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...

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)...

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

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

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...

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...

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...

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...

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...

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...

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...

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

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}}}...

Transforms between a discrete domain and a continuous domain are not discrete transforms. For example, the discrete-time Fourier transform and the Z-transform...

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

⁡ ( z ) = 2 T [ z − 1 z + 1 + 1 3 ( z − 1 z + 1 ) 3 + 1 5 ( z − 1 z + 1 ) 5 + 1 7 ( z − 1 z + 1 ) 7 + ⋯ ] ≈ 2 T z − 1 z + 1 = 2 T 1 − z − 1 1 + z − 1...

variables. Z-transform, a generalization of the DTFT to the entire complex plane Modified discrete cosine transform (MDCT) Discrete Hartley transform (DHT)...

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}}...

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...

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

{=}0} ) Discrete-time systems use the Z-transform and are plotted in the z-plane: z = A e j ϕ {\displaystyle z=Ae^{j\phi }} Real frequency components...

In combinatorics, the binomial transform is a sequence transformation (i.e., a transform of a sequence) that computes its forward differences. It is closely...

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

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...