Z-Transformation Die bilaterale Z-Transformation eines Signals x[n] ist die formale Reihe X(z): wobei n alle ganzen Zahlen durchläuft und z, im Allgemeinen, eine komplexe Zahl der Form ist. A ist der Betrag von z und φ der Winkel der komplexen Zahl in Polarkoordinaten. Alternativ kann z auch als Realteil σ und Imaginärteil ω beschrieben werden.
Linearität. Die Z-Transformierte von zwei linear verknüpften Signalen ist die lineare Verknüpfung der beiden z-transformierten Signale.
http://en.wikipedia.org/wiki/Digital_filters https://ccrma.stanford.edu/~jos/filters/Matlab_Filter_Implementation.html The Impulse response from a simple audio system. Showing the original impulse, with high frequencies boosted, then with low frequencies boosted. In signal processing, the impulse response, or impulse response function (IRF), of a dynamic system is its output when presented with a brief input signal, called an impulse. More generally, an impulse response refers to the reaction of any dynamic system in response to some external change
The impulse response, often denoted H(z) or h(n) is a measurement of how a filter will respond to the delta function. For example, given a difference equation, one would set x(0) = 1 and x(n) = 0 for n > 0 and evaluate. In the case of linear time-invariant FIR filters, the impulse response is exactly equal to the sequence of filter coefficients h(n) = bn. In general, the impulse response is a characterization of the filter's behaviour. A plot of the impulse response will help to reveal how a filter will respond to a sudden, momentary disturbance.