Howtosignalprocessing
- Can you add sinusoids with different frequencies?
- How many Hz does a sine wave have?
- What is the formula for a sine wave?
- Why are sine waves of different frequencies orthogonal?
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.
How many Hz does a sine wave have?
A frequency of 1000Hz, or 1 kHz, means that the sine wave goes through 1000 complete cycles in 1 s. If we are considering audible sound waves then the human ear has a frequency range of about 20Hz-20kHz.
What is the formula for a sine wave?
In its most general form, the sine wave can be described using the function y=a*sin(bx), where: a is known as the amplitude of the sine wave. b is known as the periodicity.
Why are sine waves of different frequencies orthogonal?
As we saw previously, the sine and cosine curves of different frequencies are orthogonal to each other because they average against each other to zero. In fact, they form an orthonormal basis of the vector space of functions on [0,2π].
