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@Piezoid
Created May 22, 2023 20:30
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{
"cells": [
{
"cell_type": "code",
"execution_count": 1,
"id": "0bd815a7-2874-4bea-9315-e8f9ec1ce11a",
"metadata": {},
"outputs": [],
"source": [
"import sympy as sp\n",
"import numpy as np\n",
"from matplotlib import pyplot as plt\n",
"%matplotlib inline"
]
},
{
"cell_type": "code",
"execution_count": 2,
"id": "69c38175-f150-4822-b6f4-adfd9b5d12c9",
"metadata": {},
"outputs": [],
"source": [
"t, x = sp.symbols('t x', real=True)\n",
"lbd, P = sp.symbols('lambda P', real=True, positive=True)\n",
"n, i = sp.symbols('n i', integer=True, positive=True)\n",
"tau = sp.pi*2"
]
},
{
"cell_type": "code",
"execution_count": 3,
"id": "ba0f2306-7c36-44a0-9d5e-35dc98029547",
"metadata": {},
"outputs": [
{
"data": {
"text/latex": [
"$\\displaystyle \\begin{cases} 1 & \\text{for}\\: t < \\frac{P \\lambda}{4} \\\\0 & \\text{for}\\: t < - \\frac{P \\lambda}{4} + \\frac{P}{2} \\\\-1 & \\text{otherwise} \\end{cases}$"
],
"text/plain": [
"Piecewise((1, t < P*lambda/4), (0, t < -P*lambda/4 + P/2), (-1, True))"
]
},
"execution_count": 3,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"# Defined on a half period [0, P/2]; then on [-P/2, 0], y(t) = y(-t) \n",
"y = sp.Piecewise(\n",
" (1, t < P*lbd/4),\n",
" (0, t < P/2 - P*lbd/4),\n",
" (-1, True)\n",
")\n",
"\n",
"def inner_product(x, y, var=t, range=(0,P/2)):\n",
" a,b = range\n",
" r = sp.integrate(x * sp.conjugate(y), (var, a, b)) / (b - a)\n",
" return r\n",
"\n",
"y"
]
},
{
"cell_type": "code",
"execution_count": 4,
"id": "954d6db3-7075-47ab-bb46-77932dbfab4c",
"metadata": {},
"outputs": [
{
"data": {
"text/latex": [
"$\\displaystyle \\frac{4 \\sin{\\left(\\pi \\lambda \\left(n + \\frac{1}{2}\\right) \\right)}}{\\pi \\left(2 n + 1\\right)}$"
],
"text/plain": [
"4*sin(pi*lambda*(n + 1/2))/(pi*(2*n + 1))"
]
},
"execution_count": 4,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"# No sine harmonics since the function is even. Also, the odd symmetry\n",
"# around (P/4, 0) means that there is no even cosine harmonics. We go\n",
"# straight for the odd cosine harmonics:\n",
"g = sp.cos(tau*t*(2*n + 1)/P)\n",
"an = 2 * inner_product(y, g, range=(0, P/2))\n",
"\n",
"# For simplification of the piecewise function, substitute the lambda parameter with a some bijection in the [0,1] range\n",
"lbds = sp.sin(lbd)**2\n",
"an = an.subs(lbd, lbds).simplify().subs(lbds, lbd) # then subs back to lambda\n",
"an"
]
},
{
"cell_type": "code",
"execution_count": 5,
"id": "2ffe8c77-b4d7-4b1a-b911-ebb6f87e727c",
"metadata": {},
"outputs": [
{
"data": {
"text/latex": [
"$\\displaystyle \\frac{8 \\sin^{2}{\\left(\\pi \\lambda \\left(n + \\frac{1}{2}\\right) \\right)}}{\\pi^{2} \\left(2 n + 1\\right)^{2}}$"
],
"text/plain": [
"8*sin(pi*lambda*(n + 1/2))**2/(pi**2*(2*n + 1)**2)"
]
},
"execution_count": 5,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
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",
"text/plain": [
"<Figure size 640x480 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"p = inner_product(an*g, an*g).simplify()\n",
"pl = sp.lambdify((n, lbd), p)\n",
"rg = np.arange(0,31)\n",
"p1 = pl(rg, 1)\n",
"p1 /= p1[0]\n",
"p2 = pl(rg, float(0.742002))\n",
"p2 /= p2[0]\n",
"\n",
"plt.scatter(rg*2+1, p1, label=r'$\\lambda=1$')\n",
"plt.scatter(rg*2+1, p2, label=r'$\\lambda=0.742$')\n",
"plt.yscale('log')\n",
"plt.ylabel(r'$\\| F_n \\|^2 / \\| F_1 \\|^2$')\n",
"plt.xlabel('$n$')\n",
"plt.legend()\n",
"\n",
"p"
]
},
{
"cell_type": "code",
"execution_count": 6,
"id": "111f0df1-0a51-4e44-9a0c-dfad8c0ffe5e",
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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",
