Z-transform

The Z-transform is a mathematical tool used in engineering and signal processing to analyze discrete signals—like digital audio or data sequences. It converts a sequence of numbers into a complex frequency domain, making it easier to understand and manipulate the signal's behavior over time. Think of it as turning a series of steps into a smooth curve, revealing patterns and properties not obvious in the original data. This helps in designing filters, analyzing system stability, and solving difference equations, much like how the Fourier transform helps analyze continuous signals.