How to Generate a Basic Sinusoid

Find out how to construct a simple sinusoid.

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Mastering the DSP toolkit starts with a basic sinusoidal signal.

A sinusoid

As a function of time tt, a real sinusoid is given by:

x(t)=Acos(2πft+ϕ)x(t) = A \cos(2\pi f t+\phi)

There are three parameters that determine the actual signal:

  • Amplitude AA
  • Frequency ff in cycles/sec or ω=2πf\omega=2\pi f in radians/sec, and the time period is T=1fT=\frac{1}{f} or 2πω\frac{2\pi}{\omega}
  • Phase ϕ\phi

It’s a convention to use a cosine wave because we know that a sine wave is also a cosine wave with a specific phase.

sin2πft=cos(2πft90)\sin 2\pi f t = \cos \left(2\pi f t - 90^\circ\right)

A really basic sinusoid with A=1A=1, f=1f=1 and ϕ=0\phi=0 is shown below:

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