MRSP_Optimization_FilterBanks.ipynb

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      "source": [
        "<center>\n",
        "    <img src=\"https://github.com/GuitarsAI/MRSP_Notebooks/blob/master/images/msp_header.png?raw=1\">\n",
        "</center>\n",
        "\n",
        "#### Prof. Dr. -Ing. Gerald Schuller <br> Jupyter Notebook: Renato Profeta"
      ]
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      "source": [
        "# Optimization of Filter Banks"
      ]
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        "%%html\n",
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      "source": [
        "## Goal"
      ]
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    {
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      "source": [
        "Obtain a filter bank from our structure or product $H(z)=F_a⋅D(z)\\cdot G(z)$ .... , which has \"good\" subband filters, i.e. a good or sufficient stopband attenuation and not much pass band attenuation. An example could be a desired stopband attenuation of -60dB and a pass band attenuation of less than -3dB."
      ]
    },
    {
      "cell_type": "markdown",
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        "id": "7QhhotGqFbnz"
      },
      "source": [
        "## Problem to solve:"
      ]
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      "source": [
        "The coefficients which determine the frequency responses are the coefficients in our cascade or product, the coefficients in our matrices $e_j^i , h , g_j^i  \\dots$\n",
        "\n",
        "They result in the frequency response in a nonlinear way, hence the usual filter design approaches don't work here, previous approaches like the Remez-exchange algorithm.\n",
        "\n",
        "Those traditional filter design algorithms can also be seen as optimization algorithms for more or less linear problems (or quadratic if we take the mean squared error).\n",
        "\n",
        "We can read out the resulting analysis baseband prototype impulse response $h_a(n)$ for instance by computing the sparse folding matrix the product:\n",
        "\n",
        "$$\\large\n",
        "H(z) = F_a \\cdot D(z) \\cdot \\prod_{n=0}^{P-1} G_n(z) \\cdot \\prod_{m=0}^{Q-1} H_m(z)$$\n",
        "\n",
        "(without the transform matrix T ), and then compare it with eq. (1) of Lesson 14,\n",
        "\n",
        "$$\\large\n",
        "F_a(z) = \\\\\n",
        "\\large\n",
        "\\left[ \n",
        "    \\begin{array}{cccccc} \n",
        "    . & 0 & -H_{2N-1}^{\\downarrow 2N}\\left(-z^2\\right)\\cdot z^{-1} & \n",
        "    -H_{N-1}^{\\downarrow 2N}\\left(-z^2\\right)\\cdot z^{-1} & 0 & . \\\\ \n",
        "    . & . & 0 & 0 & . & . \\\\\n",
        "    -H_{1.5N}^{\\downarrow 2N}\\left(-z^2\\right)\\cdot z^{-1} & 0 & . & \n",
        "    . & 0 & -H_{\\frac{N}{2}}^{\\downarrow 2N}\\left(-z^2\\right) \\\\\n",
        "    -H_{1.5N-1}^{\\downarrow 2N}\\left(-z^2\\right)\\cdot z^{-1} & 0 & . & \n",
        "    . & 0 & H_{\\frac{N}{2}-1}^{\\downarrow 2N}\\left(-z^2\\right) \\\\\n",
        "    0 & . & 0 & . & . & 0 \\\\\n",
        "    . & 0 & -H_{N}^{\\downarrow 2N}\\left(-z^2\\right)\\cdot z^{-1} & \n",
        "    H_{0}^{\\downarrow 2N}\\left(-z^2\\right) & 0 & . \\\\\n",
        "    \\end{array}\n",
        "\\right]\n",
        "$$\n",
        "\n",
        "with\n",
        "\n",
        "$$\\large\n",
        "H_{n}^{\\downarrow 2N}(z) := \\sum_{m=0}^{\\infty}h_a(m2N+n)\\cdot z^{-m}\n",
        "$$"
      ]
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      "source": [
        "In this way we obtain ha(n) , and hence its frequency response, from our matrix coefficients\n",
        "$x=[h1, h2, ... , e_j^i ,... ,h_j^i , ...]$. We can do the same for the synthesis side, or we restrict the (sub-) matrices to have det(.)=-1, in which case the synthesis baseband impulse response is the same as for the analysis.\n",
        "\n",
        "Another possibility to obtain the analysis baseband impulse response is to compute the polyphase matrix $H(z)$. Its first column contains the **polyphase elements of the first subband filter in reverse order.** This can be used to read out its impulse response $h_0(n)$. To obtain $h_a(n)$ we simply divide $h_0(n)$ by the modulation function for the first subband (for k=0)."
      ]
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      "source": [
        "## Our approach:"
      ]
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      "source": [
        "Since we now have this non-linear dependency of our baseband impulse response from the matrix coefficients, we need to use “more powerful” optimization algorithms, which are made for just mostly convex error functions.\n",
        "\n",
        "We first define an **error function**, and then we use an **optimization** algorithm to minimize this error function. This error function can be the sum of the magnitudes, or the squares, of the **differences between our obtained frequency response**, given our unknown variables at some point, **and our desired frequency response.** \n",
        "\n",
        "To give the stop band attenuation and the pass band ripples different weights, we can also **assign weights to the different frequency regions** for our error function.\n",
        "\n",
        "So our starting point is a vector of all of our unknowns of our matrices, $x=[h1, h2, ... , e_j^i ,... ,h_j^i , ...]=[x_1,x_2]$. We now define a function which computes the baseband impulse response out of these unknowns, by multiplying our matrices to obtain our final folding matrix or the polyphase matrix, and then read out the baseband impulse response.\n",
        "\n",
        "This then yields the baseband prototype for our coefficient set x , which we call $h_x(n)$ This is now used to compute a **weighted frequency response, at k frequency points**, with weights $w_i$ for each frequency point:\n",
        "\n",
        "$$\\large\n",
        "H_i= \\sum_{n=0}^{L\\cdot N-1} h_x(n)\\cdot e^{j\\omega_i\\cdot n)} \\cdot w_i, \\text{for i = 0,...,k-1}$$\n",
        "<cite>(see also Schuller, Smith: “New Framework for Modulated Perfect Reconstruction Filter Banks”, IEEE Transactions on Signal Processing, August 1996)</cite>\n",
        "\n",
        "For instance we can use \"freqz\" to compute $H_i$ (by default it computes 512 equally spaced frequency points), and then multiply it with the weights $w_i$.\n",
        "\n",
        "We choose as many frequency points as necessary to sufficiently cover our frequency response. Usually it should be **several times the length of our filter**, to avoid sampling the frequency response accidentally near its zeros. The more important frequency points in terms of attenuation get the higher weights."
