From 50239a4d90ef89fd3d44e471cbe4671103291653 Mon Sep 17 00:00:00 2001 From: Kai Vogelgesang Date: Fri, 19 Sep 2025 23:21:37 +0200 Subject: [PATCH] Translate project pages --- U02_1_Input.en.ipynb | 42 ++++++------- U02_2_Freq_Shift.en.ipynb | 54 ++++++++--------- U02_3_Low_Pass.en.ipynb | 123 +++++++++++++++++++------------------- U02_4_Sync.en.ipynb | 46 +++++++------- U02_5_Output.en.ipynb | 54 ++++++++--------- 5 files changed, 160 insertions(+), 159 deletions(-) diff --git a/U02_1_Input.en.ipynb b/U02_1_Input.en.ipynb index ff75a2f..fff44c0 100644 --- a/U02_1_Input.en.ipynb +++ b/U02_1_Input.en.ipynb @@ -25,18 +25,18 @@ "id": "6ab69020", "metadata": {}, "source": [ - "In diesem Projekt arbeiten wir mit Audio-Daten.\n", - "Um das Einlesen möglichst unkompliziert zu halten, stellen wir die Eingabe in einem einfachen Format bereit:\n", + "In this project, we work with audio data.\n", + "To facilitate reading it into your program, we provide the inputs in a simple format:\n", "\n", "```{admonition} Format\n", - "Die erste Zeile enthält $n$, die Anzahl der Samples ($0 \\leq n < 2^{32}$).\n", + "The first line contains $n$, the number of samples ($0 \\leq n < 2^{32}$).\n", "\n", - "Danach folgen $n$ Zeilen mit jeweils einem Sample $x$ als ganze Zahl ($-2^{15} \\leq x < 2^{15}$)\n", + "Afterwards, $n$ lines follow, each with one sample $x$ as an integer ($-2^{15} \\leq x < 2^{15}$).\n", "```\n", "\n", - "Die Abtastrate $f_S$ ist dabei 16640 Hz.\n", + "The sampling rate $f_s$ is fixed at 16640 Hz.\n", "\n", - "## Beispiel\n", + "## Example\n", "```\n", "10\n", "623\n", @@ -52,7 +52,7 @@ "```\n", "\n", "```{note}\n", - "Die Werte der Samples sind hier zwar ganze Zahlen, aber für den Rest des Projekts ergibt es Sinn sie hier schon in Floating-Point Werte umzuwandeln.\n", + "Although the samples are given as integer numbers, for the rest of the project it makes sense to convert them into a floating point format at this point already.\n", "```" ] }, @@ -61,32 +61,32 @@ "id": "cfcac6c9", "metadata": {}, "source": [ - "# Visualisierung\n", + "# Visualization\n", "\n", - "In diesem Projekt kann es sehr hilfreich sein, sich nach jedem Arbeitsschritt das Ergebnis zu visualisieren.\n", - "Das können wir zum Beispiel so tun:\n", - "- Das Signal enthält 2 Zeilen mit je 2080 Pixeln pro Sekunde. Mit $f_S = 16640\\text{Hz}$ haben wir also 4 Samples pro Pixel.\n", - "- Wir nehmen jedes 4. Sample, falls es komplex ist berechnen wir den Betrag $(a + ib \\mapsto \\sqrt{a^2+b^2} =\\mathrel{\\vcenter{:}} v)$.\n", - "- Wir finden $v_{min}$ und $v_{max}$, den kleinsten bzw. größten so erhaltenen Wert.\n", - " Dann skalieren wir jedes $v$ nach $255 \\cdot (v - v_{min}) / (v_{max} - v_{min})$.\n", - " Damit bekommen wir einen Wert zwischen 0 und 255.\n", - "- Diese Werte können wir jetzt als Pixel in einer Bilddatei abspeichern.\n", - " Dazu können wir zum Beispiel das [](pgm-format) benutzen.\n", + "It can be helpful during this project to visualize the result after every step.\n", + "Wen can do this for example like this:\n", + "- The signal contains 2 lines with 2080 pixels each per second. With $f_S = 16640\\text{Hz}$, we have 4 samples per pixel.\n", + "- We take every 4th sample. For complex numbers, we calculate the magnitude $(a + ib \\mapsto \\sqrt{a^2+b^2} =\\mathrel{\\vcenter{:}} v)$.\n", + "- We find $v_{min}$ and $v_{max}$, the smallest and largest values we obtained.\n", + " Then we scale each $v$ to $255 \\cdot (v - v_{min}) / (v_{max} - v_{min})$.\n", + " The result is a value between 0 and 255.\n", + "- We can save these values as pixels in an image file.\n", + " To do this, we can use the [](pgm-format) for example.\n", " \n", "```{figure} img/reference/raw_full_scaled.webp\n", "---\n", "name: fig:raw_full.en\n", "---\n", - "Visualisierung direkt nach dem Einlesen.\n", - "Man kann das Bild fast schon erkennen, es ist aber noch sehr dunkel.\n", + "Visualization, directly after reading the input.\n", + "The image can be discerned already, but it is quite dark.\n", "```\n", "\n", "```{figure} img/reference/raw_detail.webp\n", "---\n", "name: fig:raw_detail.en\n", "---\n", - "Detailansicht.\n", - "Hier sieht man deutliche vertikale Streifen, die von der Modulation auf den 2.4kHz Carrier kommen.\n", + "Detail view.\n", + "We can clearly see vertical lines, stemming from the modulation onto the 2.4 kHz carrier.\n", "```" ] } diff --git a/U02_2_Freq_Shift.en.ipynb b/U02_2_Freq_Shift.en.ipynb index e58bfbc..3ebb6c8 100644 --- a/U02_2_Freq_Shift.en.ipynb +++ b/U02_2_Freq_Shift.en.ipynb @@ -5,7 +5,7 @@ "id": "e67c2a43", "metadata": {}, "source": [ - "# Frequenz-Shift" + "# Frequency Shift" ] }, { @@ -17,7 +17,7 @@ "---\n", "name: fig:raw_waterfall.en\n", "---\n", - "Wasserfall-Diagramm. Wir können die beiden Kopien des Spektrums bei $\\pm2.4\\text{kHz}$ erkennen.\n", + "Waterfall diagram. We can see both copies of the spectrum at $\\pm2.4\\text{kHz}$.\n", "```" ] }, @@ -26,64 +26,64 @@ "id": "cbe50415", "metadata": {}, "source": [ - "Als ersten Schritt wollen wir die Kopie des Spektrums bei 2.4kHz \"auf die 0\" verschieben.\n", + "As a first step, we want to shift the copy of the spectrum at 2.4 kHz to zero.\n", "\n", - "Im Frequenz-Bereich können wir diese Verschiebung als eine Faltung mit einem Peak bei -2.4kHz darstellen.