Before this:What is DSP?
What is a signal?
Key takeaways A signal is a value that changes over time. The sine wave is its fundamental building block, described by three numbers: amplitude (height/strength), frequency (cycles per second), and phase (timing offset). A rotating arrow — a phasor — captures all three at once, which is why signals map so neatly onto the complex plane you’ll meet next.
Before we turn signals into numbers, we need the vocabulary for talking about them. This lesson is that vocabulary. It builds directly on what DSP is and sets up sampling, where the wave becomes data.
What counts as a signal?
A signal is simply any quantity that varies — usually over time. The voltage on an antenna, air pressure at a microphone, the brightness of a pixel down a scan line: all signals. In radio the signal we care about is the strength of an electromagnetic radio wave measured at the receiver, moment to moment.
What makes a signal useful is that its variation carries information. A flat, unchanging value says nothing; the changes are the message.
The sine wave: the atom of signals
The most important signal is the sinusoid — a smooth, repeating wave. It matters because it is the one shape a linear filter can never distort: a sine goes in, a sine of the same frequency comes out, only scaled and shifted. Every other signal can be built by adding sines together, an idea the Fourier transform makes exact.
The three numbers that describe it
A pure sine is fully pinned down by three quantities:
| Property | What it means | Change it and… |
|---|---|---|
| Amplitude | height of the wave — its strength | the signal gets louder or weaker (AM) |
| Frequency | cycles per second, in hertz | the pitch/tuning shifts (FM/FSK) |
| Phase | where in the cycle it starts (its timing) | the wave slides left or right (PSK) |
Those three are exactly the properties a transmitter varies to send information — modulation is nothing more than deliberately changing one of them in step with a message.
The phasor: one arrow for all three
Here is the idea that makes everything later click. Picture the sine wave not as a squiggle but as an arrow spinning around a circle. The arrow’s length is the amplitude, how fast it spins is the frequency, and the angle it starts at is the phase. That spinning arrow is called a phasor, and its shadow on a horizontal line traces out the sine wave.
This is the seed of complex I/Q. When the next unit represents a sample as a point on a plane, it is just recording where that arrow points right now — a picture that becomes complex signals & I/Q.
Quick check: which three numbers fully describe a pure sine wave?
Recap
- A signal is a value that changes over time; its changes carry the information.
- The sine wave is the fundamental building block — the one shape filters don’t distort.
- Amplitude, frequency, and phase fully describe a sine; modulation varies one of them.
- A phasor — a spinning arrow — captures all three, and previews the complex plane.
Next up: how a continuous wave becomes a stream of numbers a computer can hold.
Frequently asked questions
Why is the sine wave so important in signal processing?
The sine wave is the one signal that keeps its shape through any linear filter — it comes out a sine of the same frequency, only scaled and delayed. That property makes sines the natural building blocks of every other signal, which is exactly why the Fourier transform describes any signal as a sum of them.
What is the difference between amplitude, frequency, and phase?
Amplitude is how tall the wave is (its strength), frequency is how many cycles it completes each second (how fast it wiggles), and phase is where in its cycle it starts (its timing offset). Those three numbers fully describe a pure sine wave, and modulation works by deliberately changing one of them.