IQ signal generation

A cosine wave of any frequency and phase can be expressed as the sum of its i and q components. Where i is the amplitude of a cosine wave and q the amplitude of a sine wave. Select the frequency and phase of the cosine wave and then use the i and q sliders to match the dashed red line. You can press the Set Automatically button to compute the required values of i and q.

Parameters y(t) = cos(2π · 100 · t − 0°)
Frequency (f)
100Hz
1 Hz1000 Hz
Phase (φ)
0°
360°
Period T
10.00ms
\(y(t) = \cos(2\pi f\,t - \phi)\)
\(y(t)\)
\(i\cos(2\pi f t)+q\sin(2\pi f t)\)
showing 3.0 cycles
Zoom 3.0 cycles

\(y(t)\) can be expressed as the sum of a cosine and a sine wave with amplitudes \(i\) and \(q\) respectively:

\[y(t) = i\cos(2\pi f\,t) + q\sin(2\pi f\,t)\]

where \(i = \cos(\phi),\quad q = \sin(\phi)\)

IQ Components Adjust \(i\) and \(q\) to match \(y(t)\)
i — In-phase
1.00
−11
q — Quadrature
0.00
−11