Howtosignalprocessing
Key Equations
| Sum Formula for Cosine | cos(α+β)=cosαcosβ−sinαsinβ |
|---|---|
| Difference Formula for Cosine | cos(α−β)=cosαcosβ+sinαsinβ |
| Sum Formula for Sine | sin(α+β)=sinαcosβ+cosαsinβ |
| Difference Formula for Sine | sin(α−β)=sinαcosβ−cosαsinβ |
| Sum Formula for Tangent | tan(α+β)=tanα+tanβ1−tanαtanβ |
- Is the sum of two sinusoids a sinusoid?
- What is sum of sinusoids?
- How do you combine two sinusoidal functions?
Is the sum of two sinusoids a sinusoid?
The Sum of Two Real Sinusoidal Functions
As it turns out, as you might expect, the sum of two equal-frequency real sinusoids is itself a single real sinusoid.
What is sum of sinusoids?
The sum of sinusoids with the same frequency is also a sinusoid. Remembering The angle sum rule, we can write any sinusoid as a weighted sum of a sine and a cosine: (2)Asin(ωt+θ)=Asin(ωt)cos(θ)+Acos(ωt)sin(θ)=A′sin(ωt)+A″cos(ωt)
How do you combine two sinusoidal functions?
Adding two sinusoids of the same f'requency but ditl'erent amplitudes and phases results in another sinusoid (sin or cos) of same fiequency. The resulting amplitude and phase are different from the amplitude, and phase of the two original sinusoids, as illustrated with the example below.
