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A Matter Of Frequency: The Nyquist Plot Explained

The most informative frequency domain plot, by far

Harry Nyquist is famed for his work on feedback circuit analysis.

His Nyquist plot makes visual simultaneously the following viewpoints of the signal:

       1. The real part
       2. The imaginary part
       3. The magnitude
       4. The phase angle between the real and
       imaginary parts
       5. The polarity of the system
       6. The causality or non-causality of the
       time behavior
       7. The presence of resonant systems
       8. Non-signal synchronization by

The Nyquist plot can be used in sound system work, where in acoustics the real part is particle pressure and the imaginary part is particle velocity (near a boundary or in a standing wave) and in impedance measurements where the real part is the resistance and the imaginary part is the reactance.

Let’s label some key observations to be made about the Nyquist plot of a pair of loudspeakers.

Figure 1: The analytic signal displayed as a Heyser Spiral.

Dennis Gabor proposed the “analytic signal” which Richard Heyser developed into what has since been named the Heyser Spiral.

The Nyquist plot is the “end view” shadow of the complex analytic signal

An Interesting Anomaly
Apparent non-causal’ signals are being encountered more frequently these days. A non-causal signal is one that arrives before it is sent. Impossible you say?

Yes, in the real world, to the best of our knowledge that is true. But in the world of measurements, thanks to digital technology, we find our measurements telling us a signal is not causal Let’s look at an example:

Figure 2: The “end view” of the Heyser Spiral (Nyquist).

We have a two-way loudspeaker with a crossover frequency of 2 kHz. The energy-time curve (ETC) shows the tweeter arriving before the woofer (Fig. 3-Pg. 2).

We now choose to call the woofer arrival the time point of reference, while attempting to measure the full-range response.

When we do this our measurement instruments will see the tweeter energy as arriving before we sent the signal and the Nyquist will rotate counter clockwise above crossover, indicating non-causality on the instrument, which is not aware that the woofer arrival was chosen as the time reference.

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