ADC Resolution Is Not Measurement Accuracy
A 16-bit reading can be impressively stable and consistently wrong. Worked voltage examples separate quantization, reference error, noise, calibration, and the uncertainty of the whole measurement.
Signals and Signaling
Why Decibels Add While Power Ratios Multiply
A negative signal level is not negative power, and two power readings cannot usually be added as decibels. Worked examples follow a signal chain and expose the references hidden behind familiar dB labels.
Signals Are Everywhere. Why Do We Notice So Few of Them?
A connected but silent phone call, six invented sensor readings, and an empty graph reveal the difference between a signal, a message, and the explanation we build around them.
The Small Dip Produced by a Planetary Transit
A star briefly dims. A planet is one possible explanation, but the depth, repetition, neighboring stars, and measurement process must agree. Worked examples trace the inference from lost light to a candidate world.
Sonar and the Time of a Returning Echo
An echo returning after 0.4 seconds seems to offer a simple distance. The investigation becomes more interesting when sound speed, beam direction, overlapping returns, and the reference for depth enter the calculation.
Traffic Lights and the Shared Rules Behind a Signal
A button press, a detector call, a controller decision, and a green indication are different events. Following them through a constructed intersection reveals why signalling depends on shared rules and observable state.
Seismic Waves as Evidence of Earthquakes
A seismogram records motion at one place. Locating its source requires arrival times, a model of the Earth, and agreement across stations. A calculated example exposes both the power and the limits of that inference.
How a Neuronal Signal Begins
A spike looks like a discrete event, but its beginning depends on continuous voltage, current, and channel dynamics. Simple calculations reveal what the computer analogy captures and what it leaves out.
Aliasing and the Apparently Backward Wheel
A wheel that seems to reverse, two waves that leave identical samples, and a misleading vibration trace expose the missing information inside a digital recording.
What Bandwidth Actually Limits
A wider channel can carry more, but only after we state what happens to signal power, noise, coding, and the rest of the path. A numerical investigation separates spectral width from useful delivery.
A Connected Call with Silence at Both Ends
The call timer is moving, but nobody can hear. A constructed SIP and RTP investigation follows negotiated addresses, packet counters, and decoded audio to find what the connected indicator cannot prove.
Attenuation and Dispersion: Two Ways an Optical Signal Can Fail
A receiver can report enough light and still struggle to recover the data. A constructed fibre link separates missing optical power from signals that arrive spread across time.
One Message Arriving Along Several Paths
A radio receiver can hear several delayed versions of the same transmission. Two-path calculations show why their sum can strengthen, fade, or distort—and why a signal-strength number cannot explain the link by itself.
Time and Frequency: Two Views of One Observation
A clean spectrum can conceal timing, and a densely plotted FFT can promise more detail than a recording contains. Two calculated examples investigate what changes when we change the view.