SAMPLE / PREDICT / COMPARE

From the left half-plane to the unit circle

Keep the same continuous mode and change the sampling period. Does a smaller discrete pole mean faster motion in seconds?

02 / CHECK YOUR PREDICTION

Did the result match your prediction?

Choose a measurable prediction before changing a setting. Record the current result, change one condition, then check. This compares complete recordings, not the replay cursor.

MeasureMy prediction after one change

Prediction and baseline stay in memory for this page only. Use Start a new prediction to choose a new baseline.

Observe and compare

s = σ ± jω → z = exp(sT), |z| = exp(σT), x(t) = exp(σt) cos(ωt)

Decaying mode · |z| < 1

z=0.63041 ± j0.64909 · |z|=0.90484 · Principal angle=0.8 rad

Inspect time (s)

t=0 s · x(t)=1

Cyan: continuous mode. White circles: exact samples. Changing T does not change the continuous curve.

Pinned dashed traces compare the primary signal (continuous x or total y); the list preserves the settings. Up to three comparisons stay in page memory.

Explain what changed

Continue in Lecture Room →

Read the related Field Journal →

MathWorks — Continuous-discrete conversion methods

Change one condition

Real part σ (1/s)

Angular frequency ω (rad/s)

Sample period T (s)

Exact analytic signals. No numerical integration, noise, delay or quantization.

Observe and compare

s = σ ± jω → z = exp(sT), |z| = exp(σT), x(t) = exp(σt) cos(ωt)

Decaying mode · |z| < 1

z=0.63041 ± j0.64909 · |z|=0.90484 · Principal angle=0.8 rad

Inspect time (s)

t=0 s · x(t)=1

Cyan: continuous mode. White circles: exact samples. Changing T does not change the continuous curve.

Pinned dashed traces compare the primary signal (continuous x or total y); the list preserves the settings. Up to three comparisons stay in page memory.