E2-Sinusoids_&_DFT.ipynb

{
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   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Exercise 2: Sinusoids and the DFT\n",
    "\n",
    "Doing this exercise you will get a better understanding of the basics elements and operations that take place in the Discrete Fourier Transform (DFT). There are five parts: 1) Generate a sinusoid, 2) Generate a complex sinusoid, 3) Implement the DFT, 4) Implement the IDFT, and 5) Compute the magnitude spectrum of an input sequence.\n",
    "\n",
    "### Relevant Concepts\n",
    "\n",
    "A real sinusoid in discrete time domain can be expressed by:\n",
    "\n",
    "\\begin{equation}\n",
    "x[n] = A\\cos(2 \\pi fnT + \\varphi)\n",
    "\\end{equation}\n",
    "\n",
    "where, $x$ is the array of real values of the sinusoid, $n$ is an integer value expressing the time index, $A$ is the amplitude value of the sinusoid, $f$ is the frequency value of the sinusoid in Hz, $T$ is the sampling period equal to $1/fs$, fs is the sampling frequency in Hz, and $\\varphi$ is the initial phase of the sinusoid in radians.\n",
    "\n",
    "A complex sinusoid in discrete time domain can be expressed by:\n",
    "\n",
    "\\begin{equation}\n",
    "\\bar{x}[n] = Ae^{j(\\omega nT + \\varphi)} = A\\cos(\\omega nT + \\varphi)+ j A\\sin(\\omega nT + \\varphi)\n",
    "\\end{equation}\n",
    "\n",
    "where, $\\bar{x}$ is the array of complex values of the sinusoid, $n$ is an integer value expressing the time index, $A$ is the amplitude value of the sinusoid, $e$ is the complex exponential number, $\\omega$ is the frequency of the sinusoid in radians per second (equal to $2 \\pi f$), $T$ is the sampling period equal $1/fs$, fs is the sampling frequency in Hz and $\\varphi$ is the initial phase of the sinusoid in radians.\n",
    "\n",
    "The $N$ point DFT of a sequence of real values $x$ (a sound) can be expressed by:\n",
    "\n",
    "\\begin{equation}\n",
    "X[k] = \\sum_{n=0}^{N-1} x[n]e^{-j2 \\pi kn/N}  \\hspace{1cm} k=0,...,N-1\n",
    "\\end{equation}\n",
    "\n",
    "where $n$ is an integer value expressing the discrete time index, $k$ is an integer value expressing the discrete frequency index, and $N$ is the length of the DFT.\n",
    "\n",
    "The IDFT of a spectrum $X$ of length $N$ can be expressed by:\n",
    "\n",
    "\\begin{equation}\n",
    "x[n] = \\frac{1}{N} \\sum_{k=0}^{N-1} X[k]e^{j2 \\pi kn/N}  \\hspace{1cm} n=0,...,N-1\n",
    "\\end{equation}\n",
    "\n",
    "where, $n$ is an integer value expressing the discrete time index, $k$ is an integer value expressing the discrete frequency index, and $N$ is the length of the spectrum $X$.\n",
    "\n",
    "The magnitude of a complex spectrum $X$ is obtained by taking its absolute value: $|X[k]| $\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Part 1 - Generate a sinusoid\n",
    "\n",
    "Complete the function `gen_sine` to generate a real sinusoid (use `np.cos()`) given its amplitude `A`, frequency `f` (Hz), initial phase `phi` (radians), sampling rate `fs` (Hz) and duration `t` (seconds). \n",
    "\n",
    "All the input arguments to this function `(A, f, phi, fs and t)` are real numbers such that `A`, `t` and `fs` are positive, and `fs > 2*f` to avoid aliasing. The function should return a numpy array `x` of the generated sinusoid. \n",
    "\n",
    "Use the function `cos` of the numpy package to compute the sinusoidal values."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "def gen_sine(A, f, phi, fs, t):\n",
    "    \"\"\"\n",
    "    Inputs:\n",
    "        A (float) =  amplitude of the sinusoid\n",
    "        f (float) = frequency of the sinusoid in Hz\n",
    "        phi (float) = initial phase of the sinusoid in radians\n",