"text/plain": [
"<Figure size 640x480 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"harmonics = an*g\n",
"fond = harmonics.subs(n, 0).simplify()\n",
"\n",
"subs = {P: 1, lbd:1} # Pure square wave\n",
"funcs = [\n",
" y,\n",
" fond,\n",
" sp.summation(harmonics, (n, 1, 10)),\n",
"]\n",
"funcs = [sp.Piecewise(\n",
" (f, t > 0), \n",
" (f.subs(t,-t), True)\n",
" ).subs(subs) for f in funcs]\n",
"sp.plot(*funcs, (t, -subs[P]/2, subs[P]/2));"
]
},
{
"cell_type": "code",
"execution_count": 7,
"id": "f746c957-0097-4f91-a63e-4e1946aadf82",
"metadata": {},
"outputs": [
{
"data": {
"text/latex": [
"$\\displaystyle \\frac{8 \\sin^{2}{\\left(\\frac{\\pi \\lambda}{2} \\right)}}{\\pi^{2}}$"
],
"text/plain": [
"8*sin(pi*lambda/2)**2/pi**2"
]
},
"execution_count": 7,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"fond_pow = inner_product(fond, fond)\n",
"fond_pow"
]
},
{
"cell_type": "code",
"execution_count": 8,
"id": "c63fa173-52c1-442b-8240-c3555688705a",
"metadata": {},
"outputs": [
{
"data": {
"text/latex": [
"$\\displaystyle \\lambda$"
],
"text/plain": [
"lambda"
]
},
"execution_count": 8,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"y_pow = inner_product(y,y)\n",
"y_pow = y_pow.subs(lbd, lbds).simplify().subs(lbds,lbd)\n",
"y_pow"
]
},
{
"cell_type": "code",
"execution_count": 9,
"id": "288c2c62-a7f3-44b9-9479-c2ae326ff832",
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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",
"text/plain": [
"<Figure size 640x480 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"data": {
"text/plain": [
"(0.74201929640710318, 1.1701195194867927)"
]
},
"execution_count": 9,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"snr = fond_pow / (y_pow - fond_pow)\n",
"dsnr = snr.diff(lbd)\n",
"sp.plot(snr, dsnr/8, (lbd, 0, 1))\n",
"\n",
"lbd_s = sp.nsolve(dsnr, lbd, 0.6, prec=17)\n",
"fond_a_s = an.evalf(subs={n:0, lbd: lbd_s}, n=17)\n",
"lbd_s, fond_a_s"
]
},
{
"cell_type": "code",
"execution_count": 10,
"id": "6ba5732c-4814-484d-8563-93d2d3a511b0",
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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",
"text/plain": [
"<Figure size 640x480 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"data": {
"text/plain": [
"<sympy.plotting.plot.Plot at 0x7fa73c2f2890>"
]
},
"execution_count": 10,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"subs = {P: 1, lbd:lbd_s}\n",
"funcs = [\n",
" y,\n",
" sp.summation(harmonics, (n, 1, 10)),\n",
" fond,\n",
"]\n",
"funcs = [sp.Piecewise(\n",
" (f, t > 0), \n",
" (f.subs(t,-t), True)\n",
" ).subs(subs) for f in funcs]\n",
"sp.plot(*funcs, (t, -subs[P]/2, subs[P]/2))"
]
},
{
"cell_type": "code",
"execution_count": 11,
"id": "304df2ac-9c19-472d-ac33-53375782c471",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"SNR square: 2.07\n",
"SNR optimal: 3.45\n",
"Harmonics reduction: 40.1%\n"
]
}
],
"source": [
"snr_sq = sp.sqrt(snr).evalf(subs={lbd: 1})\n",
"snr_s = sp.sqrt(snr).evalf(subs={lbd: lbd_s})\n",
"print(f'SNR square: {snr_sq:.2f}\\nSNR optimal: {snr_s:.2f}\\nHarmonics reduction: {100*(snr_s-snr_sq)/snr_s:.1f}%')"
]
},
{
"cell_type": "code",
"execution_count": 12,
"id": "c3f1d394-a9e8-4c6d-b8ce-df4cc500887f",
"metadata": {},
"outputs": [
{
"data": {
"text/latex": [
"$\\displaystyle \\begin{cases} 1 & \\text{for}\\: t < \\frac{P \\lambda}{4} \\\\0 & \\text{for}\\: t < - \\frac{P \\lambda}{4} + \\frac{P}{2} \\\\-1 & \\text{otherwise} \\end{cases}$"
],
"text/plain": [
"Piecewise((1, t < P*lambda/4), (0, t < -P*lambda/4 + P/2), (-1, True))"
]
},
"execution_count": 12,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"y"
]
},
{
"cell_type": "code",
"execution_count": 13,
"id": "961f49cc-4729-49d4-b74f-219974fd357d",
