{ "cells": [ { "cell_type": "markdown", "metadata": { "colab_type": "text", "id": "view-in-github" }, "source": [ "\"Open " ] }, { "cell_type": "markdown", "metadata": { "id": "nBpk5JQqghzq" }, "source": [ "# DFT\n", "## Abstract notations\n", "### History\n", "The Fourier transform is one of the key tools in Biomedical Data Science. Its namesake is [Jean Baptiste Fourier](https://en.wikipedia.org/wiki/Joseph_Fourier), who was a 18th century French mathemetician who made fundamental discoveries into harmonic analysis. Its fair to say that Fourier's discoveries are some of the most fundamental in all of a mathematics and engineering and is the foundation for signal processing.\n", "\n", "One of his main discoveries was the Fourier series, the idea that a function can be decomposed into building blocks of trigonometric functions. \n", "\n", "### Some notation\n", "Let $<,>$ be a so-called inner product. For example $ = \\sum_{m=1}^n a_m b_m$ if $a$ and $b$ are two vectors. But, $=\\int_0^1 a(t)b(t)dt$ if $a$ and $b$ are two functions on $[0,1]$. (There is a nice generality between Fourier results on data and Fourier results on functions and other spaces. However, we'll largely focus on discrete data, so think of the first definition.) We can define the norm as $ = ||a||^2$, so that, the distance between two vectors is $||a-b||$. \n", "\n", "Consider a basis, that is a set of vectors, $b_k$ so that $||b_k|| = 1$ and $= I(k=j)$ and the set of vectors, ${\\cal H}$, that can be written as $\\sum_{k=1}^k b_k c_k$ for some constants $c_k$, then for any element $x\\in H$ we have that the best approximation using any subset of the indices, $S$, is of the form\n", "\n", "$$\n", "\\sum_{k\\in S} b_k .\n", "$$\n", "\n", "For real vectors and the basis we consider, every vector can be written as a sum of the basis elements. You can have weird functions that can't be written out as sums of the basis elements, but they're weird functions. \n", "\n", "## More practically\n", "The basis we're interested in is $b_k$ which has element $m$ equal to $e^{-2\\pi i m k/n} = \\cos(2\\pi mk/n) + i \\sin (2\\pi mk / n)$ for $k=0,..., n-1$. Here, notice, we quit using the index $i$ since now it stands for the complex unit.\n", "This basis satisfies our rules of $ = I(j=k)$ and having norm 1. So that, given any vector $x$, our best approximation to it is\n", "\n", "$$\n", "\\sum_{k=0}^{n-1} b_k = \\sum_{k=0}^{n-1} b_k F_k\n", "$$\n", "\n", "where \n", "\n", "$$\n", "F_k = \\sum_{m=0}^{n-1} x_m e^{-2\\pi i m k / n}\n", "= \\sum_{m=0}^{n-1} x_m [\\cos(2\\pi m k / n) + i \\sin(2\\pi m k / n)].\n", "$$\n", "\n", "The collection of elements, $F = (F_0, \\ldots F_{n-1})$ are called the (discrete) Fourier coeficients and the operation that takes $x$ and converts it into $F$ is called the (discrete) Fourier transform.\n", "\n", "Let's consider the case where $x=(1 ~4 ~9 ~16)'$. So then\n" ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "colab": { "base_uri": "https://localhost:8080/" }, "id": "6Qda_NLJgatz", "outputId": "8b132755-67c4-4d8f-a7fc-8ee06857a7e0" }, "outputs": [ { "data": { "text/plain": [ "array([ 30. +0.j, -8.+12.j, -10. -0.j, -8.-12.j])" ] }, "execution_count": 1, "metadata": {}, "output_type": "execute_result" } ], "source": [ "import numpy as np\n", "import matplotlib.pyplot as plt\n", "x = np.arange(1,5,1) ** 2\n", "t = np.arange(0, 4, 1)\n", "n = 4\n", "F0 = np.sum(x * np.exp(-2 * 1j * np.pi * t * 0 / n))\n", "F1 = np.sum(x * np.exp(-2 * 1j * np.pi * t * 1 / n))\n", "F2 = np.sum(x * np.exp(-2 * 1j * np.pi * t * 2 / n))\n", "F3 = np.sum(x * np.exp(-2 * 1j * np.pi * t * 3 / n))\n", "\n", "np.round([F0, F1, F2, F3], 3)" ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "colab": { "base_uri": "https://localhost:8080/" }, "id": "cJxJ3SCiugbj", "outputId": "ab3e8698-6745-4759-84bc-7b79e56dd4bc" }, "outputs": [ { "data": { "text/plain": [ "array([ 30. +0.j, -8.+12.j, -10. +0.j, -8.-12.j])" ] }, "execution_count": 2, "metadata": {}, "output_type": "execute_result" } ], "source": [ "F = np.fft.fft(x)\n", "F" ] }, { "cell_type": "markdown", "metadata": { "id": "g-Y4wrTliPxP" }, "source": [ "Let's give a more realistic example. Consider two cosine waves, one fast, one slow. Let's add them together and see if the FFT can figure out what we've done." ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "colab": { "base_uri": "https://localhost:8080/", "height": 282 }, "id": "CsAwWJ2jiNc_", "outputId": "48f27ae5-7fe3-48a2-b876-2077d1fd4aaa" }, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 3, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "n = 1000\n", "t = np.arange(0, n, 1)\n", "c1 = np.cos(2 * np.pi * t * 5 / n)\n", "c2 = np.cos(2 * np.pi * t * 20 / n)\n", "plt.plot(t, c1)\n", "plt.plot(t, c2)\n", "plt.show" ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "colab": { "base_uri": "https://localhost:8080/", "height": 282 }, "id": "aPix8992j3Oa", "outputId": "2cb42462-a4d9-4b33-98c2-d6abb20a518f" }, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 4, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "x = c1 + .5 * c2\n", "plt.plot(t, x)\n", "plt.show\n" ] }, { "cell_type": "code", "execution_count": 5, "metadata": { "colab": { "base_uri": "https://localhost:8080/", "height": 282 }, "id": "f7FjtYXskEDv", "outputId": "b83ba4a2-252b-4142-c212-485dad0f31ab" }, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/plain": [ "(array([ 5, 20, 980, 995]),)" ] }, "execution_count": 5, "metadata": {}, "output_type": "execute_result" } ], "source": [ "a = np.fft.fft(x)\n", "b = a.real ** 2 + a.imag ** 2\n", "plt.plot(b)\n", "plt.show()\n", "np.where(b > 1e-5)" ] }, { "cell_type": "markdown", "metadata": { "id": "1OAHZJA8j1SW" }, "source": [ "### Some notes\n", "We can go backwards from the Fourier coefficients to the signal using the inverse transform. Also, for real signals sometimes people will multiply the signal by $(-1)^t$ in order for the plot of the norm of the coeficients (the power spectrum as its called) to look nicer." ] }, { "cell_type": "code", "execution_count": 6, "metadata": { "colab": { "base_uri": "https://localhost:8080/", "height": 265 }, "id": "wFO3auwelaG0", "outputId": "c16842b5-9834-47a1-95a8-06c45570a83c" }, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "## Plotting the spectrum so that it's in the middle\n", "a = np.fft.fft(x * (-1) ** t)\n", "b = a.real ** 2 + a.imag ** 2\n", "plt.plot(b)\n", "plt.show()\n" ] }, { "cell_type": "code", "execution_count": 7, "metadata": { "colab": { "base_uri": "https://localhost:8080/", "height": 300 }, "id": "0FJN0pkUkcD1", "outputId": "68f5a85f-3886-4672-98eb-cf6ed7118911" }, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "/home/bcaffo/miniconda3/envs/ds4bio_new/lib/python3.10/site-packages/matplotlib/cbook.py:1699: ComplexWarning: Casting complex values to real discards the imaginary part\n", " return math.isfinite(val)\n", "/home/bcaffo/miniconda3/envs/ds4bio_new/lib/python3.10/site-packages/matplotlib/cbook.py:1345: ComplexWarning: Casting complex values to real discards the imaginary part\n", " return np.asarray(x, float)\n" ] }, { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "## demonstrating going backwards\n", "a = np.fft.fft(x)\n", "b = np.fft.ifft(a)\n", "\n", "plt.plot(b)\n", "plt.show()\n" ] }, { "cell_type": "markdown", "metadata": { "id": "r28w10Vxiey2" }, "source": [ "### Filtering\n", "\n", "Filtering is the process of allowing certain frequency bands to be retained while others to be discarded. Imagine in our case that we want the low frequency band to pass and to get rid of the higher frequency. In this case we want a low pass filter. There's a lot of ways to filter signals, but let's just do it by simple thresholding. The slightly tricky thing about this in practical problems, is making sure that you're filtering at the frequencies that you want to. As an example, we have 1,000 time points. Say one time point is 1/100 of a second so that we have ten second of data. We have two cosine functions, one that is at 5 oscillations per 10 seconds (0.5 Hz) and one at 20 oscillations per 10 seconds (2 hz). Let's filter out anything ove 0.5 Hz." ] }, { "cell_type": "code", "execution_count": 8, "metadata": { "colab": { "base_uri": "https://localhost:8080/", "height": 265 }, "id": "S8IJIa9uk8cd", "outputId": "b91f3c4e-83c7-4c32-c855-3f40c5ff12c2" }, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "## demonstrating hard filtering\n", "a = np.fft.fft(x)\n", "n = a.size\n", "timestep = 1/100\n", "## a function that shows what the frequencies are in the units you want\n", "w = np.fft.fftfreq(n, timestep)\n", "\n", "\n", "b = a\n", "b[(abs(w) > .5)] = 0\n", "c = np.fft.ifft(b).real\n", "plt.plot(c)\n", "plt.show()" ] } ], "metadata": { "colab": { "collapsed_sections": [], "include_colab_link": true, "name": "Intro to DFT", "provenance": [] }, "interpreter": { "hash": "a55c7c6e504dc9cc53e0313e06c735eecd5d3bb2f64ea91c4a4bba922f8c28bf" }, "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": "3.10.13" } }, "nbformat": 4, "nbformat_minor": 4 }