      ]
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      "source": [
        "The same can also be done for the synthesis, but remember that this is only necessary if we don't have det(..)=-1, because for det(..)=-1, we obtain identical prototype impulse responses for analysis and synthesis, and we only need to optimize the analysis (Lecture 13 and 14).\n",
        "\n",
        "We also need to have a vector containing the weighted desired frequency response, which would be 1 for the pass band (multiplied by the corresponding weights), and zeros in the stop band. We call this **d **(for desired).\n",
        "\n",
        "Our error function of our vector of unknowns *x* is now:\n",
        "\n",
        "$$\\large\n",
        "f(x) = \\sum_{i=1}^{2k} \\mid H_i(x)-d_i \\mid^2=(\\mathbf{H-d})\\overline{(\\mathbf{H-d})^T} $$\n",
        "\n",
        "(row times column vector). Now we just need to minimize this function f(x) with respect to our vector of unknows *x*.\n",
        "\n",
        "This leads us to optimization in general. The goal of optimization is to find the vector *x* which minimizes the error function f(x).\n"
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        "%%html\n",
        "<center>\n",
        "<iframe width=\"560\" height=\"315\" src=\"https://www.youtube.com/embed/rn_7bq3BGRQ?rel=0\" frameborder=\"0\" allow=\"accelerometer; encrypted-media; gyroscope; picture-in-picture\" allowfullscreen></iframe>\n",
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      "source": [
        "We know: in a minimum, the functions derivative is zero:\n",
        "$$\\large\n",
        "f'(x):=\\frac{df(x)}{dx}=0$$\n",
        "\n",
        "An approach to iteratively find the zero of a function is **Newtons method.** Take some function f(x), where x is not a vector but just a number, then we can find its zero as depicted in the following picture:\n",
        "\n",
        "<center>\n",
        "    <img src=\"https://github.com/GuitarsAI/MRSP_Notebooks/blob/master/images/Lecture15_01_newtons.png?raw=1\" width=\"600\"/>\n",
        "    <small> from https://tutorial.math.lamar.edu/classes/calci/newtonsmethod.asp </small>\n",
        "</center>\n",
        "              \n",
        "with the iteration:\n",
        "$$\\large\n",
        "x_{k+1}=x_k-\\dfrac{f(x_k)}{f'(x_k)}, \\text{k=0,1,2...}$$\n",
        "\n",
        "Observe: Sometimes we need to compute the derivative numerically, by evaluating the function a few times in the neighborhood, and eg. compute $\\dfrac{\\Delta f}{\\Delta x}$ , for a small $\\Delta x$ (there more involved methods for it).\n",
        "\n",
        "Now we want to find the zero not of f(x) , but of f'(x) , hence we simply replace f(x) by f'(x) and obtain the following iteration,\n",
        "$$\\large\n",
        "x_{k+1}=x_k-\\dfrac{f'(x_k)}{f''(x_k)}$$\n",
        "\n",
        "To obtain a minimum (not a maximum) we need the condition $f''(x_k)>0$"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
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      "source": [
        "## Example for finding a zero of a function:"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "g81RYkLuFboA"
      },
      "source": [
        "Compute $\\sqrt{2}$ numerically by finding the zero of the function $f(x)=x^2-2$.\n",
        "\n",
        "We know the solution is $\\sqrt{2}$ . Now apply Newtons Method to find this solution numerically. The first derivative is $f'(x)=2x$.\n",
        "\n",
        "The Newton iteration is \n",
        "\n",
        "$$\\large\n",
        "x_{k+1}=x_k-\\dfrac{f(x_k)}{f'(x_k)}=x_k - \\dfrac{x_k^2-2}{2x_k}$$\n",
        "\n",
        "In ipython and with a starting value of 1 this becomes:"
      ]
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    {
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        "id": "0ePV0LTrFboB",
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      "source": [
        "x=1.0\n",
        "for i in range(3):\n",
        "    x=x-(x**2-2)/(2*x)\n",
        "    print(x)"
      ],
      "execution_count": null,
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          "text": [
            "1.5\n",
            "1.4166666666666667\n",
            "1.4142156862745099\n"
          ],
          "name": "stdout"
        }
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      "source": [
        "(True value: 1.4142135623730951)\n",
        "\n",
        "We see: after only 3 iterations we obtain $\\sqrt{2}$ with 6 digits accuracy!"
