Complex Sinusoids
The complex function: facilitates many kinds of mathematical operations involving, due in large part to Euler's simplification:
This very useful form is often referred to as a complex sinusoid, and it preserves the distinction between positive and negative .
- For positive values, it is also called the analytic representation of .
The Fourier transform of produces a non-zero response only at frequency .
- The transform of has responses at both and, which reflects the fact that is insufficient to determine the sign of .
- An alternative, and surprisingly useful, viewpoint is that both frequencies are present, as implied by the inverse of Euler's formula: .
Read more about this topic: Negative Frequency
Famous quotes containing the word complex:
“All of life and human relations have become so incomprehensibly complex that, when you think about it, it becomes terrifying and your heart stands still.”
—Anton Pavlovich Chekhov (1860–1904)