diff --git a/config/en/mkdocs.yaml b/config/en/mkdocs.yaml
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--- a/config/en/mkdocs.yaml
+++ b/config/en/mkdocs.yaml
@@ -112,7 +112,10 @@ nav:
       - 'Second order differential equations': mathematics/ordinary-differential-equations/second-order-ode.md
       - 'Systems of linear differential equations': mathematics/ordinary-differential-equations/systems-of-linear-ode.md
       - 'The Laplace transform': mathematics/ordinary-differential-equations/laplace-transform.md
-
+    - 'Mathematical physics': 
+      - 'Signal analysis': 
+        - 'Signals': mathematics/mathematical-physics/signal-analysis/signals.md
+        
   - 'Physics':
     - physics/index.md
     
diff --git a/docs/en/mathematics/mathematical-physics/signal-analysis/signals.md b/docs/en/mathematics/mathematical-physics/signal-analysis/signals.md
new file mode 100644
index 0000000..27b641e
--- /dev/null
+++ b/docs/en/mathematics/mathematical-physics/signal-analysis/signals.md
@@ -0,0 +1,219 @@
+# Signals 
+
+## Definitions
+
+> *Definition*: a signal is a function of space and time.
+> * Output can be analog or quantised.
+> * Input can be continuous or discrete.
+
+<br>
+
+> *Definition*: a signal can be sampled at particular moments $k T_s$ in time, with $k \in \mathbb{Z}$ and $T_s \in \mathbb{R}$ the sampling period. For a signal $f: \mathbb{R} \to \mathbb{R}$ sampled with a sampling period $T_s$ may be denoted by
+>
+> $$
+>   f[k] = f(kT_s), \qquad \forall k \in \mathbb{Z}.
+> $$
+
+<br>
+
+> *Definition*: signal transformations on a function $x: \mathbb{R} \to \mathbb{R}$ obtaining the function $y: \mathbb{R} \to \mathbb{R}$ are given by
+>
+> | Signal transformation | Time | Amplitude |
+> | :-: | :-: | :-: |
+> | Reversal | $y(t) = x(-t)$ | $y(t) = -x(t)$ |
+> | Scaling | $y(t) = x(at)$ | $y(t) = ax(t)$ |
+> | Shifting | $y(t) = x(t - b)$ | $y(t) = x(t) + b$ |
+>
+> for all $t \in \mathbb{R}$. 
+
+For sampled signals similar definitions hold. 
+
+### Symmetry
+
+> *Definition*: consider a signal $f: \mathbb{R} \to \mathbb{R}$ which is defined in an interval which is symmetric around $t = 0$, we define.
+>
+> * $f$ is *even* if $f(t) = f(-t)$, $\forall t \in \mathbb{R}$.
+> * $f$ is *odd* if $f(t) = -f(-t)$, $\forall t \in \mathbb{R}$. 
+
+For sampled signals similar definitions hold.
+
+> *Theorem*: every signal can be decomposed into symmetric parts.
+
+??? note "*Proof*:"
+
+    Will be added later.
+
+### Periodicity
+
+> *Definition*: a signal $f: \mathbb{R} \to \mathbb{R}$ is defined to be periodic in $T$ if and only if 
+>
+> $$
+>   f(t + T) = f(t), \qquad \forall t \in \mathbb{R}. 
+> $$
+
+For sampled signals similar definitions hold.
+
+> *Theorem*: a summation of two periodic signals with periods $T_1, T_2 \in \mathbb{R}$ respectively is periodic if and only if 
+>
+> $$
+>   \frac{T_1}{T_2} \in \mathbb{Q}.
+> $$
+
+??? note "*Proof*:"
+
+    Will be added later.
+
+### Signals
+
+> *Definition*: the Heaviside step signal $u: \mathbb{R} \to \mathbb{R}$ is defined by 
+>
+> $$
+>   u(t) = \begin{cases} 1 &\text{ if } t > 0,\\ 0 &\text{ if } t < 0,\end{cases}
+> $$
+>
+> for all $t \in \mathbb{R}$. 