    "        fs (float) = sampling frequency of the sinusoid in Hz\n",
    "        t (float) =  duration of the sinusoid (is second)\n",
    "    Output:\n",
    "        x (numpy array) = generated sinusoid\n",
    "    \"\"\"\n",
    "    return A*np.cos(2*np.pi*f*np.arange(fs*t)/fs+phi)\n",
    "\n",
    "    "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now call and test the `gen_sine()` function. If you use `A=1.0, f = 10.0, phi = 1.0, fs = 50` and `t = 0.1`, the output numpy array should be:\n",
    "\n",
    "```\n",
    "array([ 0.54030231, -0.63332387, -0.93171798,  0.05749049,  0.96724906])\n",
    "```\n",
    "\n",
    "To generate a sinewave that you can hear, it should be longer and with a higher sampling rate. For example you can use `A=1.0, f = 440.0, phi = 1.0, fs = 5000` and `t = 0.5`. To play it import the `Ipython.display` package and use `ipd.display(ipd.Audio(data=x, rate=fs))`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "array([ 0.54030231, -0.63332387, -0.93171798,  0.05749049,  0.96724906])\n"
     ]
    }
   ],
   "source": [
    "# RESULT CHECK\n",
    "\n",
    "# Initialize sine parameters\n",
    "A = 1.0\n",
    "f = 10.0\n",
    "phi = 1.0\n",
    "fs = 50\n",
    "t = 0.1\n",
    "\n",
    "x = gen_sine(A,f,phi,fs,t)\n",
    "\n",
    "print(x.__repr__())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
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type=\"audio/wav\" />\n",
       "                    Your browser does not support the audio element.\n",
       "                </audio>\n",
       "              "
      ],
      "text/plain": [
       "<IPython.lib.display.Audio object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# SAMPLE PLAY\n",
    "\n",
    "import IPython.display as ipd\n",
    "\n",
    "#Initialize sine parameters\n",
    "A = 1.0\n",
    "f = 440.0\n",
    "phi = 1.0\n",
    "fs = 5000\n",
    "t = 0.5\n",
    "\n",
    "x = gen_sine(A,f,phi,fs,t)\n",
    "\n",
    "\n",
    "# Displaying sine signal\n",
    "ipd.display(ipd.Audio(data=x, rate=fs))\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Part 2 - Generate a complex sinusoid \n",
    "\n",
    "Complete the `gen_complex_sine()` function to generate the complex sinusoid that is used in DFT computation of length `N` (samples), corresponding to the frequency index `k`. Note that the complex sinusoid used in DFT computation has a negative sign in the exponential function.\n",
    "\n",
    "The amplitude of such a complex sinusoid is `1`, the length is `N`, and the frequency in radians is `2*pi*k/N`.\n",
    "\n",
    "The input arguments to the function are two positive integers, `k` and `N`, such that `k < N-1`. The function should return `c_sine`, a numpy array of the complex sinusoid. Use the function `exp()` of the numpy package to compute the complex sinusoidal values."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "def gen_complex_sine(k, N):\n",
    "    \"\"\"\n",
    "    Inputs:\n",
    "        k (integer) = frequency index of the complex sinusoid of the DFT\n",
    "        N (integer) = length of complex sinusoid in samples\n",
    "    Output:\n",
    "        c_sine (numpy array) = generated complex sinusoid (length N)\n",
    "    \"\"\"\n",
    "    return np.exp(-1j*2*np.pi*k*np.arange(N)/N)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now run an test the `gen_complex_sine()` function. If you run it using `k=1` and `N=5`, the function should return the following numpy array:\n",
    "\n",
    "```\n",
    "array([ 1.0 + 0.j,  0.30901699 - 0.95105652j, -0.80901699 - 0.58778525j, -0.80901699 + 0.58778525j, 0.30901699 + 0.95105652j])\n",
    "```"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[ 1.00000000+0.j          0.30901699-0.95105652j -0.80901699-0.58778525j\n",