      ]
    },
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      "cell_type": "markdown",
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      "source": [
        "### Example"
      ]
    },
    {
      "cell_type": "markdown",
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        "id": "pTE0URf7FboD"
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      "source": [
        "Find the minimum of cos(x) . We know a minimum is at $x=\\pi$ , so this is also a way to numerically determine $\\pi$.\n",
        "We have:\n",
        "$$\\large\n",
        "f(x)=cos(x) \\\\\n",
        "\\large\n",
        "f'(x)=-sin(x) \\\\\n",
        "\\large\n",
        "f''(x)=-cos(x)\n",
        "$$\n",
        "\n",
        "Newton update:\n",
        "$$\\large\n",
        "x_{new}=x_{old}-\\dfrac{f'(x_{old})}{f''(x_{old})}=x_{old}-\\dfrac{sin(x_{old})}{cos(x_{old})}$$\n",
        "\n",
        "In ipyhton we simply repeatedly use the expression:\n",
        "`x=x-sin(x)/cos(x)`\n",
        "\n",
        "We start with x=3 and preoceed with the Newton update:"
      ]
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      "source": [
        "import math as m\n",
        "x=100\n",
        "for i in range(3):\n",
        "    x=x-m.sin(x)/m.cos(x)\n",
        "    print(x)\n"
      ],
      "execution_count": null,
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          "output_type": "stream",
          "text": [
            "100.58721391515692\n",
            "100.53090551669032\n",
            "100.53096491487345\n"
          ],
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      "source": [
        "We see that this iteration indeed converges to $\\pi$ ! It computes $\\pi$ =3.141592653589793 with an accuracy of 10 digits after only 2 iterations!\n",
        "\n",
        "Observe: if you start with x=1, it converges to 0, which is a **maximum** of our function, which also has the first derivative as zero! This shows that we still need to check the second derivative, to see if it is a minimum or a maximum. \n",
        "\n",
        "If we start with x=100, it converges to $32\\pi$, which is a minimum, but perhaps not the expected minimum. This shows that **starting point is important**!"
      ]
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        "%%html\n",
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      "source": [
        "For a **multi-dimensional** function, where the argument *x* is a vector, the first derivative is a vector called \"Gradient\", with symbol Nabla $\\nabla$ , because we need the derivative with respect to each element of the argument vector *x*:\n",
        "\n",
        "$$\\large\n",
        "\\nabla f(x)=\n",
        "\\left(\n",
        "\\begin{array}{c}\n",
        "\\dfrac{\\partial f}{\\partial x_1} \\\\\n",
        "\\vdots \\\\\n",
        "\\dfrac{\\partial f}{\\partial x_n} \\\\\n",
        "\\end{array}\n",
        "\\right)\n",
        "$$\n",
        "\n",
        "(where n is the number of unknowns in the argument vector **x**). For the **second derivative** we need to take each element of the gradient vector and again take the derivative to each element of the argument vector. Hence we obtain a matrix, the **Hesse Matrix**, as matrix of second derivatives:\n",
        "\n",
        "$$\\large\n",
        "H_f(x)=\n",
        "\\left(\n",
        "\\begin{array}{ccc}\n",
        "    \\dfrac{\\partial^2 f}{\\partial x_1 \\partial x_1} & \\dots & \\dfrac{\\partial^2 f}{\\partial x_1 \\partial x_n} \\\\\n",
        "    \\vdots & \\ddots & \\vdots \\\\\n",
        "    \\dfrac{\\partial^2 f}{\\partial x_n \\partial x_1} & \\dots & \\dfrac{\\partial^2 f}{\\partial x_n \\partial x_n} \\\\\n",
        "\\end{array}\n",
        "\\right)\n",
        "$$\n",
        "\n",
        "Observe that this Hesse Matrix is symmetric (for \"reasonable\" function we consider, like continuous functions). Using these definitions we can generalize our Newton algorithm to the multi-dimensional case. The one-dimensional iteration:\n",
        "\n",
        "\n",
        "$$\\large\n",
        "x_{k+1}=x_k-\\dfrac{f'(x_k)}{f''(x_k)}$$\n",
        "\n",
        "turns into the multi-dimensional iteration:\n",
        "\n",
        "$$\\large\n",
        "x_{k+1}=x_k-H_f^{-1}(x_k)\\nabla f(x_k)$$\n",
        "\n",
        "For a minimum, $H_f(x)$ must be positive definite (all eigenvalues are positive).\n",
        "\n",
        "The problem here is that for the Hesse matrix we need to compute $n^2$ second derivatives, which can be computationally too complex, and then we need to invert this matrix. Hence we now make the simplifying assumption, that the Hesse matrix can be written as a **diagonal matrix with constant values on the diagonal.**\n",
        "\n",
        "Observe that this is mostly a very crude approximation, but since we have an iteration with many small updates it can still work:\n",
        "\n",
        "$$\\large\n",
        "H_f(x_k)=\\dfrac{1}{\\alpha}\\cdot \\mathbf{I}\n",
        "$$\n",
        "\n",
        "The best value of $\\alpha$ depends on how good it approximates the Hesse matrix.\n",
        "\n",
        "Hence our iteration $x_{k+1}=x_k-H_f^{-1}(x_k)\\nabla f(x_k)$ turns into:\n",
        "\n",
        "$$\\large\n",
        "\\begin{equation}\n",
        "x_{k+1}=x_k-\\alpha \\cdot \\nabla f(x_k)\n",
        "\\end{equation}\n",
        "$$\n",
        "\n",
        "which is much simpler to compute. This is also called **\"Steepest Descent\"**, because the gradient tell us the direction of the steepest descent, or **\"Gradient Descent\"**.\n",
        "\n",
        "We see that the update of *x* consists only of the gradient $\\nabla f(x_k)$ scaled by the factor $\\alpha$. In each step, we reduce the value of f(x) by moving *x* in the direction of the gradient. If we make $\\alpha$ larger, we obtain larger update steps and hence quicker convergence to the minimum, but it may oscillate around the minimum. For smaller $\\alpha$ the steps become smaller, but it will converge more precisely to the minimum.\n",
        "\n",
        "Because of the update direction along the gradient, this method is also called **\"Gradient Descent\"**."
