Phase (Audio Signal)
Definition
Phase (Audio Signal)
Phase describes the time relationship of a periodic signal relative to a reference point, expressed in degrees (0 to 360) or radians. In audio measurement, phase response shows the frequency-dependent delay through a system. Proper phase alignment between multiple speakers ensures constructive addition rather than cancellation. SonaVyx displays phase alongside magnitude in transfer function measurement.
Phase = arctan(Im[H(f)] / Re[H(f)]) degrees, where H(f) is the complex transfer function
How Phase Is Measured
Phase is extracted from the complex transfer function H(f) by computing the arctangent of the imaginary to real component ratio at each frequency. SonaVyx displays wrapped phase (-180 to +180 degrees) and can unwrap the phase to show accumulated delay. Group delay — the negative derivative of phase with respect to frequency — reveals frequency-dependent timing differences critical for crossover alignment.
Practical Example
Two speakers covering the same area show 180 degrees phase difference at the crossover frequency of 1.2 kHz, causing a deep cancellation notch. SonaVyx identifies the polarity inversion and the engineer swaps the polarity of one speaker. The phase difference at crossover drops to near 0 degrees, and the magnitude dip disappears, restoring smooth coverage through the crossover region.
Phase vs Polarity
Phase and polarity are often confused but are fundamentally different. Polarity is a fixed inversion of the entire signal — swapping positive and negative. Phase is a frequency-dependent time delay that varies with frequency. Reversing polarity adds exactly 180 degrees at all frequencies simultaneously. A 1 ms delay adds 360 degrees at 1 kHz, 720 degrees at 2 kHz, and 180 degrees at 500 Hz — the phase shift increases linearly with frequency.
Wrapped vs Unwrapped Phase
Wrapped phase constrains values between -180 and +180 degrees, causing apparent jumps when the phase crosses these boundaries. Unwrapped phase removes these jumps, revealing the total accumulated delay. Unwrapped phase is more useful for understanding system latency and comparing delay between speakers. A linearly decreasing unwrapped phase indicates constant group delay (all frequencies delayed equally).
Group Delay
Group delay is the negative derivative of phase with respect to frequency: τg = -dφ/dω. It represents the time delay experienced by a narrow band of frequencies. Constant group delay means all frequencies arrive at the same time (linear phase). Variable group delay causes temporal smearing of transients. Crossover filters and room reflections are common sources of group delay variation in sound systems.
Phase in Speaker Alignment
When multiple speakers cover the same area, their phase responses must align at the crossover frequency for coherent summation. A phase difference of 90 degrees at crossover reduces summation by 3 dB. A 180-degree difference causes complete cancellation. SonaVyx displays the phase of each speaker's transfer function, enabling engineers to adjust delay and polarity for optimal phase alignment at the crossover point.
Try It Now
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