      " -0.80901699+0.58778525j  0.30901699+0.95105652j]\n"
     ]
    }
   ],
   "source": [
    "# call gen_complex_sine\n",
    "c_sine = gen_complex_sine(1,5)\n",
    "\n",
    "print(c_sine)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Part 3 - Implement the discrete Fourier transform (DFT)\n",
    "\n",
    "Complete the function `dft()` to implement the discrete Fourier transform (DFT) equation given above. Given a sequence `x` of length `N`, the function should return its spectrum of length `N` with the frequency indexes ranging from 0 to `N-1`.\n",
    "\n",
    "The input argument to the function is a numpy array `x` and the function should return a numpy array `X`, the DFT of `x`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "def dft(x):\n",
    "    \"\"\"\n",
    "    Input:\n",
    "        x (numpy array) = input sequence of length N\n",
    "    Output:\n",
    "        X (numpy array) = N point DFT of the input sequence x\n",
    "    \"\"\"\n",
    "    X = np.array([])\n",
    "    \n",
    "    for k in range (x.size):\n",
    "        c_sine = gen_complex_sine(k,x.size)\n",
    "        X = np.append(X,sum(x*c_sine))\n",
    "        \n",
    "    return X"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now run and test the function `dft()`. If you run it using as input `x = np.array([1, 2, 3, 4])`, the function shoulds return the following numpy array:\n",
    "\n",
    "```\n",
    "array([10.0 + 0.0j,  -2. +2.0j,  -2.0 - 9.79717439e-16j, -2.0 - 2.0j])\n",
    "```\n",
    "\n",
    "Note that you might not get an exact 0 in the output because of the small numerical errors due to the limited precision of the data in your computer. Usually these errors are of the order 1e-15 depending on your machine."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "array([ 10. +0.00000000e+00j,  -2. +2.00000000e+00j,  -2. -9.79717439e-16j,\n",
      "        -2. -2.00000000e+00j])\n"
     ]
    }
   ],
   "source": [
    "# call dft\n",
    "x = np.array([1,2,3,4])\n",
    "\n",
    "X = dft(x)\n",
    "\n",
    "print(X.__repr__())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Part 4 - Implement the inverse discrete Fourier transform (IDFT)\n",
    "\n",
    "Complete the function `idft()` to implement the inverse discrete Fourier transform (IDFT) equation given above. Given a frequency spectrum `X` of length `N`, the function should return its IDFT `x`, also of length `N`. Assume that the frequency index of the input spectrum ranges from 0 to `N-1`.\n",
    "\n",
    "The input argument to the function is a numpy array `X` of the frequency spectrum and the function should return a numpy array of the IDFT of `X`.\n",
    "\n",
    "Remember to scale the output appropriately."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "def idft(X):\n",
    "    \"\"\"\n",
    "    Input:\n",
    "        X (numpy array) = frequency spectrum (length N)\n",
    "    Output:\n",
    "        x (numpy array) = N point IDFT of the frequency spectrum X\n",
    "    \"\"\"\n",
    "    x = np.array([])\n",
    "    \n",
    "    n = np.arange(-X.size/2,X.size/2)\n",
    "    k = np.arange(-X.size/2,X.size/2)\n",
    "    \n",
    "    for k in range(X.size):\n",
    "        c_sine = gen_complex_sine(k,X.size)\n",
    "        x = np.append(x,1/X.size*sum(X*np.conjugate(c_sine)))\n",
    "        \n",
    "    return x"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now run and test the `idft()` function. If you run it with the input `X = np.array([1 ,1 ,1 ,1])`, the function should return the following numpy array: \n",
    "\n",
    "```\n",
    "array([  1.00000000e+00 +0.00000000e+00j,   -4.59242550e-17 +5.55111512e-17j,   0.00000000e+00 +6.12323400e-17j,   8.22616137e-17 +8.32667268e-17j])\n",
    "```\n",
    "\n",
