the Z-transform converts a discrete-time signal, which is a sequence of real or complex numbers, into a complex valued frequency-domain (the z-domain...

The chirp Z-transform (CZT) is a generalization of the discrete Fourier transform (DFT). While the DFT samples the Z plane at uniformly-spaced points along...

the Laplace transform evolved naturally as a result. Laplace's use of generating functions was similar to what is now known as the z-transform, and he gave...

advanced z-transform is an extension of the z-transform, to incorporate ideal delays that are not multiples of the sampling time. The advanced z-transform is...

in the s-plane to the unit circle, | z | = 1 {\displaystyle |z|=1} , in the z-plane. Other bilinear transforms can be used for warping the frequency...

The 2D Z-transform, similar to the Z-transform, is used in multidimensional signal processing to relate a two-dimensional discrete-time signal to the...

In mathematics, the discrete Fourier transform (DFT) converts a finite sequence of equally-spaced samples of a function into a same-length sequence of...

behavior of this transform has been extensively studied since Fisher introduced it in 1915. Fisher himself found the exact distribution of z for data from...

bilateral Z-transform.  I.e.: S 2 π ( ω ) = S z ( z ) | z = e i ω = S z ( e i ω ) , {\displaystyle S_{2\pi }(\omega )=\left.S_{z}(z)\,\right|_{z=e^{i\omega...

expressed as a Z-transform. The NUDFT-I of a sequence x [ n ] {\displaystyle x[n]} of length N {\displaystyle N} is X ( z k ) = X ( z ) | z = z k = ∑ n = 0...

Fourier transform on R or Rn, notably includes the discrete-time Fourier transform (DTFT, group = Z), the discrete Fourier transform (DFT, group = Z mod N)...

(unilateral) Z-transform F ( z ) {\displaystyle F(z)} , then a final value theorem establishes conditions under which lim k → ∞ f [ k ] = lim z → 1 ( z − 1 )...

multidimensional Z transform is given by F ( z 1 , z 2 , … , z m ) = ∑ n 1 = − ∞ ∞ ⋯ ∑ n m = − ∞ ∞ f ( n 1 , n 2 , … , n m ) z 1 − n 1 z 2 − n 2 … z m − n m {\displaystyle...

The matched Z-transform method, also called the pole–zero mapping or pole–zero matching method, and abbreviated MPZ or MZT, is a technique for converting...

transform is equal to a modified Z-transform: Z ′ { x [ z ] } = Z { x [ z + 1 ] } z + 1 {\displaystyle {\mathcal {Z}}'\{x[z]\}={\frac {{\mathcal {Z}}\{x[z+1]\}}{z+1}}}...

The short-time Fourier transform (STFT) is a Fourier-related transform used to determine the sinusoidal frequency and phase content of local sections...

{\displaystyle x(t)} . The starred transform is similar to the Z transform, with a simple change of variables, where the starred transform is explicitly declared...

Hadamard transform (also known as the Walsh–Hadamard transform, Hadamard–Rademacher–Walsh transform, Walsh transform, or Walsh–Fourier transform) is an...

Z[u(n)]={\dfrac {z}{z-1}}} Converted output after z-transform Y ( z ) = T ( z ) U ( z ) = T ( z ) z z − 1 {\displaystyle Y(z)=T(z)U(z)=T(z){\dfrac {z}{z-1}}} Perform...

and the Radon transform can be expressed in these coordinates by: R f ( α , s ) = ∫ − ∞ ∞ f ( x ( z ) , y ( z ) ) d z = ∫ − ∞ ∞ f ( ( z sin ⁡ α + s cos...

in terms of the Z-transform of the filter impulse response: H ^ ( z )   ≜ ∑ n = − ∞ ∞ h [ n ] ⋅ z − n . {\displaystyle {\widehat {H}}(z)\ \triangleq \sum...

published it in 1910. The transform is z = ζ + 1 ζ , {\displaystyle z=\zeta +{\frac {1}{\zeta }},} where z = x + i y {\displaystyle z=x+iy} is a complex variable...

The Z transform H ( z ) = Z { h [ n ] } = ∑ n = − ∞ ∞ h [ n ] z − n {\displaystyle H(z)={\mathcal {Z}}\{h[n]\}=\sum _{n=-\infty }^{\infty }h[n]z^{-n}}...

wavelet transform; in practice by any suitable sampling procedure under the condition that the signal is highly oversampled, so P J [ f ] ( x ) := ∑ n ∈ Z s...

for "fractional Fourier transform" was introduced by Bailey and Swartztrauber as essentially another name for a z-transform, and in particular for the...

then the Z-transform is   X ( z ) = 1 1 − 1.5 z − 1 {\displaystyle \ X(z)={\frac {1}{1-1.5z^{-1}}}} which has a pole at z = 1.5 {\displaystyle z=1.5} and...

transform Z-transform Karhunen–Loève transform Affine transformation (Euclidean geometry) Bäcklund transform Bilinear transform Box–Muller transform Burrows–Wheeler...

Mellin transform is an integral transform that may be regarded as the multiplicative version of the two-sided Laplace transform. This integral transform is...

Laplace transforms are closely related to the Fourier transform, the Mellin transform, the Z-transform and the ordinary or one-sided Laplace transform. If...

systems. Fourier transform – aperiodic signals, transients. Laplace transform – electronic circuits and control systems. Z transform – discrete-time signals...