\n", - "Wie können wir so einen Peak erzeugen?\n", + "In the frequency domain, we can represent this shift as a convolution with a singular peak at -2.4kHz.\n", + "How can we create such a peak?\n", "\n", - "Wir erinnern uns:\n", - "$\\sin(2\\pi f t)$ und $\\cos(2\\pi f t)$ hatten Peaks bei $\\pm f$.\n", + "We remember:\n", + "$\\sin(2\\pi f t)$ and $\\cos(2\\pi f t)$ have peaks at $\\pm f$.\n", "\n", - "Genauer gesagt:\n", + "To be precise:\n", "```{math}\n", "\\begin{align*}\n", "\\sin(2\\pi f_0 t) \\,&\\circ\\!\\!-\\!\\!\\bullet\\, \\left\\{\\begin{array}{rcl}\n", " \\frac{1}{2}i &∶& f = -f_0 \\\\\n", " -\\frac{1}{2}i &:& f = f_0 \\\\\n", - " 0 &:& \\text{sonst} \\\\\n", + " 0 &:& \\text{otherwise} \\\\\n", "\\end{array}\\right. \\\\\n", "\\cos(2\\pi f_0 t) \\,&\\circ\\!\\!-\\!\\!\\bullet\\, \\left\\{\\begin{array}{rcl}\n", " \\frac{1}{2} &∶& f \\in \\{-f_0, f_0\\} \\\\\n", - " 0 &:& \\text{sonst} \\\\\n", + " 0 &:& \\text{otherwise} \\\\\n", "\\end{array}\\right. \\\\\n", "\\end{align*}\n", "```\n", "\n", - "Damit haben wir jeweils zwei Peaks.\n", - "Wir können Sinus und Cosinus aber geschickt kombinieren so dass sich einer davon aufhebt:\n", - "Wenn wir den Sinus mit $i$ multiplizieren bekommen wir:\n", + "That is two peaks each\n", + "We can however combine sine and cosine so that one of them cancels out:\n", + "If we multiply the sine term with $i$, we get:\n", "```{math}\n", "i \\cdot \\sin(2\\pi f_0 t) \\,&\\circ\\!\\!-\\!\\!\\bullet\\, \\left\\{\\begin{array}{rcl}\n", " i \\cdot \\frac{1}{2}i = -\\frac{1}{2} &∶& f = -f_0 \\\\\n", " i \\cdot -\\frac{1}{2}i = \\frac{1}{2} &:& f = f_0 \\\\\n", - " 0 &:& \\text{sonst} \\\\\n", + " 0 &:& \\text{otherwise} \\\\\n", "\\end{array}\\right.\n", "```\n", - "Und wenn wir jetzt noch den Cosinus addieren:\n", + "And if we now add the cosine term:\n", "```{math}\n", "\\cos(2\\pi f_0 t) + i\\sin(2\\pi f_0 t) \\,&\\circ\\!\\!-\\!\\!\\bullet\\, \\left\\{\\begin{array}{rcl}\n", " \\frac{1}{2} -\\frac{1}{2} = 0 &∶& f = -f_0 \\\\\n", " \\frac{1}{2} + \\frac{1}{2} = 1 &:& f = f_0 \\\\\n", - " 0 &:& \\text{sonst} \\\\\n", + " 0 &:& \\text{otherwise} \\\\\n", "\\end{array}\\right.\n", "```\n", - "Damit haben wir genau den Peak bei $f_0$.\n", + "This yields exactly one peak at $f_0$.\n", "\n", "```{note}\n", - "Den Ausdruck $\\cos(x) + i\\sin(x)$ habt ihr vielleicht schon mal in der [Eulerschen Formel](https://de.wikipedia.org/wiki/Eulersche_Formel) gesehen.\n", + "The expression $\\cos(x) + i\\sin(x)$ may be familliar from [Euler's formula](https://en.wikipedia.org/wiki/Euler's_formula).\n", "```\n", "\n", - "Um den Frequenz-Shift durchzuführen, können wir also einfach in der Zeit-Domain (= auf den Samples) mit dieser Funktion multiplizieren.\n", - "Dazu gehen wir so vor:\n", - "- Für jedes Sample $s$ berechnen wir den aktuellen Zeitpunkt $t$.\n", - " Durch die Abtastrate $f_S = 16640\\text{Hz}$ wissen wir, dass der Zeitabstand zwischen zwei Samples genau $1/16640\\text{s}$ ist.\n", - "- Dann berechnen wir $\\cos(2\\pi \\cdot -2400 \\cdot t) + i \\cdot \\sin(2\\pi \\cdot -2400 \\cdot t)$ und erhalten einen komplexen Wert $a + bi$.\n", - "- Diesen multiplizieren wir mit $s$ und erhalten $a \\cdot s + (b \\cdot s)i$ und speichern ihn als neues, komplexes Sample.\n", + "To perform the frequency shift, we can simply multiply in the time domain (= each sample) with this function.\n", + "We do this as follows:\n", + "- For every sample $s$, we calculate the current time $t$.\n", + " Since the sampling rate $f_S$ equals $16640\\text{Hz}$ we know that the duration in between two samples is exactly $1/16640\\text{s}$.\n", + "- We then calculate $\\cos(2\\pi \\cdot -2400 \\cdot t) + i \\cdot \\sin(2\\pi \\cdot -2400 \\cdot t)$ and obtain a complex result $a + bi$.\n", + "- We multiply $s$ with this, resulting in $a \\cdot s + (b \\cdot s)i$, which we save as our new (complex) sample.\n", "\n", "```{note}\n", - "Für dieses Projekt reicht es theoretisch aus, komplexe Zahlen als Paare von jeweils zwei reelle Zahlen zu speichern.\n", - "In manchen Programmiersprachen gibt es aber auch explizite Typen, um komplexe Zahlen darzustellen, z.B. [std::complex](https://en.cppreference.com/w/cpp/numeric/complex) in C++.\n", - "In Python kann man sie sogar einfach mit `a + b * 1j` erzeugen.\n", + "For this project, it is sufficient to represent complex numbers as pairs of two real numbers.\n", + "But in some programming languages, there are explicit types for complex numbers, e.g., [std::complex](https://en.cppreference.com/w/cpp/numeric/complex) in C++.\n", + "In Python, you can simply use `a + b * 1j`.\n", "```" ] } diff --git a/U02_3_Low_Pass.en.ipynb b/U02_3_Low_Pass.en.ipynb index 5f1c670..b9a0555 100644 --- a/U02_3_Low_Pass.en.ipynb +++ b/U02_3_Low_Pass.en.ipynb @@ -17,26 +17,26 @@ "---\n", "name: fig:shifted_waterfall.en\n", "---\n", - "Wasserfall-Diagramm nach dem Frequenz-Shift. Eine Kopie ist zur 0 gewandert, die andere auf -4.8kHz.\n", - "Außerdem ist die sogenannte *DC-Komponente*, die vorher auf der 0 war, jetzt bei -2.4kHz.\n", + "Waterfall diagram after the frequency shift. One copy has moved to zero, the other to -4.8kHz.\n", + "We also see the so-called *DC-component*, previously at zero, at -2.4kHz now.\n", "```\n", "\n", - "Im nächsten Schritt filtern wir das Signal, so dass nur die Kopie des Basisbands übrig bleibt.