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 valued frequency-domain (the z-domain or z-plane) representation.

In mathematics, the complex plane is the plane formed by the complex numbers, with a Cartesian coordinate system such that the horizontal x -axis, called the real axis, is formed by the real numbers, and the vertical y -axis, called the imaginary axis, is formed by the imaginary numbers.

May 22, 2022 · The Z-plane is a complex plane with an imaginary and real axis referring to the complex-valued variable \(z\). The position on the complex plane is given by \(re^{j \theta}\) and the angle from the positive, real axis around the plane is denoted by \(\theta\).

Z-plane may refer to: z = e sT, the domain of the z-transform; z = x + iy, the complex plane in general

Relationship between the s-plane and the z-plane. The s-plane is a rectangular coordinate system with F expressing the distance along the real (horizontal) axis, and T the distance along the imaginary (vertical) axis.

Z-plane overview. The z-plane below is comprised of a unit circle and a number of lines within. There are two line types?constant frequency and constant damping ratio. The dominant feature of the plane is the unit circle- the unit circle is the zero-damping coefficient contour.

We visualize this by putting the \(z\)-plane on the left and the \(w\)-plane on the right. We then draw various curves and regions in the \(z\)-plane and the corresponding image under \(z^2\) in the \(w\)-plane.

Complex Numbers as Vectors in the Complex Plane. A complex number z= x+iy can be identi ed as a point P(x;y) in the xy-plane, and thus can be viewed as a vector OP in the plane. All the rules for the geometry of the vectors can be recast in terms of complex numbers. For example, let w= s+ itbe another complex number. Then the point for

Stability of a discrete linear system can be determined by analyzing the transfer function H(z) given by the Z-transform. The transfer function H(z) can be evaluated to determine the frequency response of a discrete system. Digital filters can be analyzed and designed using the …

The pole-zero pattern in the z-plane specifies the algebraic expression for the z-transform. In addition, the ROC must be indicated either implicitly or explicitly. There are a number of properties of the ROC in relation to the poles of the z-transform and in relation to characteristics of the signal in the time domain that often imply the ROC.