+
+For a sampled function the Heaviside step signal is given by
+
+$$
+    u[k] = \begin{cases} 1 \text{ if } k \geq 0, \\ 0 \text{ if } k < 0, \end{cases}
+$$
+
+for all $k \in \mathbb{Z}$. 
+
+> *Definition*: the rectangular signal $\text{rect}: \mathbb{R} \to \mathbb{R}$ is defined by
+>
+> $$
+>   \text{rect} (t) = \begin{cases} 1 &\text{ if } |t| < \frac{1}{2}, \\ 0 &\text{ if } |t| > \frac{1}{2},\end{cases}
+> $$
+>
+> for all $t \in \mathbb{R}$. 
+
+The rect signal can be normalised obtaining the scaled rectangular signal $D: \mathbb{R} \to \mathbb{R}$ defined by
+
+$$
+    D(t, \varepsilon) = \begin{cases} \frac{1}{\varepsilon} &\text{ if } |t| < \frac{\varepsilon}{2},\\ 0 &\text{ if } |t| > \frac{\varepsilon}{2},\end{cases}
+$$
+
+for all $t \in \mathbb{R}$. 
+
+The following signal has been derived from the scaled rectangular signal $D: \mathbb{R} \to \mathbb{R}$ used on a signal $f: \mathbb{R} \to \mathbb{R}$ for
+
+$$
+    \lim_{\varepsilon \;\downarrow\; 0} \int_{-\infty}^{\infty} f(t) D(t, \varepsilon)dt = \lim_{\varepsilon \;\downarrow\; 0} \frac{1}{\varepsilon} \int_{-\frac{\varepsilon}{2}}^{\frac{\varepsilon}{2}} f(t) dt = f(0),
+$$
+
+using the mean [value theorem for integrals](../calculus/integration.md#the-mean-value-theorem-for-integrals).
+
+> *Definition*: the Dirac signal $\delta$ is a generalized signal defined by the properties 
+>
+> $$
+> \begin{align*}
+>   \delta(t - t_0) = 0 \quad \text{ for } t \neq t_0,& \\
+>   \int_{-\infty}^\infty f(t) \delta(t - t_0) dt = f(t_0),&
+> \end{align*}
+> $$
+>
+> for a signal $f: \mathbb{R} \to \mathbb{R}$ continuous in $t_0$. 
+
+For sampled signals the $\delta$ signal is given by
+
+$$
+    \delta[k] = \begin{cases} 1 &\text{ if } k = 0, \\ 0 &\text{ if } k \neq 0.\end{cases}
+$$
+
+## Signal sampling
+
+We already established that a signal $f: \mathbb{R} \to \mathbb{R}$ can be sampled with a sampling period $T_s \in \mathbb{R}$ obtaining $f[k] = f(kT_s)$ for all $k \in \mathbb{Z}$. We can also define a *time-continuous* signal $f_s(t)$ that represents the sampled signal using the Dirac signal, obtaining
+
+$$
+    f_s(t) = f(t) \sum_{k = - \infty}^\infty \delta(t - k T_s), \qquad \forall t \in \mathbb{R}.
+$$
+
+> *Definition*: the sampling signal or impulse train $\delta_{T_s}: \mathbb{R} \to \mathbb{R}$ is defined as
+>
+> $$
+>   \delta_{T_s}(t) = \sum_{k = - \infty}^\infty \delta(t - k T_s)
+> $$
+>
+> for all $t \in \mathbb{R}$ with a sampling period $T_s \in \mathbb{R}$. 
+
+Then integration works out since we have
+
+$$
+    \int_{-\infty}^\infty f(t) \delta_{T_s}(t) dt = \sum_{k = -\infty}^\infty \int_{-\infty}^\infty f(t) \delta(t - k T_s) dt = \sum_{k = -\infty}^\infty f [k],
+$$
+
+by definition.
+
+## Convolutions
+
+> *Definition*: let $f,g: \mathbb{R} \to \mathbb{R}$ be two continuous signals, the convolution product is defined as 
+>
+> $$
+> f(t) * g(t) = \int_{-\infty}^\infty f(u)g(t-u)du
+> $$
+>
+> for all $t \in \mathbb{R}$. 
