Sinusoids

Sum of sinusoids with different frequency

Sum of sinusoids with different frequency
  1. Can you add sinusoids with different frequencies?
  2. What is the frequency of a sum of sinusoids?
  3. When two periodic sinusoids signals of different frequencies are added then the result is?
  4. How do you find sum of sinusoidal?

Can you add sinusoids with different frequencies?

Adding sinusoids with different frequencies results in a signal that is no longer sinusoidal. But is it periodic? If the frequencies of the added sinusoids are integer multiples of the fundamental, the resulting signal will be periodic. Figure 2: Adding sinusoids at 3, 6, 9 Hz produces a periodic signal at 3 Hz.

What is the frequency of a sum of sinusoids?

For a sum of sinusoids, the fundamental frequency is the greatest common divisor of all the involved frequencies, assuming it exists. In your example, the fundamental is 50 Hz.

When two periodic sinusoids signals of different frequencies are added then the result is?

When two sinusoids of different frequencies are added together the result is another sinusoid modulated by a sinusoid.

How do you find sum of sinusoidal?

By the well-known addition formula, Asin(ωt+ϕ)=Asin(ωt)cos(ϕ)+Acos(ωt)sin(ϕ)=A′sin(ωt)+A″cos(ωt). a linear combination of two or more sinusoids can be expressed as a linear combination of a sine and a cosine, hence can be expressed as a single sinusoid.

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