As I'm learning about DSP I can understand the process of taking a continuous signal into a discrete signal. I understand an oscillator producing different types of signals, including a periodic signals (especially sinusoids), phase shifts and amplitudes etc.,
I'm following a coursera class, and reading DSP theory.. Rather than blindly using the DSP libraries out there I want to know exactly why something is happening. My 1st roadblock is this:
- If we already have enough samples of amplitudes collected at a reasonably sample rate (using Nyquist-Shannon) Why does it matter that a signal (Sinusoid) can be broken down into other sinusoids? Aren't the samples enough to reconstruct the original signal/sound?
- What is advantageous by knowing that the Fast Fourier Transform can decompose a signal into multiple signals?
- The sinusoids that make up a single sinusoid also have other sinusoids that compose them. If a signal has say 5 sinusoids, those 5 sinusoids, according to DFT if I'm correct, can also each have sinusoids.. Isn't this recursive or infinite? At what point can we say we have "enough" sinusoids to represent a signal.
Thanks in advance for the clarification & patience.