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Pole-Zero Analysis by Mind Map: 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

2. Usage in ECG

2.1. Uses a property of poles and zeros position on Z domain

2.2. Relationship between the pole pattern in the z-plane and component wave pattern in the time signal is established

2.3. Use of the result that IDCT of the impulse response of a second-order system function with 2 poles and 2 zeros gives a bell-shaped biphasic wave called a fractional component and vice versa

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