From 841c7082c93f822cbb366a7eb39836fc2ca452b5 Mon Sep 17 00:00:00 2001
From: Klagarge <remi@heredero.ch>
Date: Fri, 2 Feb 2024 13:03:42 +0100
Subject: [PATCH] add beginning of lab6-filter

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+<header><h1>
+Lab 06 - Filters
+</h1></header>
+
+----------
+
+In this laboratory on digital filters, the main objective is to understand how digital filters work.
+We will use MATLAB to simulate and implement these filters on a digital signal processor (DSP).
+
+# Analog filter design
+
+We must design Butterworth low-pass filter that cuts at 1kHz as shown with the following equation :
+
+$$
+F(s) = \frac{1}{\frac{s^{2}}{\omega_c^{2}} + s\cdot\frac{1.414}{\omega_c} + 1}
+$$
+
+In according to the sample theory, we have to choose at least 2 times the maximum frequency of the signal.
+In this case, the maximum frequency is 1 kHz, so we have to choose a sample frequency of 2 kHz.
+
+## Transfer function
+For calculate the transfer function, we have to calculate the poles and zeros of the filter.
+
+$$
+p_{di} = e^{p_{ai} \cdot T} \qquad z_{di} = e^{z_{ai} \cdot T}
+$$
+
+- $k_a$, $p_{ai}$ and $z_{ai}$ are the gain, poles and zeros of the analog filter that the representation `zpk`.
+Be careful, $k_a$ is not the DC gain.
+- $k_d$, $p_{di}$ and $z_{di}$ are the gain, poles and zeros of the digital filter.
+
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