The Z-transform can be used to convert a discrete signal to a complex valued frequency domain representation. So basically, the Z-transform is a way to change a sequence of numbers (which represent a signal in time) into a format that shows how different frequencies (or pitches) are present in that signal, using complex numbers. In practice, it is used to simplify complex operations on signals to a more simpler form(for example, a convolution between to signals is a multiplication in the Z-domain).
| \( X \) | This symbol describes the Z-Transform, a mathematical tool used in digital signal processing and control systems to analyze discrete-time signals. |
| \( \infty \) | This is the symbol for infinity, a concept representing the idea of something without bound or end. It represents an unbounded quantity larger than any real number. |
| \( \sum \) | This is the summation symbol in mathematics, it represents the sum of a sequence of numbers. |
| \( n \) | This symbol represents any given whole number, \( n \in \htmlClass{sdt-0000000014}{\mathbb{W}}\). |
| \( x \) | This symbol describes a discrete function. Discrete meaning that it only has a valid output for inputs from the set of integers \( \htmlClass{sdt-0000000122}{\mathbb{Z}} \). |
| \( z \) | This symbol represents the complex frequency variable used in the Z-Transform. |