"metadata": {},
"outputs": [],
"source": [
"p0, a = sp.symbols('p0 a', real=True, positive=True)\n",
"\n",
"t_cruise = P*lbd/4\n",
"t_decel = P/2 - t_cruise\n",
"\n",
"# Piecewise integration by hand because sympy is really bad with interval (inequalities, min/max) simplifications...\n",
"v_accel = sp.integrate(a , (t, 0, t))\n",
"v_cruise = v_accel.subs(t, t_cruise)\n",
"v_decel = v_cruise - sp.integrate(a , (t, t_decel, t))\n",
"\n",
"p_accel = sp.integrate(v_accel, (t, 0, t))\n",
"p_cruise = p_accel.subs(t, t_cruise) + sp.integrate(v_cruise, (t, t_cruise, t))\n",
"p_decel = p_cruise.subs(t, t_decel) + sp.integrate(v_decel, (t, t_decel, t))"
]
},
{
"cell_type": "code",
"execution_count": 14,
"id": "ef420747-15f6-46dd-afbc-b03852dbafcb",
"metadata": {},
"outputs": [
{
"data": {
"text/latex": [
"$\\displaystyle \\lambda$"
],
"text/plain": [
"lambda"
]
},
"execution_count": 14,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"# By how much the velocity should be reduced\n",
"v_cruise/v_cruise.subs(lbd, 1)"
]
},
{
"cell_type": "code",
"execution_count": 15,
"id": "6fdd6aae-81c9-42d0-8b10-a20df08d2fc3",
"metadata": {},
"outputs": [
{
"data": {
"text/latex": [
"$\\displaystyle \\begin{cases} \\frac{a \\left(P^{2} \\lambda^{2} - 2 P^{2} \\lambda + 16 t^{2}\\right)}{32} & \\text{for}\\: t < \\frac{P \\lambda}{4} \\\\\\frac{P a \\lambda \\left(- P + 4 t\\right)}{16} & \\text{for}\\: t < \\frac{P \\left(2 - \\lambda\\right)}{4} \\\\\\frac{a \\left(- P^{2} \\lambda^{2} + 2 P^{2} \\lambda - 4 P^{2} + 16 P t - 16 t^{2}\\right)}{32} & \\text{otherwise} \\end{cases}$"
],
"text/plain": [
"Piecewise((a*(P**2*lambda**2 - 2*P**2*lambda + 16*t**2)/32, t < P*lambda/4), (P*a*lambda*(-P + 4*t)/16, t < P*(2 - lambda)/4), (a*(-P**2*lambda**2 + 2*P**2*lambda - 4*P**2 + 16*P*t - 16*t**2)/32, True))"
]
},
"execution_count": 15,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"# Piecewise definition\n",
"p = sp.Piecewise(\n",
" (p_accel, t < t_cruise),\n",
" (p_cruise, t < t_decel),\n",
" (p_decel, True)\n",
")\n",
"# Centering\n",
"p0 = p_decel.subs(t,P/2)\n",
"p = sp.simplify(p - p0/2)\n",
"p"
]
},
{
"cell_type": "code",
"execution_count": 16,
"id": "06d3bcc2-fe28-4c50-ae8d-e822b5ff5ce6",
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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",
"text/plain": [
"<Figure size 640x480 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"subs = {P: 1, a:1}\n",
"funcs = [\n",
" (2*p/p0).subs(lbd, lbd_s),\n",
" (2*p/p0).subs(lbd, 1),\n",
" -sp.cos(t*tau/P),\n",
"]\n",
"funcs = [sp.Piecewise(\n",
" (f, t > 0), \n",
" (f.subs(t,-t), True)\n",
" ).subs(subs) for f in funcs]\n",
"sp.plot(*funcs, (t, -subs[P]/2, subs[P]/2));"
]
},
{
"cell_type": "code",
"execution_count": 17,
"id": "a5ca4a4d-38c8-45f9-8cb7-e00b60b6ab02",
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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",
"text/plain": [
"<Figure size 640x480 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"subs = {P: 1, a:1}\n",
"funcs = [\n",
" (2*p/p0).subs(lbd, lbd_s),\n",
" (2*p/p0).subs(lbd, 1),\n",
" -sp.cos(t*tau/P),\n",
"]\n",
"funcs = [sp.Piecewise(\n",
" (f, t > 0), \n",
" (f.subs(t,-t), True)\n",
" ).diff(t).subs(subs) for f in funcs]\n",
"sp.plot(*funcs, (t, -subs[P]/2, subs[P]/2));"
]
}
],
"metadata": {
"kernelspec": {
"display_name": "Python 3 (ipykernel)",
"language": "python",
"name": "python3"
},
"language_info": {
"codemirror_mode": {
"name": "ipython",
"version": 3
},
"file_extension": ".py",
"mimetype": "text/x-python",
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython3",
"version": "3.11.3"
}
},
"nbformat": 4,
"nbformat_minor": 5
}
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