# Pole-Zero Analysis

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Pole-Zero Analysis

## 1. Syntax

### 1.1. zplane(z,p)

1.1.1. Plot the zeros defined in vector column z and the poles specified in vector column p

### 1.2. zplane(b,a)

1.2.1. Roots are used to locate the transfer function zeros and poles represented by the numerator coefficients b and the denominator coefficients a

### 1.3. [hz,hp,ht] = zplane(___)

1.3.1. Return the handle vectors to zero lines, hz, and hp pole lines. Ht is a handle vector for the circle line of axes/unit and text objects.

### 1.4. zplane(d)

1.4.1. Finds the transfer function's zeros and poles represented by the digital filter, d

### 1.5. [vz,vp,vk] = zplane(d)

1.5.1. Returns the zeros (vector vz), poles (vector vp), and gain (scalar vk) corresponding to the digital filter d

## 3. Input Argument

### 3.1. z, p — Zeros and poles

3.1.1. Zeros and poles, specified as column vectors or matrices

### 3.2. b, a — Transfer function coefficients row vectors

3.2.1. Transfer function coefficients, specified as row vectors. The transfer function is defined in terms of z–1: H(z) = B(z) / A(z) = b(1)+b(2)z−1+⋯+b(n+1)z−n / a(1)+a(2)z−1+⋯+a(m+1)z−m

### 3.3. d — Digital filter

3.3.1. Digital filter, specified as a digitalFilter object

## 4. Output Argument

### 4.1. hz, hp, ht — Vectors of handles vectors

4.1.1. Vectors of handles to the zero lines, hz, and the pole lines, hp, of the pole-zero plot

### 4.2. vz, vp, vk — Zeros, poles, and gain column vectors and scalar

4.2.1. Zeros, poles, and gain of a digital filter, d, returned as column vectors and a scalar