      ]
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      "source": [
        "### Example"
      ]
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        "%%html\n",
        "<center>\n",
        "<iframe width=\"560\" height=\"315\" src=\"https://www.youtube.com/embed/-6HBvDv4l50?rel=0\" frameborder=\"0\" allow=\"accelerometer; encrypted-media; gyroscope; picture-in-picture\" allowfullscreen></iframe>\n",
        "</center>"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/html": [
              "<center>\n",
              "<iframe width=\"560\" height=\"315\" src=\"https://www.youtube.com/embed/-6HBvDv4l50?rel=0\" frameborder=\"0\" allow=\"accelerometer; encrypted-media; gyroscope; picture-in-picture\" allowfullscreen></iframe>\n",
              "</center>\n"
            ],
            "text/plain": [
              "<IPython.core.display.HTML object>"
            ]
          },
          "metadata": {
            "tags": []
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        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "CdpQ8JrmFboH"
      },
      "source": [
        "Find the 2-dimensional minimum of the function:\n",
        "$$\\large\n",
        "f(x_1,x_2)=cos(x_1)-sin(x_2)\n",
        "$$\n",
        "\n",
        "Its gradient is:\n",
        "$$\\large\n",
        "\\nabla f(x_1,x_2)=[-sin(x_1), -cos(x_2)]\n",
        "$$\n",
        "\n",
        "In ipython we choose $\\alpha=1$ and a starting point of $[x1, x2]=[2,2]$:\n"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "dzwPbNs4FboH",
        "outputId": "a00da804-3b53-40e4-9559-5debf34abd86"
      },
      "source": [
        "import numpy as np\n",
        "alpha=1;\n",
        "#start:\n",
        "x=np.array([2,2])\n",
        "for i in range(3):\n",
        "    x= x -alpha*np.array([-m.sin(x[0]), -m.cos(x[1])])\n",
        "    print(x)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "[2.90929743 1.58385316]\n",
            "[3.13950913 1.5707967 ]\n",
            "[3.14159265 1.57079633]\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "iTM1cVrQFboH"
      },
      "source": [
        "We see: the minimum is obtained for $x_1=3.14159265$ (exact value: $\\pi =3.141592653589793$) and $x_2=1.57079633$ (exact value: $\\dfrac{π}{2} =1.5707963267948966$).\n",
        "\n",
        "**Observe** that we needed **3 iterations** to obtain 9 digit accuracy in this 2-dimensional case. In the 1-dimensional case with the **Newton** iteration we needed only **2 iterations** for the same accuracy."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "dKNzg2O0FboI"
      },
      "source": [
        "## Python Example for the Optimization of an MDCT Filter Bank"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "dSOvAHkZFboI"
      },
      "source": [
        "The function \"optimfuncMDCT\" contains an optimization of the baseband prototype, with det(..)=-1, for a given number of subbands, set in the main part of the program, for instance N=8."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "hide_input": true,
        "id": "OCsVXod4FboI",
        "outputId": "f4582345-b384-4455-a7e4-bb4b62578b0b"
      },
      "source": [
        "%%html\n",
        "<center>\n",
        "<iframe width=\"560\" height=\"315\" src=\"https://www.youtube.com/embed/6eV8svWxaZg?rel=0\" frameborder=\"0\" allow=\"accelerometer; encrypted-media; gyroscope; picture-in-picture\" allowfullscreen></iframe>\n",
        "</center>"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/html": [
              "<center>\n",
              "<iframe width=\"560\" height=\"315\" src=\"https://www.youtube.com/embed/6eV8svWxaZg?rel=0\" frameborder=\"0\" allow=\"accelerometer; encrypted-media; gyroscope; picture-in-picture\" allowfullscreen></iframe>\n",
              "</center>\n"
            ],
            "text/plain": [
              "<IPython.core.display.HTML object>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "YFIWWINxFboJ"
      },
      "source": [
        "# Imports\n",
        "import numpy as np\n",
        "import scipy as sp\n",
        "import scipy.optimize\n",
        "import scipy.signal as sig\n",
        "import matplotlib.pyplot as plt"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "iNPA9olaFboJ"
      },
      "source": [
        "# -*- coding: utf-8 -*-\n",
        "\"\"\"\n",
        "Created on Thu Feb 04 16:59:32 2016\n",
        "@author: Max\n",
        "after Matlab function by Gerald Schuller\n",
        "Modified July 2016, Gerald Schuller\n",
        "\"\"\"\n",
        "\n",
        "import numpy as np\n",
        "\n",