    "Notice that the output numpy array is essentially `[1, 0, 0, 0]`. Instead of exact 0 we get very small numerical values of the order of 1e-15, which can be ignored. Also, these small numerical errors are machine dependent and might be different in your case.\n",
    "\n",
    "In addition, an interesting test of the IDFT function can be done by providing the output of the DFT of a sequence as the input to the IDFT. See if you get back the original time domain sequence."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[  1.00000000e+00 +0.00000000e+00j  -4.59242550e-17 +5.55111512e-17j\n",
      "   0.00000000e+00 +6.12323400e-17j   8.22616137e-17 +8.32667268e-17j]\n"
     ]
    }
   ],
   "source": [
    "# call idft\n",
    "X = np.array([1 ,1 ,1 ,1])\n",
    "\n",
    "x = idft(X)\n",
    "\n",
    "print(x)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Part 5 - Compute the magnitude spectrum\n",
    "\n",
    "Complete the function `gen_mag_spectrum()` to compute the magnitude spectrum of an input sequence `x` of length `N`. The function should return an `N` point magnitude spectrum with frequency index ranging from 0 to `N-1`.\n",
    "\n",
    "The input argument to the function is a numpy array `x` and the function should return a numpy array of the magnitude spectrum of `x`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "def gen_mag_spec(x):\n",
    "    \"\"\"\n",
    "    Input:\n",
    "        x (numpy array) = input sequence of length N\n",
    "    Output:\n",
    "        magX (numpy array) = magnitude spectrum of the input sequence x (length N)\n",
    "    \"\"\"\n",
    "    magX = abs(dft(x))\n",
    "    \n",
    "    return magX\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now run and test the function `gen_mag_spec()`. If you run `gen_mag_spec()` using as input `x = np.array([1, 2, 3, 4])`, it should return the following numpy array:\n",
    "```\n",
    "array([10.0, 2.82842712, 2.0, 2.82842712])\n",
    "```\n",
    "For a more realistic use of `gen_mag_spec()` use as input a longer signal, such as `x = np.cos(2*np.pi*200.0*np.arange(512)/1000)`, and to get a visual representation of the input and output, import the `matplotlib.pyplot` package and use `plt.plot(x)` and `plt.plot(abs(X))`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[ 10.           2.82842712   2.           2.82842712]\n"
     ]
    }
   ],
   "source": [
    "x = np.array([1, 2, 3, 4])\n",
    "\n",
    "magX = gen_mag_spec(x)\n",
    "\n",
    "print(magX)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "import IPython.display as ipd\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f3894224208>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f388f838208>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f389402c7f0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#call gen_mag_spec and plot result\n",
    "f = 200\n",
    "fs = 1000\n",
    "N = 512\n",
    "\n",
    "xn = np.cos(2*np.pi*f*np.arange(N)/fs)\n",
    "\n",
    "magXn = gen_mag_spec(xn)\n",
    "\n",
    "t = np.arange(N)/fs\n",
    "plt.plot(t,xn)\n",
    "plt.axis([0,N/fs,-1,1])\n",
    "plt.xlabel('seconds')\n",
    "plt.ylabel('amplitude')\n",
    "plt.show()\n",
    "\n",
    "plt.plot(np.arange(N/2)*fs/N,magXn[0:int(N/2)])\n",
    "plt.show()\n",
    "\n",
    "# logaritmic scale\n",
    "log = 20*np.log10(2*magXn[0:int(N/2)]/N)        #To normalize it multiplied by two to obtain a 0 dB sinusoid\n",
    "plt.plot(fs*np.arange(N/2)/(N),log)\n",
    "# plt.axis([0,N/2,-80,0])\n",
    "plt.ylim([-50,0])\n",
    "plt.xlabel('Frequency [Hz]')\n",
    "plt.ylabel('Amplitude [dB]')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "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",
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