\n", - "Weil darin 4160 Pixel pro Sekunde übertragen werden, reicht es im Spektrum von -2080 bis 2080 Hz (Das hängt mit dem Nyquist-Kriterium zusammen).\n", + "In the next step we filter the signal, such that only one copy of the baseband remains.\n", + "Since it contains 4160 pixels per second, it extends from -2080 to 2080 Hz in the spectrum (this is related to the nyquist criterion).\n", "\n", - "Wir wollen also im Spektrum alles entfernen, was nicht in diesem Frequenz-Intervall liegt.\n", - "Das können wir als Multiplikation mit einer sogenannten Rechteck-Funktion ausdrücken:\n", + "Therefore, we want to remove everything in the spectrum that is outside of this frequency interval.\n", + "This can be represented as a multiplication with a so-called rectangle function:\n", "```{math}\n", "\\text{rect}(f) = \\left\\{\\begin{array}{rcl}\n", " 1 &∶& -\\frac{1}{2} < f < \\frac{1}{2} \\\\\n", - " 0 &:& \\text{sonst} \\\\\n", + " 0 &:& \\text{otherwise} \\\\\n", "\\end{array}\\right.\n", "```" ] }, { "cell_type": "code", - "execution_count": 7, + "execution_count": 1, "id": "3706c744", "metadata": { "tags": [ @@ -46,7 +46,7 @@ "outputs": [ { "data": { - "image/png": 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xwq0FAgAA1IXTIWfixInav3+/JOnFF1/UXXfdpbi4OP3pT39Sv379lJycrCVLlri9UKChVTNLAoAGwuEHd3D6ctXevXvtTxZfuHChnnnmGSUnJ9uX9+vXT0888YRuv/1291UJAADgJKfP5AQEBNgHGx85ckT9+/d3WB4fH+9wOQsAgLpi0mO4wumQM3z4cD333HOSpMGDB+vNN990WP7666+rS5cu7qkOAACgjpy+XPXUU09p4MCBGjx4sOLi4jR37lzl5OSoe/fu2r17tzZt2qS33367PmoFAACoNafP5ERERGjr1q1KSEjQmjVrZBiG8vLy9M9//lMdOnTQxo0bdd1119VHrQAAALVWp3lygoODlZmZqczMTHfXA3gcYwAAwBycPpPzWw4fPsydVQAAwOPcHnJ++OEHLV++3N2bBTyAmToAT2GeKriD05er3n333Qsu/+abb+pcDAAAgLs4HXJGjx4ti8Ui4wIDFyxEcACAG/AsObjC6ctV4eHheuutt1RRUVHta8uWLfVRJwAAgFOcDjmxsbHKz8+vcflvneUBAABoCE5frpoxY4ZKSkpqXN6lSxetX7/epaIAAABc5XTIGTRo0AWXN2/eXIMHD65zQYCncR4SAMzBbbeQc4kKAAB4E7eFHKvVqp07d7prc4DHcZMg4DkW5qmCGzh9uSotLa3a9vLycmVmZqpNmzaSpKysLNcqAwAAcIHTIWfevHmKjo5WcHCwQ7thGNq5c6eaN2/OPDkAALdgJARc4XTIefLJJ/XCCy9o7ty5uuaaa+ztTZs21bJly3TFFVe4tUAAAIC6cHpMzkMPPaSVK1dqypQpuv/++3X27Nn6qAsAAMAldRp43K9fP+Xn5+v48eOKi4vTjh07uEQFAAC8itOXq85r0aKFli9frhUrVigxMVHl5eXurAvwGMYAAIA51DnknHfzzTfryiuvVH5+vjp16uSOmgAAAFzm9OWqWbNmVXl2VYcOHTRq1Cg1b97cbYUBnsYFWMCDOADhBk6HnO+++07Dhw9Xhw4dNGXKFH3wwQcqKyurj9oAAADqzOmQs2TJEhUWFuq1115Ty5YtNW3aNIWEhOiGG27Q3//+d/3www/1UScA4CLEEDm4wqmQ88ADD+jMmTPy8fHRoEGDNHv2bO3evVuff/654uPj9fzzzysiIkJXXXWV5syZoyNHjtRX3QAAABfkVMiZN2+eTp48KUmaMGGCTp06JUnq3r27HnjgAW3cuFGHDx/Wbbfdpk8++USvvfaa+ysGAACoBadCTkREhAoKCiRJL7/8sn7++ecqfdq2batJkybpnXfe0f333++WIgEAAJzlVMi57777NHLkSA0aNEiS9MorrygvL0+nT5+ul+IATzAYBQAApuBUyLnnnnu0efNmDRs2TIZhaMGCBRowYIACAwPVvXt33XzzzcrMzNQHH3xQX/UCAADUitOTAfbu3Vu9e/fWsmXLlJubq+bNm+vLL79UQUGBCgoK9M477+iJJ55QcXFxfdQLNBieVAJ4Docf3KHOMx7v3bvX/v/j4+MVHx9vf28wLz4AAPAwpy5XHTp0qFb9zj+sk1vIAQCu4I9muMKpkNOvXz/ddddd+uKLL2rsc/LkSS1evFg9e/bUP/7xD5cLBAAAqAunLld9/fXXeuKJJ/T73/9e/v7+io2NVUREhPz9/fXjjz/q66+/1ldffaW+fftq9uzZuu666+qrbgAAgAty6kxOmzZtlJWVpaNHj2r+/Pnq2rWrTpw4YR+fM27cOOXn5ys3N5eAAwAAPKpOA4+bNWumG2+8UTfeeKO76wE8jiEAAGAOTj+g87wBAwbIZrO5sxYAAAC3qXPI2bRpk86cOVOl3Waz6cEHH3SpKMAbWJipA/AY5qmCOzgdcm688UZlZmbKYrHo2LFjVZaXlJRozpw5bikOAHBx4/IxXOH0mJyOHTvqvffek2EYio6OVps2bRQdHa3o6GjFxMRo9+7dCg8Pr49aAQAAas3pkJOVlSVJ8vPz08aNG/X9999r69atKigo0Ntvv62KigrNnj3b7YUCAAA4o86PdcjOzlazZs00atQojRo1yp01AQAAuKzOA4/vvfdeff7551Xa9+/fz8M5AQCAx9U55OzevVtDhgyp0r5u3TqNHTvWlZoAj2KcIwCYQ51DTmBgoH788ccq7YMGDdKmTZtcKgoAAMBVdQ45w4YNq/ZWcR8fH5WVlblUFOANmKcD8BzmqYI71DnkPP744/r44491ww03aPv27ZKkM2fO6KmnnlLv3r3dViAAAEBd1PnuqsjISG3atElTpkxRdHS0rFarzp07p6CgIP3v//6vO2sEAABwWp1DjiR16tRJq1ev1rfffqtt27apadOmio+PV+vWrd1VHwAAQJ24FHLO69Spkzp16uSOTQEAALhFncfknDx5Unfeeae6dOmi7t276+jRoy4Xs2DBAkVFRcnf31/x8fHKy8ur1XorVqyQxWLR6NGjXa4BAACYQ51DTkpKirZv367Zs2fr22+/1enTpyVJ06dP1/z5853e3sqVK5WWlqb09HRt2bJF0dHRSkpKqvYhoL928OBB3X///Ro0aFCdvgdQBU8EBABTqHPI+eCDD7Rw4UL94Q9/kK+vr709KSlJy5cvd3p7WVlZSk5O1sSJE3XFFVdo0aJFCggI0JIlS2pcp7y8XOPGjdNjjz2mSy65pE7fAwAAmFOdQ45hGGrZsmWV9q5du2rv3r1ObausrEz5+flKTEz8d2E+PkpMTFRubm6N6/33f/+32rVrp0mTJv3mZ5SWlspmszm8gAthnhzAczj+4A51DjnDhw/XK6+8UqW9pKREFif/6zxx4oTKy8sVGhrq0B4aGqrCwsJq1/n000/10ksvafHixbX6jIyMDAUFBdlfkZGRTtUIAGh4XD2GK+p8d1VmZqZiY2Ml/XJWx2Kx6MyZM3r88cfVt29ftxVYneLiYt16661avHixQkJCarXOzJkzlZaWZn9vs9kIOgAAmFidQk55ebny8/O1bt06zZgxQ6dOnVL//v1VXFyswMBArV692qnthYSEyNfXV0VFRQ7tRUVFCgsLq9J///79OnjwoEaOHGlvq6iokCQ1adJEu3fv1qWXXuqwjtVqldVqdaouAADQeNUp5Pj6+mrs2LH66quvtHbtWh06dMhhMsBWrVo5tT0/Pz/FxsYqOzvbfht4RUWFsrOzlZqaWqV/t27d7I+SOO+RRx5RcXGxnnnmGc7QAACAul+u6tevnw4cOKBLLrlEHTt2VMeOHV0qJC0tTbfddpvi4uLUv39/zZs3TyUlJZo4caIkafz48Wrfvr0yMjLk7++vnj17OqwfHBwsSVXaAQDAxanOIeeee+7Rww8/rDfffNMtZ07GjBmj48ePa9asWSosLFRMTIzWrFljH4x86NAh+fjUeZw0UGuMcwQAc6hzyBkzZowkqUePHrr++us1ZMgQ9enTR7169ZKfn1+dtpmamlrt5SlJysnJueC6y5Ytq9NnAgAAc6pzyDlw4IC2bdumgoICbdu2TRkZGTp48KCaNGmiyy+/XF9++aU76wQanEVM1AF4Ckcf3KHOIef8Qzmvv/56e1txcbEKCgoIOAAAtzC4gAwXuOUp5Oe1bNlSgwYN4jlSAADA4xjJCwAATImQAwAATImQAwAATImQA1TCAwEBwBwIOQAAwJQIOUBNmKgD8BiLhQMQriPkAAC8FpeP4QpCDgAAMCVCDgAAMCVCDgAAMCVCDgAAMCVCDlCJwUhHADAFQg4AADAlQg5QA2bpADzn/PHHeVW4gpADAABMiZADAABMiZADAABMiZADAABMiZADAABMiZADVMLdHABgDoQcAABgSoQcoAYWCzPlAB7zr8OPGcjhCkIOAAAwJUIOAAAwJUIOAAAwJUIOAAAwJUIOAAAwJUIOUAk3cwCAORByAACAKRFygBowSw7gOeePP06swhWEHAAAYEqEHAAAYEqEHAAAYEqEHAAAYEqEHAAAYEqEHKAS7uYAAHMg5AAAAFMi5AA1sDBRDuAxln8dgMxADlcQcgAAgCkRcgAAgCkRcgAAgCkRcgAAgCkRcgAAgCkRcoBKDG7nAABTIOQAALwYf3Sg7gg5QA2YJgfwHOapgjsQcgAAgCkRcgAAgCkRcgAAgCkRcgAAgCkRcgAAgCkRcgAAgCkRcgAAXou5OeEKrwo5CxYsUFRUlPz9/RUfH6+8vLwa+y5evFiDBg1Sq1at1KpVKyUmJl6wP+AsCxN1AB7D0Qd38JqQs3LlSqWlpSk9PV1btmxRdHS0kpKSdOzYsWr75+TkaOzYsVq/fr1yc3MVGRmpoUOH6siRIw1cOQAA8EZeE3KysrKUnJysiRMn6oorrtCiRYsUEBCgJUuWVNv/lVde0d13362YmBh169ZNL774oioqKpSdnd3AlQMAAG/kFSGnrKxM+fn5SkxMtLf5+PgoMTFRubm5tdrGqVOndPbsWbVu3bra5aWlpbLZbA4vAABgXl4Rck6cOKHy8nKFhoY6tIeGhqqwsLBW23jwwQcVERHhEJR+LSMjQ0FBQfZXZGSky3UDAADv5RUhx1WZmZlasWKF3n77bfn7+1fbZ+bMmTp58qT9dfjw4QauEgAANKQmni5AkkJCQuTr66uioiKH9qKiIoWFhV1w3Tlz5igzM1Pr1q1T7969a+xntVpltVrdUi/MjVtWAcAcvOJMjp+fn2JjYx0GDZ8fRJyQkFDjerNnz9bjjz+uNWvWKC4uriFKBQA0IP7mgCu84kyOJKWlpem2225TXFyc+vfvr3nz5qmkpEQTJ06UJI0fP17t27dXRkaGJOmpp57SrFmz9OqrryoqKso+dqdFixZq0aKFx74HzIN5OgDPYZ4quIPXhJwxY8bo+PHjmjVrlgoLCxUTE6M1a9bYByMfOnRIPj7/PvH03HPPqaysTDfeeKPDdtLT0/XnP/+5IUsHAABeyGtCjiSlpqYqNTW12mU5OTkO7w8ePFj/BQEAgEbLK8bkAAAAuBshBwAAmBIhBwAAmBIhB6jE4KZVADAFQg4AwGsxOSdcQcgBasI0HYDHcPjBHQg5AADAlAg5AADAlAg5AADAlAg5AADAlAg5AADAlAg5QCXcsgoA5kDIAQB4LSbnhCsIOUANLMzUAXiMhcMPbkDIAQAApkTIAQAApkTIAQAApkTIAQAApkTIAQAApkTIASrhhlXAezBvFVxByAEAAKZEyAFqwDwdgCdxAMJ1hBwAAGBKhBwAAGBKhBwAAGBKhBwAAGBKhBygEm5ZBQBzIOQAALwWf3TAFYQcAABgSoQcoAbM0gF4DvNUwR0IOQAAwJQIOQAAwJQIOQAAwJQIOQAAwJQIOUAlhrhnFQDMgJADAPBa/NEBVxBygBpwCyvgORx+cAdCDgAAMCVCDgAAMCVCDgAAMCVCDgAAMCVCDgAAMCVCDlCJwR2rAGAKhBwAgNfijw64gpAD1MDCTB2AxzBPFdyBkAMAAEyJkAMAAEyJkAMAAEyJkAMAAEyJkAMAAEyJkAMAAEyJkAMAAEyJkAPUgHk6AM9hniq4AyEHAACYEiEHAACYEiEHAACYkleFnAULFigqKkr+/v6Kj49XXl7eBfu/8cYb6tatm/z9/dWrVy+tXr26gSoFAADezmtCzsqVK5WWlqb09HRt2bJF0dHRSkpK0rFjx6rt/9lnn2ns2LGaNGmStm7dqtGjR2v06NHasWNHA1cOAAC8kcUwvONB9vHx8erXr5/mz58vSaqoqFBkZKTuuecePfTQQ1X6jxkzRiUlJXrvvffsbb/73e8UExOjRYsW/ebn2Ww2BQUF6eTJkwoMDHTb9yg9V67jxaVu2x4a3t9zv9ULG77Rzf0ilXlDb0+XA1yUfvdktgptZ/TSbXG6PKylp8tBHfk18VG7lv5u3aYzv7+buPWT66isrEz5+fmaOXOmvc3Hx0eJiYnKzc2tdp3c3FylpaU5tCUlJWnVqlXV9i8tLVVp6b/Dh81mc73wanz1vU1/WPhZvWwbAC42k5Zv9nQJcEHfjsF66+6BHvt8rwg5J06cUHl5uUJDQx3aQ0NDtWvXrmrXKSwsrLZ/YWFhtf0zMjL02GOPuafgC7BIsjbxmquAqKNmfr66pls7T5cBXLSuj4nQ33MPyjuuNaCumvp69vehV4SchjBz5kyHMz82m02RkZFu/5w+HVtp91+Gu327AHAxefi67nr4uu6eLgONnFeEnJCQEPn6+qqoqMihvaioSGFhYdWuExYW5lR/q9Uqq9XqnoIBAIDX84rrKn5+foqNjVV2dra9raKiQtnZ2UpISKh2nYSEBIf+kvThhx/W2B8AAFxcvOJMjiSlpaXptttuU1xcnPr376958+appKREEydOlCSNHz9e7du3V0ZGhiRp6tSpGjx4sObOnasRI0ZoxYoV2rx5s1544QVPfg0AAOAlvCbkjBkzRsePH9esWbNUWFiomJgYrVmzxj64+NChQ/Lx+feJpwEDBujVV1/VI488oocfflhdu3bVqlWr1LNnT099BQAA4EW8Zp6chlZf8+QAAID648zvb68YkwMAAOBuhBwAAGBKhBwAAGBKhBwAAGBKhBwAAGBKhBwAAGBKhBwAAGBKhBwAAGBKhBwAAGBKXvNYh4Z2fqJnm83m4UoAAEBtnf+9XZsHNly0Iae4uFiSFBkZ6eFKAACAs4qLixUUFHTBPhfts6sqKir0/fffq2XLlrJYLA362TabTZGRkTp8+DDPzWok2GeNC/ur8WGfNS6e3F+GYai4uFgREREOD+6uzkV7JsfHx0cdOnTwaA2BgYEczI0M+6xxYX81PuyzxsVT++u3zuCcx8BjAABgSoQcAABgSoQcD7BarUpPT5fVavV0Kagl9lnjwv5qfNhnjUtj2V8X7cBjAABgbpzJAQAApkTIAQAApkTIAQAApkTIAQAApkTIqSelpaWKiYmRxWJRQUGBw7Ivv/xSgwYNkr+/vyIjIzV79uwq67/xxhvq1q2b/P391atXL61evdphuWEYmjVrlsLDw9WsWTMlJiZq79699fmVTOfgwYOaNGmSOnfurGbNmunSSy9Venq6ysrKHPqxvxqfBQsWKCoqSv7+/oqPj1deXp6nSzK9jIwM9evXTy1btlS7du00evRo7d6926HPmTNnlJKSojZt2qhFixa64YYbVFRU5NDn0KFDGjFihAICAtSuXTvNmDFD586dc+iTk5Ojvn37ymq1qkuXLlq2bFl9fz3Ty8zMlMVi0bRp0+xtpthfBurFvffeawwfPtyQZGzdutXefvLkSSM0NNQYN26csWPHDuO1114zmjVrZjz//PP2Phs3bjR8fX2N2bNnG19//bXxyCOPGE2bNjW2b99u75OZmWkEBQUZq1atMrZt22Zcf/31RufOnY3Tp0835Nds1D744ANjwoQJxtq1a439+/cb77zzjtGuXTvjvvvus/dhfzU+K1asMPz8/IwlS5YYX331lZGcnGwEBwcbRUVFni7N1JKSkoylS5caO3bsMAoKCozrrrvO6Nixo/Hzzz/b+0yePNmIjIw0srOzjc2bNxu/+93vjAEDBtiXnzt3zujZs6eRmJhobN261Vi9erUREhJizJw5097nm2++MQICAoy0tDTj66+/Np599lnD19fXWLNmTYN+XzPJy8szoqKijN69extTp061t5thfxFy6sHq1auNbt26GV999VWVkLNw4UKjVatWRmlpqb3twQcfNC6//HL7+5tuuskYMWKEwzbj4+ONu+66yzAMw6ioqDDCwsKMp59+2r78p59+MqxWq/Haa6/V07e6OMyePdvo3Lmz/T37q/Hp37+/kZKSYn9fXl5uREREGBkZGR6s6uJz7NgxQ5Lx8ccfG4bxy3/zTZs2Nd544w17n507dxqSjNzcXMMwfvm308fHxygsLLT3ee6554zAwED7MfjAAw8YPXr0cPisMWPGGElJSfX9lUypuLjY6Nq1q/Hhhx8agwcPtoccs+wvLle5WVFRkZKTk/Xyyy8rICCgyvLc3FxdddVV8vPzs7clJSVp9+7d+vHHH+19EhMTHdZLSkpSbm6uJOnAgQMqLCx06BMUFKT4+Hh7H9TNyZMn1bp1a/t79lfjUlZWpvz8fIeftY+PjxITE/lZN7CTJ09Kkv14ys/P19mzZx32Tbdu3dSxY0f7vsnNzVWvXr0UGhpq75OUlCSbzaavvvrK3udCxxuck5KSohEjRlT5mZplfxFy3MgwDE2YMEGTJ09WXFxctX0KCwsd/oOQZH9fWFh4wT6/Xv7r9arrA+ft27dPzz77rO666y57G/urcTlx4oTKy8v5WXtYRUWFpk2bpoEDB6pnz56SfjkO/Pz8FBwc7NC38rFS1+PNZrPp9OnT9fF1TGvFihXasmWLMjIyqiwzy/4i5NTCQw89JIvFcsHXrl279Oyzz6q4uFgzZ870dMkXtdrur187cuSIhg0bpj/+8Y9KTk72UOWAOaSkpGjHjh1asWKFp0tBDQ4fPqypU6fqlVdekb+/v6fLqTdNPF1AY3DfffdpwoQJF+xzySWX6KOPPlJubm6VZ3nExcVp3LhxWr58ucLCwqqMTj//PiwszP6/1fX59fLzbeHh4Q59YmJinP5+ZlPb/XXe999/r6uvvloDBgzQCy+84NCP/dW4hISEyNfX94L7A/UrNTVV7733njZs2KAOHTrY28PCwlRWVqaffvrJ4exA5WOl8p1wtT3eAgMD1axZs/r4SqaUn5+vY8eOqW/fvva28vJybdiwQfPnz9fatWvNsb8aZOTPReLbb781tm/fbn+tXbvWkGS8+eabxuHDhw3D+PdA1rKyMvt6M2fOrDKQ9T/+4z8ctp2QkFBlIOucOXPsy0+ePMlA1jr47rvvjK5duxo333yzce7cuSrL2V+NT//+/Y3U1FT7+/LycqN9+/YMPK5nFRUVRkpKihEREWHs2bOnyvLzA1nffPNNe9uuXbuqHcj66zvhnn/+eSMwMNA4c+aMYRi/DGTt2bOnw7bHjh3LwGMn2Ww2h99X27dvN+Li4oz/+q//MrZv326a/UXIqUcHDhyocnfVTz/9ZISGhhq33nqrsWPHDmPFihVGQEBAlVuSmzRpYsyZM8fYuXOnkZ6eXu0tycHBwcY777xjfPnll8aoUaO4JdlJ3333ndGlSxfj2muvNb777jvj6NGj9td57K/GZ8WKFYbVajWWLVtmfP3118add95pBAcHO9wBAvebMmWKERQUZOTk5DgcS6dOnbL3mTx5stGxY0fjo48+MjZv3mwkJCQYCQkJ9uXnb0keOnSoUVBQYKxZs8Zo27Zttbckz5gxw9i5c6exYMECbiF3k1/fXWUY5thfhJx6VF3IMQzD2LZtm3HllVcaVqvVaN++vZGZmVll3ddff