        "def polmatmult( A,B ):\n",
        "    \"\"\"polmatmult(A,B)\n",
        "    multiplies two polynomial matrices (arrays) A and B, where each matrix entry is a polynomial.\n",
        "    Those polynomial entries are in the 3rd dimension\n",
        "    The thirs dimension can also be interpreted as containing the (2D) coefficient\n",
        "    exponent of z^-1.\n",
        "    Result is C=A*B;\"\"\"\n",
        "    \n",
        "    [NAx, NAy, NAz] = np.shape(A);\n",
        "    [NBx, NBy, NBz] = np.shape(B);\n",
        "    \"Degree +1 of resulting polynomial, with NAz-1 and NBz-1 being the degree of the...\"\n",
        "    Deg = NAz + NBz -1;\n",
        "    #initialize (with complex zeros):\n",
        "    C = np.zeros((NAx,NBy,Deg))#*(1+1j);\n",
        "    \"Convolution of matrices:\"\n",
        "    for n in range(0,(Deg)):\n",
        "        for m in range(0,n+1):\n",
        "            if ((n-m)<NAz and m<NBz):\n",
        "                C[:,:,n] = C[:,:,n]+ np.dot(A[:,:,(n-m)],B[:,:,m]);\n",
        "    return C\n",
        "   "
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "goMX_BMpFboJ"
      },
      "source": [
        "# -*- coding: utf-8 -*-\n",
        "\"\"\"\n",
        "Created on Thu Feb 04 17:34:26 2016\n",
        "from Matlab\n",
        "@author: Max, Gerald Schuller\n",
        "\"\"\"\n",
        "\n",
        "import numpy as np\n",
        "def Dmatrix(N):\n",
        "    \"\"\"produces a delay matrix D(z), which has delay z^-1 on the upper half of its diagonal\n",
        "    in a 3D polynomial representation (exponents of z^-1 are in the third dimension) \n",
        "    N is number of subbands and size of the polynomial matrix (NxN) \n",
        "    N is even\"\"\" \n",
        "    D=np.zeros((N,N,2));    \n",
        "    D[:,:,0] = np.diag(np.append(np.zeros((1,int(N/2))), np.ones((1,int(N/2)))));\n",
        "    D[:,:,1] = np.diag(np.append(np.ones((1,int(N/2))), np.zeros((1,int(N/2)))));  \n",
        "    return D;\n"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "RsySsybyFboJ"
      },
      "source": [
        "# -*- coding: utf-8 -*-\n",
        "\"\"\"\n",
        "Created on Thu Feb 04 18:29:15 2016 from Matlab, author: Max, \n",
        "Gerald Schuller, Sep. 2017\n",
        "\"\"\"\n",
        "from __future__ import print_function  \n",
        "import numpy as np\n",
        "def symFmatrix(f):\n",
        "    \"\"\"produces a diamond shaped folding matrix F from the coefficients f\n",
        "    (f is a 1-d array)\n",
        "    which leads to identical analysis and synthesis baseband impulse responses\n",
        "    Hence has det 1 or -1\n",
        "    If N is number of subbands, then f is a vector of size 1.5*N coefficients.\n",
        "    N is even\n",
        "    returns: F of shape (N,N,1)\n",
        "    \"\"\"   \n",
        "    sym=1.0; #The kind of symmetry: +-1\n",
        "    N = int(len(f)/1.5);\n",
        "    F=np.zeros((N,N,1))\n",
        "    F[0:int(N/2),0:int(N/2),0]=np.fliplr(np.diag(f[0:int(N/2)]))\n",
        "    F[int(N/2):N,0:int(N/2),0]=np.diag(f[int(N/2):N])\n",
        "    F[0:int(N/2),int(N/2):N,0]=np.diag(f[N:(N+int(N/2))])\n",
        "    ff = np.flipud((sym*np.ones((int(N/2))) - (f[N:(int(1.5*N))])*f[N-1:int(N/2)-1:-1])/f[0:int(N/2)])     \n",
        "    F[int(N/2):N,int(N/2):N,0]=-np.fliplr(np.diag(ff))\n",
        "    return F\n",
        "   \n"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "hrX0eHUNFboK"
      },
      "source": [
        "# -*- coding: utf-8 -*-\n",
        "\"\"\"\n",
        "Created on Thu Feb 04 17:59:00 2016\n",
        "from Matlab\n",
        "@author: Tobias Heinl, Gerald Schuller\n",
        "\n",
        "Function extracts analysis baseband impulse response (reverse window function) \n",
        "from the folding matrix Fa of a cosine \n",
        "modulated filter bank, with modulation function for the analysis IR : \n",
        "h_k(n)=h(n)*cos(pi/N*(k+0.5)*(L-1-n+0.5-N/2));\n",
        "\n",
        "\"\"\" \n",
        "def Fa2h(Fa):\n",
        "    \"\"\" Function extracts analysis baseband impulse response (reverse window function) \n",
        "    from the folding matrix Fa of a cosine modulated filter bank.\n",
        "    \"\"\"\n",
        "    import numpy as np\n",
        "    [N,y,blocks] = np.shape(Fa) \n",
        "    h0 = np.zeros(blocks * N)\n",
        "    #First column of DCT-4:\n",
        "    T = np.zeros((N,1,1)) \n",
        "    T[:,0,0]=np.cos(np.pi/N*(0.5)*(np.arange(N)+0.5))\n",
        "    #Compute first column of Polyphase matrix Pa(z):\n",
