# What is the sum of two sinusoids?

## What is the sum of two sinusoids?

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. However, the exact equations for all the various forms of that single equivalent sinusoid are difficult to find in the signal processing literature.

When two periodic sinusoids added then the result is?

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

### What is the product of 2 sine waves?

When you multiply two sine waves, you end up with the sum and difference frequencies. So if the input frequency is 600KHz and the local oscillator frequency is 1055kHz, you end up with 455kHz and 1655kHz. Your IF filter is tuned to 455kHz and so you reject the 1655kHz signal. (IF stands for Intermediate Frequency).

What is the period of sum of two periodic functions?

The period of the sum of 2 periodic functions is the LCM of their periods.

#### How do you add Sinusoids to different frequencies?

You can’t add two sines of different frequencies. This is a fundamental limit which much of math and physics takes advantage of. Its also the basis of the fourier transform. To put it simply, sines of different frequencies are orthogonal.

How do you find the period of sum of two periodic functions?

If you are suppose to find period of sum of two function such that, f(x)+g(x) given that period of f is a and period of g is b then period of total f(x)+g(x) will be LCM(a,b).

## Is the sum of two periodic signals periodic?

D. Explanation: sum of two periodic signals is a periodic signal only when the ratio of their time periods is a rational number or it is the ratio of two integers. for e.g., t1/t2 = 5/7 → periodic; t1/t2 = 5 → aperiodic.

What happens when you add two sine waves?

The sum of two sine waves with the same frequency is again a sine wave with frequency . This is used for the analysis of linear electrical networks excited by sinusoidal sources with the frequency .

### How do you add sinusoids to different frequencies?

How do you find the period sum of a periodic function?

#### What happens when you add sinusoids?

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.

Is the sum of two periodic function always periodic?

Unlike the continuous case, given two discrete periodic signals, their sum is always periodic. We give a characterization for the period of the sum; as shown, the least common multiple of the periods of the signals being added is not necessarily the period of the sum.