+
+<br>
+
+> *Proposition*: the convolution product is commutative, distributive and associative. 
+
+??? note "*Proof*:"
+
+    Will be added later.
+
+> *Theorem*: let $f: \mathbb{R} \to \mathbb{R}$ be a signal then we have for the convolution product between $f$ and the Dirac signal $\delta$ and some $t_0 \in \mathbb{R}$ 
+>
+> $$
+>   f(t) * \delta(t - t_0) = f(t - t_0)
+> $$
+>
+> for all $t \in \mathbb{R}$
+
+??? note "*Proof*:"
+
+    let $f: \mathbb{R} \to \mathbb{R}$ be a signal and $t_0 \in \mathbb{R}$, using the definition of the Dirac signal 
+
+    $$
+        f(t) * \delta(t - t_0) = \int_{-\infty}^\infty f(u) \delta(t - t_0 - u)du = f(t - t_0),
+    $$
+
+    for all $t \in \mathbb{R}$. 
+
+In particular $f(t) * \delta(t) = f(t)$ for all $t \in \mathbb{R}$; $\delta$ is the unity of the convolution.
+
+The average value of a signal $f: \mathbb{R} \to \mathbb{R}$ for an interval $\varepsilon \in \mathbb{R}$ may be given by
+
+$$
+    f(t) * D(t, \varepsilon) = \frac{1}{\varepsilon} \int_{t - \frac{\varepsilon}{2}}^{t + \frac{\varepsilon}{2}} f(u)du.
+$$
+
+For sampled/discrete signals we have a similar definition for the convolution product, given by
+
+$$
+    f[k] * g[k] = \sum_{m = -\infty}^{\infty} f[m]g[k - m],
+$$
+
+for all $k \in \mathbb{Z}$. 
+
+## Correlations
+
+> *Definition*: let $f,g: \mathbb{R} \to \mathbb{R}$ be two continuous signals, the cross-correlation is defined as
+>
+> $$
+>   f(t) \star g(t) = \int_{-\infty}^\infty f(u) g(t + u)du
+> $$
+>
+> for all $t \in \mathbb{R}$. 
+
+Especially the auto-correlation of a continuous signal $f: \mathbb{R} \to \mathbb{R}$ given by $f(t) \star f(t)$ for all $t \in \mathbb{R}$ is useful, as it can detect periodicity without stating the proof. 
+
+For sampled/discrete signals a similar definition exists given by
+
+$$
+    f[k] \star g[k] = \sum_{m = -\infty}^{\infty} f[m]g[k + m],
+$$
+
+for all $k \in \mathbb{Z}$. 
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diff --git a/docs/en/physics/index.md b/docs/en/physics/index.md
index 2928a39..b00ae27 100644
--- a/docs/en/physics/index.md
+++ b/docs/en/physics/index.md
@@ -1,3 +1,14 @@
 # Physics
 
-Welcome to the physics page.
\ No newline at end of file
+Welcome to the physics page. Some special physical environments that will be used in this seection are listed and explained below.
+
+* *Principles*: a fundamental rule or concept in physics serving as a basis for reasoning. 
+* *Assumptions*: a less fundamental rule or concept in physics that is taken to be true such that certain phenoma can be simplified. 
+* *Definitions*: a precise and unambiguous description of the meaning of a physical term. It characterizes the meaning of a word by giving all the properties an only those properties that must be true.
+* *Laws*: a physical statement that is proved to be true, under the made assumptions and posed principles. In a physical text, the term law is often reserved for the most important results.
+* *Propositions*: an often interesting result, but generally less important than a law.
+* *Lemmas*: a minor result whose purpose is to help in proving a law. It is a stepping stone on the path to proving a law.
+* *Corollaries*: a result in which the proof relies heavily on a given law.
+* *Proofs*: a convincing argument that a certain physical statement is necessarily true. A proof generally uses deductive reasoning and logic but also contains some amount of ordinary language.
+
+The physics sections of this wiki are based on various books and lectures. A comprehensive list of references can be found below.
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