 ## Simple Low Pass IIR Filter Implementation Using the C Language

### 2. Introduction

##### The linear analog circuit is described with the linear differential equation or with the Laplace transformation (s plane). For example: the RC circuit (low pass filter) is described with the first order differential equation: ##### or in the Laplace form: ##### The analog method experience can be used for the digital technical. The linear digital methods are used the difference equation and z transformation (z plane). ##### There are few transformation methods of the s-plane (analog space) to z-plane (digital space): backward Euler, impulse invariance, bilinear. The article is described the simple first order filter. Backward Euler method is suitable for the case. ##### Insert the (5) in the (2) ##### Specify ##### Then the z-transformation ##### And the difference equation ### 3.2 First Order Digital IIR Filter. Fixed Point Realization with the Shift Operation.

##### Instead of the multiplication can be used the arithmetic shift operation (multiplication/division on the 2^k). The A value shall be taken 2^-k. Then the (9) can be written ##### Using the scaling S=2^k in the (10) ### 4. Appendix. Solution of the differential and difference first order equations

##### Consider the (1) differential equation with the input step signal:  ##### Then the solution of the differential equation: #####  ##### Then the solution of the difference equation: 