by Lukas T.

Name the different Discretization Methods.

all of the above are discretization methods used to convert a continuous-time signal into a discrete-time signal.


involves holding each sampled value of the continuous-time signal constant until the next value gets sampled to obtain a discrete-time signal. This produces a kind of staircase signal. Although the ZOH method is simple, it can introduce errors and distortions, especially for high-frequency signals, which can be reduced using higher-order hold methods such as linear interpolation or spline interpolation.


involves approximating the continuous-time signal with a first-order polynomial function between to adjacent sample points. Basically connects two nearby sample points with a line. The FOH method is more accurate than the ZOH method, especially for high-frequency signals, but it can still introduce errors and distortions for rapidly changing signals. To reduce these errors, higher-order hold methods such as cubic interpolation or spline interpolation can be used.

impulse invariant:

involves sampling the impulse response of the continuous-time system and using it to derive the coefficients of the discrete-time system. The assumption is that the continuous-time system is linear and time-invariant and that the sampling period is small enough to capture the system's essential dynamics. However, the method can introduce errors in the discretization process, especially for systems with high-frequency components, so careful consideration must be given to the choice of sampling period and the limitations of the method.

Tustin method

involves replacing "s" in the continuous-time transfer function with a formula that includes the discrete-time variable "z". The resulting expression is simplified, and the terms are rearranged to obtain the discrete-time transfer function. The Tustin method is preferred because it preserves the stability of the continuous-time system and approximates the integral term more accurately than the impulse invariant method. However, like any discretization method, it introduces errors, especially at high frequencies, so the choice of the sampling period must be carefully considered.

matched poles and zeros method:

involves modifying the poles and zeros of the continuous-time transfer function by replacing them with their discrete-time counterparts. This preserves the frequency response and stability properties of the continuous-time system, and the resulting transfer function can be used to implement the discrete-time system. However, the method may not be feasible for systems with complex conjugate poles or zeros that lie close to the imaginary axis, as the transformation may cause the poles and zeros to move outside the unit circle in the z-plane, leading to an unstable discrete-time system.

  • Replace each pole "p" with "exp(p*T)", where "T" is the sampling period.

  • Replace each zero "z" with "exp(z*T)".


Lukas T.


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