Was macht Z-Transformation?
Die z-Transformation oder auch Standardisierung überführt Werte, die mit unterschiedlichen Messinstrumenten erhoben wurden, in eine neue gemeinsame Einheit: in Standardabweichungs-Einheiten. Unabhängig von den Ursprungseinheiten können zwei (oder mehr) Werte nun unmittelbar miteinander verglichen werden.
Wann muss ich z standardisieren?
Standardisierung kommt allgemein immer dann zum Einsatz, wenn es darum geht Werte auf unterschiedlichen Skalen vergleichbar zu machen. Dies kennen wir auch aus dem Alltag: Wir können die Größe von Menschen in Metern (m), Zentimetern (cm), aber auch in Fuß (ft) oder Inch (in) messen.
What is the difference between the Z-transform and the DTFT?
The Z-transform with a finite range of n and a finite number of uniformly spaced z values can be computed efficiently via Bluestein’s FFT algorithm. The discrete-time Fourier transform (DTFT)—not to be confused with the discrete Fourier transform (DFT)—is a special case of such a Z-transform obtained by restricting z to lie on the unit circle.
What is the Z transform in signal processing?
Z-transform. In mathematics and signal processing, the Z-transform converts a discrete-time signal, which is a sequence of real or complex numbers, into a complex frequency-domain representation. It can be considered as a discrete-time equivalent of the Laplace transform. This similarity is explored in the theory of time-scale calculus .
How do you calculate unilateral z-transform?
Unilateral Z-transform. Alternatively, in cases where x [ n ] {displaystyle x[n]} is defined only for n ≥ 0 {displaystyle ngeq 0} , the single-sided or unilateral Z-transform is defined as. X ( z ) = Z { x [ n ] } = ∑ n = 0 ∞ x [ n ] z − n .
What is inverse Z transform with example?
Inverse Z-transform. where C is a counterclockwise closed path encircling the origin and entirely in the region of convergence (ROC). In the case where the ROC is causal (see Example 2 ), this means the path C must encircle all of the poles of X(z) . A special case of this contour integral occurs when C is the unit circle.