9247LLLDD8/P6NHjx7G+++/77C8oqLCePTRR43Q0FDDarUa1157rbF79+76/Dqms3TpUkNSta9fY381Ps8++6zRsWNHw8/Pz+jfv7+xadMmT5dkejUdS0uXLrX3OX36tHH33XcbrVq1MgICAoz//M//dPijwjAM4+DBg8bw4cONZs2aGSEhIcZ9991nnD171qHP+vXrjZiYGMPPz8+45JJLHD4DdVc55Jhhf1kMwzDq/6IYAABAw+LuKgAAYEqEHAAAYEqEHAAAYEqEHAAAYEqEHAAAYEqEHAAAYEqEHAAAYEqEHAAAYEqEHACohYMHD9qfYl8fD1YdMmSIffsFBQVu3z5wMSLkAKjRhAkT7L94f/3at2+fp0vzmHXr1ik7O9v+/s9//nO1oed8KKptYHnrrbeqPNEZgGuaeLoAAN5t2LBhWrp0qUNb27Ztq/QrKyuTn59fQ5XlMW3atFGbNm3cvt3WrVvLZrO5fbvAxYwzOQAuyGq1KiwszOHl6+urIUOGKDU1VdOmTVNISIiSkpIkSTt27NDw4cPVokULhYaG6tZbb9WJEyfs2yspKdH48ePVokULhYeHa+7cuRoyZIimTZtm72OxWLRq1SqHOoKDg7Vs2TL7+8OHD+umm25ScHCwWrdurVGjRungwYP25RMmTNDo0aM1Z84chYeHq02bNkpJSdHZs2clSTk5OdWepZowYYK7f4T2eqr7vJycnHr5PACEHAAuWL58ufz8/LRx40YtWrRIP/30k6655hr16dNHmzdv1po1a1RUVKSbbrrJvs6MGTP08ccf65133tE///lP5eTkaMuWLU597tmzZ5WUlKSWLVvqk08+0caNG9WiRQsNGzZMZWVl9n7r16/X/v37tX79ei1fvlzLli2zB6UBAwbo6NGj9tdHH30kf39/XXXVVW752VT2zDPPOHze1KlT1a5dO3Xr1q1ePg8Al6sA/Ib33ntPLVq0sL8fPny43njjDUlS165dNXv2bPuyv/zlL+rTp4+efPJJe9uSJUsUGRmpPXv2KCIiQi+99JL+53/+R9dee62kX4JShw4dnKpp5cqVqqio0IsvviiLxSJJWrp0qYKDg5WTk6OhQ4dKklq1aqX58+fL19dX3bp104gRI5Sdna3k5GT5+fkpLCxMkvR///d/uuOOO3T77bfr9ttvd/pntH37doefkSQZhuHwPigoSEFBQZJ+GX/z/PPPa926dfYaALgfIQfABV199dV67rnn7O+bN29u//+xsbEOfbdt26b169dX+YUvSfv379fp06dVVlam+Ph4e3vr1q11+eWXO1XTtm3btG/fPrVs2dKh/cyZM9q/f7/9fY8ePeTr62t/Hx4eru3btzusc/bsWd1www3q1KmTnnnmGafqOO/yyy/Xu+++69B25MgRDRkypErfrVu36tZbb9X8+fM1cODAOn0egNoh5AC4oObNm6tLly41Lvu1n3/+WSNHjtRTTz1VpW94eHit78qyWCxVzoScH0tz/nNiY2P1yiuvVFn314OimzZtWmW7FRUVDm1TpkzR4cOHlZeXpyZN6vZPop+fX5WfUXXbKiws1PXXX6877rhDkyZNqtNnAag9Qg4At+nbt6/+8Y9/KCoqqtpf8pdeeqmaNm2qzz//XB07dpQk/fjjj9qzZ48GDx5s79e2bVsdPXrU/n7v3r06deqUw+esXLlS7dq1U2BgYJ3rzcrK0uuvv67PPvusXu6Y+rUzZ85o1KhR6tatm7Kysur1swD8goHHANwmJSVFP/zwg8aOHasvvvhC+/fv19q1azVx4kSVl5erRYsWmjRpkmbMmKGPPvpIO3bs0IQJE+Tj4/hP0TXXXKP58+dr69at2rx5syZPnuxwVmbcuHEKCQnRqFGj9Mknn+jAgQPKycnRvffeq++++65Wta5bt04PPPCAnn76aYWEhKiwsFCFhYU6efKkW38m59111106fPiw/va3v+n48eP2z/v1QGkA7kXIAeA2ERER2rhxo8rLyzV06FD16tVL06ZNU3BwsD3IPP300xo0aJBGjhypxMREXXnllVXG9sydO1eRkZEaNGiQbrnlFt1///0KCAiwLw8ICNCGDRvUsWNH/eEPf1D37t01adIknTlzptZndj799FOVl5dr8uTJCg8Pt7+mTp3qvh/Ir3z88cc6evSorrjiCofP++yzz+rl8wBIFqPyhW8AaGBDhgxRTEyM5s2b5+lSanTw4EF17txZW7durZfHOjTUZwAXE87kAIATBgwYoAEDBrh9u8OHD1ePHj3cvl3gYsbAYwCohQ4dOmjv3r2SfpkF2t1efPFFnT59WpLsg7IBuIbLVQAAwJS4XAUAAEyJkAMAAEyJkAMAAEyJkAMAAEyJkAMAAEyJkAMAAEyJkAMAAEyJkAMAAEzp/wF78vE/wH3jAgAAAABJRU5ErkJggg==", + "image/png": 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", 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" ] @@ -68,7 +68,7 @@ "\n", "fig, ax = plt.subplots()\n", "ax.plot(f, rect(1/4160 * f));\n", - "ax.set_xlabel(\"Frequenz [Hz]\");\n", + "ax.set_xlabel(\"Frequency [Hz]\");\n", "ax.set_ylabel(\"$rect(f/4160)$\");" ] }, @@ -77,17 +77,17 @@ "id": "515f4212", "metadata": {}, "source": [ - "Hier haben wir das Rechteck bereits so skaliert, dass es für Frequenzen zwischen -2080 und 2080 den Wert 1 hat und sonst 0.\n", - "Das erreichen wir folgendermaßen:\n", + "Here, we have already scaled the rectangle such that its value is 1 if the input frequency is between -2080 and 2080, and 0 otherwise.\n", + "This can be done like this:\n", "```{math}\n", "\\text{rect}\\left(\\frac{1}{4160} \\cdot f\\right) = \\left\\{\\begin{array}{rcl}\n", " 1 &∶& -\\frac{1}{2} < \\frac{1}{4160} \\cdot f < \\frac{1}{2} \\Leftrightarrow -2080 < f < 2080 \\\\\n", - " 0 &:& \\text{sonst} \\\\\n", + " 0 &:& \\text{otherwise} \\\\\n", "\\end{array}\\right.\n", "```\n", "\n", - "In der Zeit-Domain entspricht das Rechteck der sogenannten $\\text{sinc}$ Funktion.\n", - "Sie ist definiert als\n", + "A rectangle in the frequency domain corresponds to the $\\text{sinc}$ in the time domain.\n", + "This function is defined as\n", "```{math}\n", "\\text{sinc}(t) \\mathrel{\\vcenter{:}}= \\left\\{\\begin{array}{ccl}\n", " \\frac{\\sin(\\pi t)}{\\pi t} &∶& t \\neq 0 \\\\\n", @@ -95,52 +95,51 @@ "\\end{array}\\right.\n", "```\n", "\n", - "Mit der Skalierung auf den Bereich von -2080 bis 2080 Hz (wegen $x[at] \\,\\circ\\!\\!-\\!\\!\\bullet\\, \\frac{1}{|a|} X \\left[\\frac{f}{a}\\right]$):\n", + "Including the scaling to -2080 to 2080 Hz, we get (due to $x[at] \\,\\circ\\!\\!-\\!\\!\\bullet\\, \\frac{1}{|a|} X \\left[\\frac{f}{a}\\right]$):\n", "```{math}\n", "\\text{rect}\\left(\\frac{1}{4160} \\cdot f\\right) \\,\\bullet\\!\\!-\\!\\!\\circ\\, 4160 \\cdot \\text{sinc}(4160 \\cdot t)\n", "```\n", "\n", - "Um das Signal zu filtern wollen wir also eine Faltung mit der $\\text{sinc}$ Funktion implementieren.\n", - "Dabei haben wir allerdings ein Problem:\n", - "Die $\\text{sinc}$ Funktion hat einen *unendlichen Träger*, also wir müssten sie an unendlich vielen Stellen auswerten.\n", + "Thus, to filter the signal, we have to implement a convolution with this $\\text{sinc}$ function.\n", + "We have one problem though:\n", + "The $\\text{sinc}$ function has *infinite support*, so we would have to evaluate it at infinitely many points.\n", "\n", - "Damit unser Programm in endlicher Zeit fertig wird, können wir nur ein endlich großes Fenster an Samples für die Faltung benutzen.\n", - "Damit ist die Berechnung nicht mehr exakt.\n", - "Den so entstehenden Fehler können wir aber mit Hilfe einer sogenannten *window function* klein halten.