Use of complex number in digital signal processing [closed]

1. How are complex numbers used in signal processing?
2. Why are signals represented as complex numbers?
3. How are imaginary numbers used in radar?
4. How are complex numbers related to sinusoidal signals?

How are complex numbers used in signal processing?

Complex numbers shorten the equations used in DSP, and enable techniques that are difficult or impossible with real numbers alone. For instance, the Fast Fourier Transform is based on complex numbers.

Why are signals represented as complex numbers?

Because complex numbers are a compact way to encode the basic trigonometric functions sin and cos, which are the basic sinusoids. Save this answer.

How are imaginary numbers used in radar?

Furthermore, the radar is scanning airplanes that can move up to 900 km/hr, making computations more difficult. Using imaginary numbers allows computers to calculate much quicker. The same calculations can be done with real numbers, but the plane would have moved somewhere else by the time the calculation is done!

How are complex numbers related to sinusoidal signals?

Complex numbers are important in signal processing because we often want, or find it useful, to break a signal down into a bunch of component sinusoids at different frequencies (more on this later, when we get to the DFT and FFT). Each component sinusoid has a magnitude and a phase (see above description of sinusoids).