        "    Pa =  polmatmult(Fa,T)\n",
        "    #Extract impulse response h0(n):\n",
        "    for m in range(blocks): \n",
        "        h0[m*N+np.arange(N)] = np.flipud(Pa[:,0,m]) \n",
        "    #Baseband prototype h(n), divide by modulation func.:\n",
        "    #h = h0 / np.cos(np.pi/N*0.5*(np.arange(blocks*N)+ 0.5+(N/2)))\n",
        "    h = -h0 / np.cos(np.pi/N*0.5*(np.arange(blocks*N-1,-1,-1)+ 0.5-(N/2)))\n",
        "    return h;  "
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "_TeiTcGGFboK",
        "outputId": "99e11acb-4a2c-4613-a75b-e44e80aed095"
      },
      "source": [
        "N=4\n",
        "x0 = -np.random.rand(int(1.5*N))\n",
        "print('Starting x0',x0)\n",
        "Fa = symFmatrix(x0)\n",
        "D = Dmatrix(N)\n",
        "Faz = polmatmult(Fa,D)\n",
        "h = Fa2h(Faz)\n",
        "print('h',h)\n",
        "\n",
        "plt.figure()\n",
        "plt.plot(h)\n",
        "plt.title('Initial Impulse Response from x0')\n",
        "plt.grid()\n",
        "w, H = sig.freqz(h,1,1024)\n",
        "pb = int(1024/N/2)\n",
        "print('pb',pb)\n",
        "\n",
        "plt.figure()\n",
        "plt.plot(20*np.log10(np.abs(H)))\n",
        "plt.title('Initial Frequency Response from x0')\n",
        "plt.grid()\n",
        "Hdes = np.concatenate((np.ones((pb,1)) , np.zeros(((1024-pb, 1)))), axis = 0)\n",
        "\n",
        "plt.figure()\n",
        "plt.plot(Hdes)\n",
        "plt.title('Desired Frequency Response')\n",
        "plt.grid()\n",
        "tb = np.round(pb)\n",
        "print(tb)\n",
        "weights = np.concatenate((np.ones((pb,1)) , np.zeros((tb, 1)), 1000*np.ones((1024-pb-tb,1))), axis = 0)\n",
        "\n",
        "plt.figure()\n",
        "plt.plot(weights)\n",
        "plt.title('Weights')\n",
        "plt.grid()"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Starting x0 [-0.13077921 -0.76606932 -0.53120745 -0.35528202 -0.33121792 -0.28339573]\n",
            "h [6.74667051 1.10885276 0.28339573 0.33121792 0.35528202 0.53120745\n",
            " 0.76606932 0.13077921]\n",
            "pb 128\n",
            "128\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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c6GZmFeFAT0T4oKiZ5eVANzOrCAd6Kj4mamaZOdAT8oiLmeXkQDczqwgHeiLymIuZZeZAT8ljLmaWkQM9EV8oama5OdAT8pWiZpaTA93MrCIc6Il4xMXMcnOgJ+RL/80sJwe6mVlFONATkXzWopnl5UA3M6sIB3oivlLUzHJzoCcUPipqZhk50M3MKsKBnogv/Tez3BzoCXnAxcxycqAn4h10M8vNgZ6Qj4maWU4OdDOzinCgp+KjomaWmQPdzKwiHOhmZhXRVaBLWiJpq6QRSVdM0u6tkkLSULou9ofxARdfLWpmuXQMdEkDwPXA+cBiYLmkxW3aHQ1cBtydupNmZtZZN3vopwEjEfFQROwGVgHL2rT7CHAt8IOE/esbPiZqZrnN6KLNXGBH0/QocHpzA0mnAPMj4jZJvz3RiiStAFYADA4O0mg09rvDAGNjY1N+ba9s374bgDsaDQ5JnO7Tsd5eqVOtUK9661Qr5Km3m0Bvl04/GiiWdAhwHXBJpxVFxEpgJcDQ0FAMDw931clWjUaDqb62V+7b820Y2cbw2cMcckjaQJ+O9fZKnWqFetVbp1ohT73dDLmMAvObpucBjzVNHw2cDDQkbQfOANbW7cCofw/dzHLrJtA3AIskLZR0GHAhsHZ8YUQ8ExGzI2JBRCwA7gKWRsS9PenxNOdzXMwsl46BHhF7gEuB9cAWYHVEbJJ0jaSlve5gv/BBUTPLrZsxdCJiHbCuZd7VE7QdPvBu9a/iPHSnu5kdfL5S1MysIhzoiXif3Mxyc6An5oOiZpaLAz0RHxQ1s9wc6In5t7nMLBcHuplZRTjQE5HHXMwsMwd6YuHDomaWiQPdzKwiHOiJ+aComeXiQDczqwgHeiI+JmpmuTnQzcwqwoFuZlYRDvREfMciM8vNgZ6Yz3Ixs1wc6In4oKiZ5eZAT8xXippZLg50M7OKcKAn4hEXM8vNgZ6YD4qaWS4OdDOzinCgJzJ+lot30M0sFwe6mVlFONAT8ZWiZpabAz2x8FFRM8vEgW5mVhEO9ER86b+Z5eZAT8wDLmaWiwPdzKwiugp0SUskbZU0IumKNst/S9JmSfdLul3Siem72h98TNTMcukY6JIGgOuB84HFwHJJi1uafR0YiojXA2uAa1N31MzMJtfNHvppwEhEPBQRu4FVwLLmBhFxR0Q8X07eBcxL283pTz4qamaZzeiizVxgR9P0KHD6JO3fBfyfdgskrQBWAAwODtJoNLrrZYuxsbEpv7ZXRra/CMCdd97JzEPThvt0rLdX6lQr1KveOtUKeertJtDbpVPbkWJJFwFDwNntlkfESmAlwNDQUAwPD3fXyxaNRoOpvrZXHrzzYfjWZt5w1hs45qhDk657OtbbK3WqFepVb51qhTz1dhPoo8D8pul5wGOtjSSdB1wFnB0RL6TpXv8Y/1fPdywys1y6GUPfACyStFDSYcCFwNrmBpJOAW4ElkbEE+m7aWZmnXQM9IjYA1wKrAe2AKsjYpOkayQtLZv9ITAL+GtJ90laO8HqKsvHRM0st26GXIiIdcC6lnlXNz0/L3G/+pbPQzezXHylqJlZRTjQE/GIi5nl5kBPzCMuZpaLAz0RXylqZrk50BPzHYvMLBcHuplZRTjQE/GIi5nl5kBPzAMuZpaLA93MrCIc6In86Me5vItuZpk40M3MKsKBnoqPippZZg70xPx76GaWiwPdzKwiHOiJeMDFzHJzoKfmERczy8SBnoiPiZpZbg70xLyDbma5ONDNzCrCgZ6IfFjUzDJzoCfmS//NLBcHeiI+KGpmuTnQE/OVomaWiwPdzKwiHOiJeMTFzHJzoCfmg6JmlosD3cysIhzoiYyf5eIddDPLxYFuZlYRDvREfKWomeXmQE8sfFTUzDLpKtAlLZG0VdKIpCvaLD9c0ufL5XdLWpC6o2ZmNrmOgS5pALgeOB9YDCyXtLil2buAXRFxEnAd8LHUHZ32POJiZpnN6KLNacBIRDwEIGkVsAzY3NRmGfCh8vka4E8kKWo4/nDRp+/m0IG0I1nPPf88M//575Kuc7qqU61Qr3rrVCtMXu9l5y7iLT9zQvL37CbQ5wI7mqZHgdMnahMReyQ9A7wc2NncSNIKYAXA4OAgjUZjSp0eGxub8mt7ZeD7L3HmnAFefOmF5OuedfhLDOj7ydc7HdWpVqhXvXWqFSav95Ftm2ns+nby9+wm0NsNJrTueXfThohYCawEGBoaiuHh4S7efl+NRoOpvraX/tP5vVnvdK23F+pUK9Sr3jrVCnnq7WZsYBSY3zQ9D3hsojaSZgDHAN9N0UEzM+tON4G+AVgkaaGkw4ALgbUtbdYCF5fP3wr8bR3Hz83Mcuo45FKOiV8KrAcGgM9GxCZJ1wD3RsRa4DPAzZJGKPbML+xlp83MbF/djKETEeuAdS3zrm56/gPgl9N2zczM9oevFDUzqwgHuplZRTjQzcwqwoFuZlYRynV2oaQngUem+PLZtFyFWnF1qrdOtUK96q1TrdC7ek+MiFe0W5At0A+EpHsjYih3Pw6WOtVbp1qhXvXWqVbIU6+HXMzMKsKBbmZWEf0a6Ctzd+Agq1O9daoV6lVvnWqFDPX25Ri6mZntq1/30M3MrIUD3cysIvou0DvdsLrfSJov6Q5JWyRtkvTecv7xkv6vpG3lf48r50vSJ8v675d0at4K9p+kAUlfl3RbOb2wvLn4tvJm44eV8/v+5uOSjpW0RtK3ym18ZsW37X8r/44fkHSrpCOqsn0lfVbSE5IeaJq339tS0sVl+22SLm73XlPVV4He5Q2r+80e4PKIeC1wBvCbZU1XALdHxCLg9nIaitoXlY8VwA0Hv8sH7L3AlqbpjwHXlbXuorjpOFTj5uN/DHwlIn4K+BmKuiu5bSXNBS4DhiLiZIqf276Q6mzfm4AlLfP2a1tKOh74IMVtPE8DPjj+j0ASEdE3D+BMYH3T9JXAlbn7lbjGLwG/AGwF5pTz5gBby+c3Asub2v+oXT88KO54dTvwH4DbKG5fuBOY0bqNKX6D/8zy+YyynXLXsB+1vgx4uLXPFd624/cWPr7cXrcBb6zS9gUWAA9MdVsCy4Ebm+bv1e5AH321h077G1bPzdSX5MqvnKcAdwODEfE4QPnfV5bN+v0z+CPgvwMvldMvB56OiD3ldHM9e918HBi/+Xi/eDXwJPDn5RDTpyXNpKLbNiK+A3wceBR4nGJ7baS62xf2f1v2dBv3W6B3dTPqfiRpFvA3wPsi4tnJmraZ1xefgaQ3A09ExMbm2W2aRhfL+sEM4FTghog4BXiOH38lb6ev6y2HDpYBC4ETgJkUQw+tqrJ9JzNRbT2tud8CvZsbVvcdSYdShPlfRsQXytn/KmlOuXwO8EQ5v58/g7OApZK2A6sohl3+CDi2vLk47F1Pv998fBQYjYi7y+k1FAFfxW0LcB7wcEQ8GREvAl8A/h3V3b6w/9uyp9u43wK9mxtW9xVJorgn65aI+ETTouYbb19MMbY+Pv/t5VH0M4Bnxr/yTXcRcWVEzIuIBRTb7m8j4teBOyhuLg771tq3Nx+PiH8Bdkj6yXLWucBmKrhtS48CZ0g6qvy7Hq+3ktu3tL/bcj3wi5KOK7/R/GI5L43cBxmmcFDiAuDbwIPAVbn7k6CeN1B85bofuK98XEAxlng7sK387/Fle1Gc6fMg8E2KMwqy1zGFuoeB28rnrwbuAUaAvwYOL+cfUU6PlMtfnbvfU6jzZ4F7y+37ReC4Km9b4MPAt4AHgJuBw6uyfYFbKY4NvEixp/2uqWxL4J1lzSPAO1L20Zf+m5lVRL8NuZiZ2QQc6GZmFeFANzOrCAe6mVlFONDNzCrCgW5mVhEOdDOzivj/1FhGTfFUGLQAAAAASUVORK5CYII=\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "OpdUUUlwFboK"
      },
      "source": [
        "\"\"\"\n",
        "Created on Thu Feb 04 19:33:24 2016\n",
        "from Matlab\n",
        "@author: Tobias Heinl, Gerald Schuller\n",
        "\n",
        "\n",
        "function for optimizing an MDCT type filter bank. \n",
        "x: unknown matirx coefficients, x: 1-d vector! \n",
        "\n",
        "\"\"\"\n",
        "\n",
        "def optimfuncMDCT(x, N):\n",
        "    \"\"\"Computes the error function for the filter bank optimization\n",
        "    for coefficients x, a 1-d array, N: Number of subbands\"\"\" \n",
        "    import numpy as np\n",
        "    import scipy.signal as sig\n",
        "   \n",
        "    #x = np.transpose(x) \n",
        "    Fa = symFmatrix(x)\n",
        "    D = Dmatrix(N)\n",
        "    Faz = polmatmult(Fa,D)\n",
        "    h = Fa2h(Faz)\n",
        "    h = np.hstack(h)\n",
        "    w, H = sig.freqz(h,1,1024)\n",
        "    pb = int(1024/N/2)\n",
        "    Hdes = np.concatenate((np.ones((pb,1)) , np.zeros(((1024-pb, 1)))), axis = 0)\n",
        "    tb = np.round(pb)\n",
        "    weights = np.concatenate((np.ones((pb,1)) , np.zeros((tb, 1)), 1000*np.ones((1024-pb-tb,1))), axis = 0) \n",
        "    err = np.sum(np.abs(H-Hdes)*weights)\n",
        "    return err  "
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "Jm8Q2ykRFboL",
        "outputId": "d1460fe3-ab86-401b-97d7-ed5f55394988"
      },
      "source": [
        "%%time\n",
        "N=8\n",
        "#Start optimization with some starting point:\n",
        "x0 = -np.random.rand(int(1.5*N))\n",
        "print(\"starting error=\", optimfuncMDCT(x0, N)) #test optim. function\n",
        "xmin = sp.optimize.minimize(optimfuncMDCT, x0, args=(N,), options={'disp':True})\n",
        "print(\"optimized coefficients=\", xmin.x)\n",
        "np.savetxt(\"MDCTcoeff.txt\", xmin.x)\n",
        "print(\"error after optim.=\", optimfuncMDCT(xmin.x, N))\n",
        "#Baseband Impulse Response:\n",
        "Fa = symFmatrix(xmin.x) \n",
        "Faz = polmatmult(Fa, Dmatrix(N))\n",
        "h = Fa2h(Faz)\n",
        "print(\"h=\", h)\n",
        "plt.figure(figsize=(10,8))\n",
        "plt.plot(h)\n",
        "plt.xlabel('Sample')\n",
        "plt.ylabel('Value')\n",
        "plt.title('Baseband Impulse Response of our Optimized MDCT Filter Bank')\n",
        "plt.grid()\n",
        "plt.figure(figsize=(10,8))\n",
        "#Magnitude Response:\n",
        "w,H=sp.signal.freqz(h) \n",
        "plt.plot(w,20*np.log10(abs(H)))\n",
        "plt.axis([0, 3.14, -60,20])\n",
        "plt.xlabel('Normalized Frequency')\n",
        "plt.ylabel('Magnitude (dB)')\n",
        "plt.title('Mag. Frequency Response of the MDCT Filter Bank') \n",
        "plt.grid()"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "starting error= 4797122905.016674\n",
            "Warning: Desired error not necessarily achieved due to precision loss.\n",
            "         Current function value: 1043146993.298535\n",
            "         Iterations: 68\n",
