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 #set page(
   paper: "a4",
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+  numbering: "1",
   margin: (top: 2.5cm, left: 2.5cm, right: 2.5cm, bottom: 2cm)
 )
 
-#if (context here().page()) != 1 [
-  #set page(
-    numbering: "1"
-  )
-]
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-  footer: context {
-    if here().page() > 1 {
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 #set text(
-  //font: "Times New Roman",
+  font: "Times New Roman",
   size: 12pt,
 )
 
 Marius Drechsler\
 Process Essay\
-May 25th, 2025
+May 17th, 2025
 
 #align(center, text(size: 17pt, weight: "bold")[
-  *The Digital Journey of a Message*
+  *The Digital Journey of Your Voice*
 ])
 
 #set align(left)
@@ -43,68 +29,65 @@ May 25th, 2025
 
 #show: word-count
 
-// Have you ever wondered what happens with your voice when you are talking to someone on the phone?
+Have you ever wondered what happens with your voice when you are talking to someone on the phone?
-When speaking over the telephone, voice signals undergo complex transformations before reaching their intended recipient.
+From the instant the soundwaves leave your throat until they reach the ear of the person you are talking to,
-From the instant the sound waves are produced by the vocal cords until they reach the recipient,
+a series of analog and digital processes collaborate to carry your message.
-a series of analog and digital processes collaborate to carry the message.
+In fact, this whole process can be broken down into three major steps -- sampling, quantisation and modulation.
-This transformation process can be broken down into three major steps -- sampling, quantisation and modulation.
+In the course of this essay, we will investigate each of these steps in more depth to understand how modern
-These steps systematically convert analogue voice signals into digital information, allowing a reliable transmission over communication networks.
-This essay will investigate each of these steps in more depth to understand how modern
 communication works on a technical level.
 
-// To start, we will take a closer look at the analogue signal that reaches your phone's microphone.
+To start, we will take a closer look at the analoue signal that reaches your phone's microphone.
-To begin, it is necessary to examine the analogue signal that reaches the microphone of a telephone.
+Every sound wave, like your voice or the tone of a guitar string, is so called time and value continuous.
-Every sound wave, such as human speech or musical tones, is called time and value continuous.
+That means, such a signal has an infinitely accurate value at each imaginable point in time.
-That means that such a signal has an infinitely accurate value at each imaginable point in time.
+However, an electronic device, for example a computer or a phone, cannot understand such an analogue signal, thus we have to first transform it into some kind of electrical signal the device can understand.
-However, an electronic device, for example a computer or a phone, cannot understand such an analogue signal, thus, it must first be transformed into an electrical signal the device can process.
+In general, we can assume that an electrical device can only process time and value disteet signals.
-//In general, we can assume that an electrical device can only process time and value discrete signals.
+To transform our original continuous signal into its discreet or rather digital representation, we can make use of the sampling and
-Generally, electronic devices can only process signals that are discrete both in time and amplitude.
+quantization steps in our communication process.
-To transform the original continuous signal into its discrete or rather digital representation, sampling and
-quantization steps are used in the communication process.
 
-In the sampling process, the analogue signal is transformed into a time-discrete and value-continuous signal.
+In the sampling process, the analogue signal is transformet into a time discreet and value continuous signal.
-Conceptually, an analog-to-digital converter (ADC) takes rapid snapshots of the amplitude of the input signal at uniform intervals and records each reading.
+Conceptually, an analog-to-digital converter (ADC) takes rapid "snapshots" of the amplitude of the input signal at uniform intervals and records each reading.
 The rate at which these snapshots occur is called sampling frequency.
-Ideally, it is desirable to maximize the interval between each of these snapshots, using the lowest possible sampling frequency.
+Ideally, we do want to maximize the timespan between each of these snapshots, using the lowest possible sampling frequency so to speak.
 The Nyquist Frequency defines this lowest possible sampling frequency as double the frequency of the originating signal @shannon.
-For example, if the frequency of the original signal is 1 MHz, the analog-to-digital converter will need to take a snapshot of the signal at a frequency of at least 2 MHz.
+For example, if the frequency of our original signal is 1 MHz, the analog-to-digital converter will need to take a snapshot of the signal at a frequency of at least 2 MHz.
-At this moment, the signal is time-discrete and value-continuous.
+At this moment, our signal now is time-discreet and value-continuous.
-To convert these time-discrete values into quantized digital values a quantizer will be used in the next step.
+To convert these time-discreet values into real bits and bytes we will make use of the quantizer in the next step.
 
-Quantization describes the operation of transforming a continuous value into its discrete form.
+Quanization describes the operation of transforming a continuous value into a discreet form.
-Consider the random placement of dots in a row on a piece of paper.
+Imagine placing random dots in a row on a piece of paper.
-A simple quantization process would be to take a ruler and for each point record the next highest marking on the ruler.
+A simple quantization process now would be to take a ruler and for each point record which is the next highest marking on the ruler.
-Analogously, the quantizer of an electronic device maps the continuous input values to predefined codewords -- a collection of bits (for example "000", "110", or "011").
+In the same sense, the quantizer of an electronic device maps the continuous input vaulues to predefined codewords -- a collection of bits (for example "000", "110" or "011").
+Our signal has now fully arrived in the digital domain.
 // Note: Maybe expand more what happened up until now
-The analogue message has now been fully digitally encoded.
+Up to this point we have completeley encoded our analogue message digitally.
 During the next steps, the digital signal will be further processed and prepared for transmission.
 
