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astellon/upsampling.ipynb

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upsampling.ipynb
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"cell_type": "markdown",
"metadata": {},
"source": [
"# Upsampling\n",
"\n",
"upsampling by using 0 insertion and frequency domain filtering"
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Julia Version 1.1.0\n",
"Commit 80516ca202 (2019-01-21 21:24 UTC)\n",
"Platform Info:\n",
" OS: Linux (x86_64-pc-linux-gnu)\n",
" CPU: Intel(R) Core(TM) i7-7700K CPU @ 4.20GHz\n",
" WORD_SIZE: 64\n",
" LIBM: libopenlibm\n",
" LLVM: libLLVM-6.0.1 (ORCJIT, skylake)\n"
]
}
],
"source": [
"versioninfo()"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {},
"outputs": [],
"source": [
"using BenchmarkTools, FFTW, Plots"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {},
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"x1 = range(0.0, stop=4π, length=16)\n",
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"y2 = cos.(x2)\n",
"plot(x1, y1)\n",
"plot!(x2, y2)"
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{
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"text/plain": [
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"function insertzero(x::AbstractVector, n::Integer)\n",
" ret = zeros(eltype(x), length(x)*n)\n",
" for i in 1:length(x)\n",
" ret[(i-1)*n+1] = x[i]\n",
" end\n",
" ret\n",
"end"
]
},
{
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"source": [
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"source": [
"z = fft(y3)\n",
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],
"source": [
"plot(real.(ifft(z)) .* 2)\n",
"plot!(y2)"
]
},
{
"cell_type": "code",
"execution_count": 10,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"upsampling (generic function with 1 method)"
]
},
"execution_count": 10,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"function upsampling(x, n)\n",
" res = insertzero(x, n)\n",
" z = fft(res)\n",
" z[cld(length(z), 2n)+1:end-cld(length(z), 2n)] .= 0\n",
" real.(ifft(z)) .* n\n",
"end"
]
},
{
"cell_type": "code",
"execution_count": 11,
"metadata": {},
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" 1199.96,105.111 1215.79,108.89 1231.63,120.177 1247.46,138.826 1263.3,164.595 1279.14,197.16 1294.97,236.12 1310.81,281.011 1326.64,331.313 1342.48,386.463 \n",
" 1358.31,445.863 1374.15,508.884 1389.98,574.871 1405.82,643.146 1421.65,713.01 1437.49,783.739 1453.32,854.592 1469.16,924.809 1484.99,993.62 1500.83,1060.25 \n",
" 1516.67,1123.93 1532.5,1183.91 1548.34,1239.48 1564.17,1289.97 1580.01,1334.79 1595.84,1373.43 1611.68,1405.45 1627.51,1430.53 1643.35,1448.43 1659.18,1459.02 \n",
" 1675.02,1462.26 1690.85,1458.18 1706.69,1446.89 1722.53,1428.55 1738.36,1403.39 1754.2,1371.66 1770.03,1333.65 1785.87,1289.7 1801.7,1240.2 1817.54,1185.56 \n",
" 1833.37,1126.3 1849.21,1062.97 1865.04,996.232 1880.88,926.812 1896.71,855.532 1912.55,783.288 1928.38,711.032 1944.22,639.751 1960.06,570.434 1975.89,504.032 \n",
" 1991.73,441.422 2007.56,383.365 2023.4,330.472 2039.23,283.179 2055.07,241.724 2070.9,206.146 2086.74,176.293 2102.57,151.842 2118.41,132.336 2134.24,117.226 \n",
" 2150.08,105.921 2165.91,97.8454 2181.75,92.487 2197.59,89.4433 2213.42,88.4582 2229.26,89.4433 2245.09,92.487 2260.93,97.8454 \n",
" \"/>\n",
"<polygon clip-path=\"url(#clip1900)\" points=\"\n",
"1958.43,251.724 2249.26,251.724 2249.26,130.764 1958.43,130.764 \n",
" \" fill=\"#ffffff\" fill-rule=\"evenodd\" fill-opacity=\"1\"/>\n",
"<polyline clip-path=\"url(#clip1900)\" style=\"stroke:#000000; stroke-width:4; stroke-opacity:1; fill:none\" points=\"\n",
" 1958.43,251.724 2249.26,251.724 2249.26,130.764 1958.43,130.764 1958.43,251.724 \n",
" \"/>\n",
"<polyline clip-path=\"url(#clip1900)\" style=\"stroke:#009af9; stroke-width:4; stroke-opacity:1; fill:none\" points=\"\n",
" 1982.43,191.244 2126.43,191.244 \n",
" \"/>\n",
"<g clip-path=\"url(#clip1900)\">\n",
"<text style=\"fill:#000000; fill-opacity:1; font-family:Arial,Helvetica Neue,Helvetica,sans-serif; font-size:48px; text-anchor:start;\" transform=\"rotate(0, 2150.43, 208.744)\" x=\"2150.43\" y=\"208.744\">y1</text>\n",
"</g>\n",
"</svg>\n"
]
},
"execution_count": 11,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"plot(upsampling(y1, 8))"
]
},
{
"cell_type": "code",
"execution_count": 12,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
" 34.481 μs (118 allocations: 134.92 KiB)\n"
]
}
],
"source": [
"xbench = range(0.0, stop=4π, length=256)\n",
"ybench = cos.(xbench)\n",
"@btime(upsampling($ybench, 8));"
]
}
],
"metadata": {
"kernelspec": {
"display_name": "Julia 1.1.0",
"language": "julia",
"name": "julia-1.1"
},
"language_info": {
"file_extension": ".jl",
"mimetype": "application/julia",
"name": "julia",
"version": "1.1.0"
}
},
"nbformat": 4,
"nbformat_minor": 2
}
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