\n", - "Eine häufig verwendete window function ist das sogenannte [Hamming-Window](https://de.wikipedia.org/wiki/Fensterfunktion#Hamming-Fenster):\n", + "Since we want our program to be done after a finite amount of time, we can only use a finite window of samples for the convolution.\n", + "This means our calculation can not be exact.\n", + "We can however keep the introduced error small, using a *window function*.\n", + "A commonly used window function is the so-called [Hamming window](https://en.wikipedia.org/wiki/Window_function#Hamming_window):\n", "```{math}\n", "w[n] \\mathrel{\\vcenter{:}}= 0.54 - 0.46 \\cdot \\cos\\left(\\frac{2 \\pi \\cdot n}{N - 1}\\right), \\quad n = 0,\\dots,N-1\n", "```\n", - "wobei $N$ die Größe des Fensters ist.\n", + "where $N$ is the size of the window (in samples).\n", "\n", - "Wir gehen also folgendermaßen vor:\n", - "- Als erstes wählen wir die Größe des Fensters.\n", - " Je mehr Samples das Fenster umfasst, desto besser wird das Ergebnis, aber die Laufzeit wird schlechter.\n", - " Für dieses Projekt können wir ein Fenster mit 64 Samples benutzen.\n", - "- Wir berechnen die sogenannten *Filter-Koeffizienten*. Für jeden Eintrag $a[n]$ setzt er sich zusammen aus $w[n]$ und einem Funktionswert $\\text{sinc}(t)$.\n", - " Der Zeitpunkt $t$ hängt von $n$ ab:\n", - " Wie schon beim Frequenz-Shift ist der Zeitabstand $1/f_S$.\n", - " Der Zeitbereich den wir abbilden wollen ist symmetrisch um die 0.\n", - " Gegeben $n$ und $N$ haben wir also\n", + "We proceed as follows:\n", + "- First we determine the window size.\n", + " The more samples it has, the more accurate the result becomes, at the cost of a longer running time.\n", + " For this project, a window size of 64 samples is fine.\n", + "- We calculate the *filter coefficients*. Every coefficient $a[n]$ is comprised of $w[n]$ and value of $\\text{sinc}(t)$, where $t$ depends on $n$:\n", + " As we have seen during the frequency shift, the time between samples is $1/f_S$.\n", + " We want a time interval that is symmetric around zero.\n", + " Given $n$ and $N$, we therefore have\n", " ```{math}\n", " t = \\frac{1}{f_S} \\cdot \\left(n - \\frac{N-1}{2}\\right)\n", " ```\n", - " Und insgesamt\n", + " And overall\n", " ```{math}\n", " a[n] = w[n] \\cdot \\text{sinc}(4160 \\cdot t)\n", " ```\n", - "- Wir skalieren $a$ noch so, dass\n", + "- Finally we scale each $a[n]$, such that\n", " ```{math}\n", " \\sum_{n=0}^{N-1} a[n] = 1\n", " ```\n", - " Deshalb haben wir auch den konstanten Faktor vor der $\\text{sinc}$ Funktion weg gelassen.\n", + " (This is what allowed us to ignore the constant factor in the $\\text{sinc}$ function.)\n", " \n", - "Hier sehen wir die $\\text{sinc}$ Funktion:" + "Here we see the $\\text{sinc}$ function:" ] }, { "cell_type": "code", - "execution_count": 17, + "execution_count": 2, "id": "949bb97c", "metadata": { "tags": [ @@ -150,7 +149,7 @@ "outputs": [ { "data": { - "image/png": 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", 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", 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" ] @@ -174,7 +173,7 @@ "\n", "fig, ax = plt.subplots()\n", "ax.plot(t, taps)\n", - "ax.set_xlabel(\"Zeit [s]\")\n", + "ax.set_xlabel(\"Time [s]\")\n", "ax.set_ylabel(\"$sinc(4160 t)$\");" ] }, @@ -183,12 +182,12 @@ "id": "9808b2f0", "metadata": {}, "source": [ - "Und hier das Hamming-Window:" + "And here the hamming window:" ] }, { "cell_type": "code", - "execution_count": 18, + "execution_count": 12, "id": "f1c92eaf", "metadata": { "tags": [ @@ -198,7 +197,7 @@ "outputs": [ { "data": { - "image/png": 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", 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", "text/plain": [ "
" ] @@ -210,8 +209,8 @@ "source": [ "fig, ax = plt.subplots()\n", "ax.plot(t, window)\n", - "ax.set_xlabel(\"Zeit [s]\")\n", - "ax.set_ylabel(\"Hamming Window\");" + "ax.set_xlabel(\"Time [s]\")\n", + "ax.set_ylabel(\"Hamming window\");" ] }, { @@ -219,12 +218,12 @@ "id": "730a4714", "metadata": {}, "source": [ - "Und hier das Produkt von beiden:" + "And here the product of both:" ] }, { "cell_type": "code", - "execution_count": 19, + "execution_count": 11, "id": "0143e3d8", "metadata": { "tags": [ @@ -234,7 +233,7 @@ "outputs": [ { "data": { - "image/png": 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", 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", 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" ] @@ -249,7 +248,9 @@ "filt = window * taps\n", "filt /= np.sum(filt)\n", "\n", - "ax.plot(t, filt);" + "ax.plot(t, filt);\n", + "ax.set_xlabel(\"Time [s]\")\n", + "ax.set_ylabel(r\"$sinc \\cdot$ window\");" ] }, { @@ -257,38 +258,38 @@ "id": "4fe418dc", "metadata": {}, "source": [ - "Jetzt verarbeiten wir die Samples nach folgendem Schema:\n", + "We now process the samples using the following scheme:\n", "```{figure} img/FIRodd.png\n", "---\n", "name: fig:FIRodd.en\n", "---\n", - "Struktur des sogenannten *FIR-Filters*.\n", - "Er berechnet die Faltung des Signals mit den Koeffizienten.\n", + "*FIR filter* structure.\n", + "It computes the convolution of the signal with the coefficients.\n", "```\n", "\n", - "Wir iterieren über die Samples, wobei wir immer die letzten $N$ Stück als $x$ betrachten.\n", - "Hier kann man z.B. mit einem [Ring buffer](https://de.wikipedia.org/wiki/Ringpuffer) arbeiten.