-A digital signal in its raw form is inefficient to transmit because of the limited underlying bandwidth.
+A digital signal in its raw form is very inefficient to transmit because of the limited underlying bandwidth.
-Since the message has to be transported over some kind of communication channel, the amount of information that can be transported in a fixed period of time is limited.
+Because we need to transport our message over some kind of communication channel, the amount of information we can transport in a fixed period of time is limited.
 The first step in solving this issue is using compression by removing irrelevant and redundant information from the signal.
 A popular example for a compression method is called Huffman Coding @huffman.
 Conceptually, the Huffman Code consists of multiple codewords of varying length where symbols with a higher probability of occurrence are assigned to the shorter codewords, thus reducing the overall size of the message.
 Since the assignment of symbols to codewords is based on their probability of occurrence, this method of compression requires information about the statistics of the incoming symbols.
-If these statistical information is not known, other compression methods such as the Lempel–Ziv–Welch algorithm can be used.
+If these statistical information are not known, other compression methods such as the Lempel–Ziv–Welch algorithm can be used.
-Furthermore, compression algorithms specifically tailored for different signal sources can be used, for example PNG for pictures, MP3 for audio or MPEG for video signals.
+Furtheremore, compression algorithms specifically tailored for different signal sources can be used, for example PNG for pictures, MP3 for audio or MPEG for video signals.
-With the analogue message digitized and compressed for easier transport over the communication channel, the message must now be prepared on a physical level for it to be transmitted using a radio wave or a data cable.
+With the analogue message digizited and compressed for easier transport over our communication channel, we will now need to prepare our message on a physical level for it to be able to be transmitted using a radio wave or a data cable.
 
-To prepare the digital and compressed message for transmission over a physical channel, digital modulation -- such as amplitude modulation -- is used.
 Currently, the message to be transmitted can be represented as a set of codewords like "00 01 10 11".
-Modulation works by defining a specific signal amplitude for every possible codeword, which is called Amplitude-Shift Keying (ASK) @modulation.
+To prepare our message digital and compressed message for transmission over a physical channel, digital modulation -- like amplitude modulation -- is used.
-The simplest form of ASK is On-Off Keying (OOK), in which a binary 1 is represented by the transmission of a wave, and a binary 0 by the absence of transmission.
+This works by defining a specific signal amplitude for every possible codeword, which is called Amplitude-Shift Keying (ASK) @modulation.
-Signal modulation is not limited to changing the amplitude of the transmission signal, thus it is also possible to alter the frequency or phase.
+The simplest form of ASK is called On-Off Keying (OOK), where we will either transmit a wave -- and signaling a binary 1 -- or not transmit anything -- and signal a 0.
-In the example above, four sine functions with varying amplitudes may be defined as the modulated signal that is being transported over the physical communication channel.
+In our example we may define four sine functions with varying amplitutes as the modulated signal that is being transported over the physical communication channel.
-Because four different Amplitude-Shifts were defined, this type of modulation is called "4 ASK" @modulation.
+Because we defined four different Amplitude-Shifts, this type of modulation is called "4 ASK" @modulation.
-Depending on the type of communication channel, a different modulation type may be used, using either one or a combination of different modulation parameters.
+Signal modulation is not limited to changing the ampliude of our transmission signal, thus we can also alter the phase or frequency of the signal.
-For example, a popular modulation type that uses a combination of amplitude shifts and phase shifts is called "Amplitude-Phase-Shift Keying (APSK)" @modulation.
+Depending on the type of communication channel we may want to choose a different modulation type using either one or a combination of different modulation parameters.
-Using modulation, the signal has been prepared on a physical level to  instruct a communication interface -- such as an antenna or an optical transmitter -- to finally transmit the message.
+For example, a popular modulation type that uses a combination of amplitude shifts and phase shifts is called "Amplitude-Phase-Shift Keying (APSK) @modulation.
+Using modulation, we prepared our signal on a physical level to  instruct a communication interface -- like an antenna or an optical transmitter -- to finally transmit our message.
 
 As final step, the receiver of the message has to process the received signals in exactly the reverse order to create a comprehensible message.
 The most important prerequisite for this to work is that both sender and receiver have agreed on the same transmission and reception conditions.
 The receiver will first need to use the correct modulation type to convert their received signal back to a set of codewords.
-Proceeding, they will decompress the message based on the used compression algorithm and use a Digital-to-Analog Converter (DAC) to transform the digital message back into sound waves which will be output by the speaker of their phone.
+Going on, they will decompress the message based on the used compression algorithm and use a Digital-to-Analog Converter (DAC) to transform the digital message back into sound waves which will be output by the speaker of their phone.
-This whole process now happens at such a high speeds that real-time communication across the globe is made possible.
+This whole process now happens at such a high speed that makes it possible for us to talk to a person on the other side of the world.
 
 //Essay has a total of #total-words words.