            "         Function evaluations: 2714\n",
            "         Gradient evaluations: 193\n",
            "optimized coefficients= [-0.12898962 -0.28614769 -0.45889834 -0.62918827 -0.77726352 -0.88849878\n",
            " -0.95819286 -0.99164919 -0.99164294 -0.95818137 -0.88848579 -0.77725265]\n",
            "error after optim.= 1043146993.298535\n",
            "h= [0.12898773 0.28613705 0.45888476 0.62917554 0.77725265 0.88848579\n",
            " 0.95818137 0.99164294 0.99164919 0.95819286 0.88849878 0.77726352\n",
            " 0.62918827 0.45889834 0.28614769 0.12898962]\n",
            "Wall time: 57.3 s\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 720x576 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 720x576 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "hide_input": true,
        "id": "EMeHngg1FboL"
      },
      "source": [
        "It starts with random coefficients, and prints their resulting error value. Then it optimizes the coefficients using \"scipy.optimize.minimize\" (it needs scipy version 0.19.1 or later), and after finishing the optimization prints out the resultingn error value, and plots the resulting baseband prototype and its magnitude frequency response.\n",
        "\n",
        "For N=4 it is fairly fast. Observe that N=8 subbands already takes some time, N=16 takes a lot longer.\n",
        "\n",
        "Observe that the resulting baseband impulse response is similar to the sine window, but not exactly the same, it is “more optimal” in our optimization functions sense."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "WcudDGtIFboL",
        "outputId": "2a9f940d-e7fe-4c2f-c7a4-ca98cf41f50e"
      },
      "source": [
        "%%time\n",
        "N=16\n",
        "#Start optimization with some starting point:\n",
        "x0 = -np.random.rand(int(1.5*N))\n",
        "print(\"starting error=\", optimfuncMDCT(x0, N)) #test optim. function\n",
        "xmin = sp.optimize.minimize(optimfuncMDCT, x0, args=(N,), options={'disp':True})\n",
        "print(\"optimized coefficients=\", xmin.x)\n",
        "np.savetxt(\"MDCTcoeff.txt\", xmin.x)\n",
        "print(\"error after optim.=\", optimfuncMDCT(xmin.x, N))\n",
        "#Baseband Impulse Response:\n",
        "Fa = symFmatrix(xmin.x) \n",
        "Faz = polmatmult(Fa, Dmatrix(N))\n",
        "h = Fa2h(Faz)\n",
        "print(\"h=\", h)\n",
        "plt.figure(figsize=(10,8))\n",
        "plt.plot(h)\n",
        "plt.xlabel('Sample')\n",
        "plt.ylabel('Value')\n",
        "plt.title('Baseband Impulse Response of our Optimized MDCT Filter Bank')\n",
        "plt.grid()\n",
        "plt.figure(figsize=(10,8))\n",
        "#Magnitude Response:\n",
        "w,H=sp.signal.freqz(h) \n",
        "plt.plot(w,20*np.log10(abs(H)))\n",
        "plt.axis([0, 3.14, -60,30])\n",
        "plt.xlabel('Normalized Frequency')\n",
        "plt.ylabel('Magnitude (dB)')\n",
        "plt.title('Mag. Frequency Response of the MDCT Filter Bank') \n",
        "plt.grid()"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "starting error= 8071027923.306213\n",
            "Warning: Desired error not necessarily achieved due to precision loss.\n",
            "         Current function value: 1142039152.954523\n",
            "         Iterations: 109\n",
            "         Function evaluations: 5679\n",
            "         Gradient evaluations: 218\n",
            "optimized coefficients= [-0.06486723 -0.13868403 -0.22025102 -0.30746628 -0.39868818 -0.49094693\n",
            " -0.58153766 -0.66713626 -0.74496602 -0.81354839 -0.8712176  -0.91711006\n",
            " -0.95157698 -0.97545976 -0.99034679 -0.99789746 -0.99789064 -0.99032938\n",
            " -0.97543203 -0.95155    -0.91707795 -0.87118318 -0.81351954 -0.74493936]\n",
            "error after optim.= 1142039152.9545228\n",
            "h= [0.06486271 0.13866398 0.22022739 0.30743836 0.39865387 0.4909082\n",
            " 0.58149714 0.66709833 0.74493936 0.81351954 0.87118318 0.91707795\n",
            " 0.95155    0.97543203 0.99032938 0.99789064 0.99789746 0.99034679\n",
            " 0.97545976 0.95157698 0.91711006 0.8712176  0.81354839 0.74496602\n",
            " 0.66713626 0.58153766 0.49094693 0.39868818 0.30746628 0.22025102\n",
            " 0.13868403 0.06486723]\n",
            "Wall time: 1min 57s\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 720x576 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 720x576 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "rDNWXmK1FboL"
      },
      "source": [
        ""
      ],
      "execution_count": null,
      "outputs": []
    }
  ]
}