\n", - "Dann berechnen wir\n", + "We iterate over the samples, using a sliding window of size $N$ as $x$.\n", + "This can be done using e.g. a [ring buffer](https://en.wikipedia.org/wiki/Circular_buffer).\n", + "We then calculate\n", "```{math}\n", "y = \\sum_{n=0}^{N-1} x[n] \\cdot a[N-1-n]\n", "```\n", - "und speichern $y$ als neues Sample.\n", + "and save $y$ as our new sample.\n", "\n", - "Visualisieren wir die so erzeugten neuen Samples, erhalten wir folgendes:\n", + "If we visualize these newly created samples, we get the following:\n", "```{figure} img/reference/filtered_detail.webp\n", "---\n", "name: fig:filtered_detail.en\n", "---\n", - "Gefiltertes Signal.\n", - "Die vertikalen Streifen sind entfernt.\n", + "Filtered signal.\n", + "The vertical lines are removed.\n", "```\n", "\n", - "Und auch im Spektrum können wir erkennen, dass nur noch die gewünschten Anteile vorhanden sind:\n", + "And in the spectrum, we can also confirm that only the part that we wanted remains:\n", "```{figure} img/reference/filtered_waterfall.webp\n", "---\n", "name: fig:filtered_waterfall.en\n", "---\n", - "Gefiltertes Signal im Wasserfall-Diagramm.\n", + "Waterfall diagram of the filtered signal.\n", "```" ] } diff --git a/U02_4_Sync.en.ipynb b/U02_4_Sync.en.ipynb index 3d487e2..b6af4b1 100644 --- a/U02_4_Sync.en.ipynb +++ b/U02_4_Sync.en.ipynb @@ -5,7 +5,7 @@ "id": "f611b5a0", "metadata": {}, "source": [ - "# Synchronisierung" + "# Synchronization" ] }, { @@ -13,45 +13,45 @@ "id": "0c5468d3", "metadata": {}, "source": [ - "Aktuell sind die Samples noch als komplexe Zahlen dargestellt.\n", - "Um weiter mit ihnen arbeiten zu können, nehmen wir jeweils den Betrag:\n", + "Currently, the samples are still represented as complex numbers.\n", + "To continue working with them, we convert them to their magnitudes:\n", "```{math}\n", "s = a + bi \\mapsto |s| = \\sqrt{a^2 + b^2}\n", "```\n", "\n", - "Hier eine Visualisierung des soweit verarbeiteten Signals:\n", + "Here is a visualization of the signal as processed so far:\n", "```{figure} img/reference/filtered_full_scaled.webp\n", "---\n", "name: fig:filtered_full_scaled.en\n", "---\n", - "Gefiltertes Signal.\n", - "Wir sehen dass die Sync-Streifen gebogen sind.\n", + "Filtered signal.\n", + "We observe that the sync lines are bent.\n", "```\n", "\n", - "Die Sync-Patterns markieren jeweils den Anfang einer Zeile.\n", - "Um das Bild \"gerade zu ziehen\" müssen wir sie finden.\n", + "The sync patterns mark the beginning of each line.\n", + "To \"straighten out\" the image, we have to find them.\n", "\n", - "Dazu gehen wir so vor:\n", - "- Sync A hat das Pattern `000011001100110011001100110011000000000`.\n", - " Wir haben 4 Samples pro Pixel, also auch pro 0/1 im Pattern.\n", - " Dieses Pattern wollen wir suchen.\n", - " Das funktioniert hier am besten, wenn wir sowohl das Pattern als auch die Samples in den Wertebereich zwischen $-1$ und $1$ skalieren.\n", - " Für jede `0` im Pattern nehmen wir also 4 mal die $-1$, und für jede `1` nehmen wir 4 mal die $1$.\n", - " Diese Sequenz von 39 * 4 = 156 Werten speichern wir als $p$.\n", - "- Jetzt betrachten wir Blöcke $x$ von 8320 Samples.\n", - " Wir finden Minimum $x_{min}$ und Maximum $x_{max}$ im Block, und skalieren so dass das Minimum bei $-1$ ist und das Maximum bei $1$:\n", + "We proceed as follows:\n", + "- Sync A has the pattern `000011001100110011001100110011000000000`.\n", + " We have 4 samples per pixel, and thus also per 0/1 in the pattern.\n", + " We want to find this pattern.\n", + " This is easiest if we scale both the pattern and our samples into the range between $-1$ and $1$.\n", + " For every `0` in the pattern, we take four $-1$s, and for every `1` we take four $1$s.\n", + " We save this sequence of 39 * 4 = 156 values as $p$.\n", + "- We now look at blocks $x$ of 8320 samples.\n", + " We find the minimum value $x_{min}$ and the maximum value $x_{max}$ within the block, and scale it such that the minimum is at $-1$ and the maximum at $1$:\n", " ```{math}\n", " x[n] \\mapsto -1 + 2 \\cdot \\frac{x[n] - x_{min}}{x_{max} - x_{min}}\n", " ```\n", - "- Wir wollen die Position finden, die \"am meisten\" mit dem Pattern übereinstimmt.\n", - " Also iterieren wir über alle Startpositionen $i$ im Block, 0 bis (8320-156).\n", - " Für jede davon berechnen wir\n", + "- We want to find the position that best matches the pattern.\n", + " To do this, we iterate over all positions $i$ in the block from 0 to (8320-156).\n", + " For each position, we compute the *correlation*\n", " ```{math}\n", " z = \\sum_{n=0}^{156} x[i + n] \\cdot p[n]\n", " ```\n", - " Die Position bei der $z$ am größten ist, ist die mit der besten Übereinstimmung.\n", - "- So können wir für jede Zeile die Anfangsposition finden.\n", - " Von dort aus gehen wir in Viererschritten über die Samples, um die Pixelwerte für die Zeile zu erhalten." + " The position with the highest $z$ value is the one that matches best.\n", + "- This way, we can find the starting position of each line.