaches the end, it wraps back to the start, creating a continuous ramp. This cyclical behavior makes it incredibly useful for a wide range of applications, particularly in audio synthesis.

The Phasor UGen is particularly useful as an index control for other unit generators like BufRd (Buffer Read) and BufWr (Buffer Write). By controlling the read or write position within a buffer, the Phasor can create interesting rhythmic and tonal patterns.

Key Parameters of the Phasor UGen

To effectively utilize the Phasor UGen, it's crucial to understand its key parameters. These parameters dictate the behavior of the ramp and allow for precise control over the generated signal.

1. Trigger (trig)

The trigger input acts as a reset mechanism for the Phasor. When the trigger input crosses from a non-positive value to a positive value, the Phasor's output immediately jumps to the resetPos value. This allows for synchronization and rhythmic control over the ramp.

2. Rate

The rate parameter determines the speed of the ramp. It specifies the amount of change per sample. For instance, a rate of 1 means that the value of each sample will be 1 greater than the preceding sample. This parameter directly influences the frequency of the ramp.

To generate a signal with a specific frequency (freq) oscillating between the start and end values, the rate should be calculated as (end - start) * freq / sr, where sr represents the sampling rate. This formula ensures that the ramp completes one cycle in the desired time.

3. Start

The start parameter defines the beginning value of the ramp. The Phasor's output will begin at this value when triggered or upon wrapping.

4. End

The end parameter specifies the ending value of the ramp. It's important to note that since the end is defined as the wrap point, its value is never actually output. The Phasor will ramp up to a value just below the end value and then immediately jump back to the start.

5. Reset Position (resetPos)

The resetPos parameter determines the value that the Phasor jumps to when triggered. By default, it's set to 0, which is equivalent to the start value. However, it can be set to any value within the range of the ramp, allowing for more complex rhythmic patterns and modulation effects.

Phasor UGen Implementations: .ar() and .kr()

The Phasor UGen is typically available in two forms:

• Phasor.ar(): This is the audio rate version, designed for signals that change rapidly and are used directly in the audio stream.
• Phasor.kr(): This is the control rate version, intended for signals that change more slowly and are used to modulate other parameters. It is often unnecessary because you can achieve the same effect by setting a different sample rate for the audio rate version.

Adding the Phasor UGen

Adding a Phasor UGen to your synthesis environment involves implementing the underlying algorithm in your chosen programming language or audio framework. This typically involves creating a class or function that encapsulates the parameters and logic for generating the ramp.

The core logic for the Phasor UGen involves:

1. Initializing the current value to the start value.
2. Incrementing the current value by the rate each sample.
3. Checking if the current value has reached or exceeded the end value. If so, wrapping back to the start value.
4. Checking the trigger input. If triggered, setting the current value to the resetPos value.
5. Outputting the current value.

Testing the Phasor UGen

Thorough testing is crucial to ensure that the Phasor UGen functions correctly and produces the expected output. This involves creating a variety of test cases that cover different parameter settings and scenarios.

Some common test cases include:

• Testing with different rate values to verify the ramp speed.
• Testing with different start and end values to ensure the ramp spans the correct range.
• Testing the trigger input to verify the reset behavior.
• Testing with different resetPos values to ensure the jump to the correct position.
• Testing both the audio rate (.ar()) and control rate (.kr()) versions (if implemented) to verify their behavior at different sample rates.

Benchmarking the Phasor UGen

Benchmarking is the process of measuring the performance of the Phasor UGen, particularly its computational cost. This is important for ensuring that the UGen is efficient and doesn't consume excessive processing power, especially in complex synthesis environments with many UGens running simultaneously.

Benchmarking typically involves measuring the execution time of the Phasor UGen for a large number of samples. This can be done using profiling tools or by manually timing the execution of the UGen's core logic. The results can then be compared to other UGens or implementations to assess its performance.

Optimization techniques, such as using efficient data structures and algorithms, can be employed to improve the performance of the Phasor UGen. Understanding the performance characteristics of the Phasor UGen is essential for building efficient and scalable audio synthesis systems.

Common Applications of the Phasor UGen

The Phasor UGen's versatility makes it a valuable tool in a wide range of audio applications.

1. Index Control for Buffers

As mentioned earlier, the Phasor is commonly used as an index control for BufRd and BufWr. By mapping the Phasor's output to the read or write position within a buffer, you can create rhythmic loops, time-stretching effects, and other interesting sonic textures.

For example, you can use a Phasor to continuously read through a buffer containing a drum loop, creating a repeating rhythm. By adjusting the rate of the Phasor, you can control the speed of the loop. You could also modulate the rate with another UGen to create tempo variations.

2. Frequency Modulation (FM) Synthesis

Phasors can be used to generate carrier and modulator signals in FM synthesis. By using one Phasor to modulate the frequency of another, you can create complex and harmonically rich sounds.

In FM synthesis, the output of one oscillator (the modulator) is used to vary the frequency of another oscillator (the carrier). The Phasor's linear ramp makes it well-suited for generating both the carrier and modulator signals. By carefully choosing the frequencies and amplitudes of the carrier and modulator, a vast range of sounds can be created, from bell-like tones to complex, evolving textures.

3. Wah-Wah Effects

By using a Phasor to control the cutoff frequency of a filter, you can create a wah-wah effect. The ramp-like nature of the Phasor sweeps the filter's cutoff frequency up and down, producing the characteristic wah sound.

In a typical wah-wah implementation, the Phasor's output is scaled and offset to map it to the desired frequency range of the filter. The rate of the Phasor determines the speed of the wah effect. By modulating the rate or the start and end values, you can create different wah-wah patterns.

4. Scanned Synthesis

Phasors can be used to scan through waveforms or samples stored in a buffer. By mapping the Phasor's output to the buffer's read position, you can effectively