Signal analysis imaginary numbers

1. How are complex numbers used in signal analysis?
2. Can a signal take complex value?
3. How are imaginary numbers used in radar?
4. Why are signals represented as complex numbers?

How are complex numbers used in signal analysis?

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.

Can a signal take complex value?

While the domain set determines the arguments of the signal, the range set determines the values of it. Therefore a real valued signal is a function whose range set is the real numbers. Consequently a complex valued signal is the one whose range set is the complex numbers.

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!

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.