\n", + " From there, we can take every fourth sample to get the pixel values for this line." ] } ], diff --git a/U02_5_Output.en.ipynb b/U02_5_Output.en.ipynb index a37e2c9..f811f35 100644 --- a/U02_5_Output.en.ipynb +++ b/U02_5_Output.en.ipynb @@ -5,7 +5,7 @@ "id": "af12be1c", "metadata": {}, "source": [ - "# Ausgabe" + "# Output" ] }, { @@ -13,30 +13,30 @@ "id": "8de61e70", "metadata": {}, "source": [ - "Wir haben jetzt Werte für die Pixel des Bildes, aber sie sind noch nicht im richtigen Bereich:\n", - "Sie müssen am Ende nämlich zwischen 0 und 255 liegen.\n", + "We now have values for each pixel in the image, but these values are not yet in the correct range.\n", + "At the end of the day, we want them to be between 0 and 255.\n", "\n", - "Um sie zu richtig zu skalieren, verwenden wir den \"Space and Marker\" Teil des Bildformats:\n", + "To scale them correctly, we use the \"space and marker\" part of the frame:\n", "\n", "```{figure} img/apt_frame_format.webp\n", "---\n", "name: fig:frame_format_output.en\n", "---\n", - "Wieder das APT Bildformat.\n", - "Nach Sync A (39 Pixel breit) folgt ein 47 Pixel breiter Space mit schwarzen Pixeln.\n", - "Analog dazu sind in der zweiten Hälfte des Bildes der ebenfalls 39 Pixel breite Sync B und ein 47 Pixel breiter Space mit weißen Pixeln.\n", + "The APT frame format again.\n", + "Sync A (39 pixels) is followed by a space of 47 black pixels.\n", + "Similarly, sync B (39 pixel) in the second half is followed by a space of 47 white pixels.\n", "```\n", "\n", - "Der Sync A folgende Space hat (bis auf den Minute Marker) weiße Pixel, und der Space nach Sync B schwarze.\n", - "Die Minute Marker ignorieren wir hier einfach :)\n", + "The space following sync A has black pixels (except for the minute markers), and the space following sync b has white pixels.\n", + "We just ignore the minute markers :)\n", "\n", - "Um die Pixelwerte in den richtigen Bereich zu skalieren können wir so vorgehen:\n", - "- Wir berechnen das Schwarz-Level $v_b$ indem wir den Durchschnitt (oder den [Median](https://de.wikipedia.org/wiki/Median)) aller Pixelwerte im ersten Space nehmen.\n", - "- Das gleiche tun wir für den Weiß-Level $v_w$ mit dem zweiten Space.\n", - "- Jetzt bilden wir jeden Pixelwert $v$ auf $(v - v_b) / (v_w - v_b)$ ab.\n", - "- Damit sind die Werte zwischen $v_b$ und $v_w$ in den Bereich zwischen 0 und 1 gewandert.\n", - "- Alle Werte kleiner als 0 oder größer als 1 werden auf 0 bzw. 1 begrenzt.\n", - "- Jetzt müssen wir nur noch jeden Wert mit 255 multiplizieren." + "We can scale the pixel values into the correct range like this:\n", + "- We calculate the black level $v_b$ by computing the average (or [median](https://en.wikipedia.org/wiki/Median)) value of all pixels in the first space.\n", + "- We do the same with the second space to get the white level $v_w$.\n", + "- We now map every pixel value $v$ to $(v - v_b) / (v_w - v_b)$.\n", + "- This has moved all values between $v_b$ and $v_w$ into the range between 0 and 1.\n", + "- All values outside this range are clamped to 0 or 1 respectively.\n", + "- Finally, we have to multiply each value with 255." ] }, { @@ -45,22 +45,22 @@ "metadata": {}, "source": [ "(pgm-format)=\n", - "## PGM-Format\n", + "## PGM format\n", "\n", "```{note}\n", - "Wer möchte, kann natürlich gerne ein anderes Format benutzen, oder eine Bibliothek wie [Pillow](https://python-pillow.org/) oder [SDL](https://www.libsdl.org/).\n", + "Feel free to use a different format, or an image library like [Pillow](https://python-pillow.org/) or [SDL](https://www.libsdl.org/).\n", "```\n", "\n", - "Um das fertige Bild in eine Datei zu schreiben, können wir zum Beispiel dieses sehr einfache Dateiformat benutzen:\n", + "To write the final image into a file, we can use this very simple file format:\n", "\n", "```{admonition} Format\n", - "Die erste Zeile enthält den String `P2`.\n", + "The first line contains the string `P2`.\n", "\n", - "Die zweite Zeile enthält zwei positive Integer $w$ und $h$, die Breite $(w)$ und Höhe $(h)$ des Bildes $(w = 2080, h \\approx 1400)$.\n", + "The second line contains two positive integers $w$ and $h$, describing the width $(w)$ and height $(h)$ of the image $(w = 2080, h \\approx 1400)$.\n", "\n", - "Die dritte Zeile enthält einen positiven Integer $v_{max} = 255$.\n", + "The third line contains the positive integer $v_{max} = 255$.\n", "\n", - "Danach folgen $h$ Zeilen mit jeweils $w$ Pixelwerten $v$ als Integer $(0 \\leq v \\leq v_{max})$.\n", + "Afterwards, $h$ lines follow, containing $w$ integer pixel values $v$ $(0 \\leq v \\leq v_{max})$.\n", "```" ] }, @@ -69,7 +69,7 @@ "id": "1ab1434e", "metadata": {}, "source": [ - "### Beispiel\n", + "### Example\n", "\n", "```\n", "P2\n", @@ -91,8 +91,8 @@ "metadata": {}, "source": [ "```{note}\n", - "Das PGM-Format ist nur für Bilder in Graustufen, aber es gibt auch z.B. das PPM-Format für farbige Bilder.\n", - "[Hier](https://en.wikipedia.org/wiki/Netpbm) könnt ihr mehr dazu lesen.\n", + "The PGM format only supports grayscale images, but there is also e.g. the PPM format for colored images.\n", + "You can read more about it [here](https://en.wikipedia.org/wiki/Netpbm).\n", "```" ] }, @@ -101,7 +101,7 @@ "id": "d16219b2", "metadata": {}, "source": [ - "Wenn wir unsere Pixelwerte so in eine Datei mit `.pgm`-Endung speichern, können wir sie mit einem Grafikprogramm wie z.B. [GIMP](https://www.gimp.org/) anschauen." + "After saving the pixel values in such a file with a `.pgm` extension, we can look at them using a graphics program like [GIMP](https://www.gimp.org/)." ] } ],