MRSP_DFT_Equivalent.ipynb

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        "<center>\n",
        "    <img src=\"https://github.com/TUIlmenauAMS/MRSP_Tutorials/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": [
        "# Transforms as Filter Banks"
      ]
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        "%%html\n",
        "<center>\n",
        "<iframe width=\"560\" height=\"315\" src=\"https://www.youtube.com/embed/4-5xq47I7gs\" frameborder=\"0\" allow=\"accelerometer; encrypted-media; gyroscope; picture-in-picture\" allowfullscreen></iframe>\n",
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      "source": [
        "## Equivalent Analysis Filters of a DFT"
      ]
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      "source": [
        "%%html\n",
        "<center>\n",
        "<iframe width=\"560\" height=\"315\" src=\"https://www.youtube.com/embed/57Vo03n-1AE\" frameborder=\"0\" allow=\"accelerometer; encrypted-media; gyroscope; picture-in-picture\" allowfullscreen></iframe>\n",
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      "source": [
        "From the definitions in lecture 2 we know that a DFT of a block of signal x is defined as:\n",
        "\n",
        "$$\\large\n",
        "X(k) =\\sum _ {n= 0}^ {N-1} x(mN+n) e^{-j \\frac{2\\pi} { N} \\cdot k \\cdot n}\n",
        "$$\n",
        "\n",
        "Hence we can rewrite the DFT as a matrix multiplication with the matrix T with the elements,\n",
        "\n",
        "$$\\large\n",
        "T_{n,k} = e^{-j \\frac{2\\pi} { N} \\cdot k \\cdot n}\n",
        "$$\n",
        "where n is the time (and row) index, and k is the frequency (and column) index.\n",
        "\n",
        "Using the signal block vector:\n",
        "\n",
        "$$\\large\n",
        "\\begin{equation}\n",
        "\\boldsymbol x (m)=[x(mN),x(mN+1), ..., x(mN+N-1)]\n",
        "\\end{equation}\n",
        "$$\n",
        "\n",
        "we can rewrite the DFT of block $m$ as a matrix multiplication,\n",
        "\n",
        "$$\\large\n",
        "\\begin{equation}\n",
        "y(m) = x(m) \\cdot T \\quad (2)\n",
        "\\end{equation}\n",
        "$$\n",
        "\n",
        "This is the matrix formulation of the DFT, where the matrix multiplication (2) is:\n",
        "\n",
        "$$\\large\n",
        "\\begin{equation}\n",
        "y_k(m) = \\sum _ {n= 0}^ {N-1} x(mN+n) e^{-j \\frac{2\\pi} { N} \\cdot k \\cdot n}\n",
        "\\end{equation} \\quad (3)\n",
        "$$\n",
        "\n",
        "Here we can now extract the equivalent impulse responses.\n",
        "\n",
        "Now we can **compare** above transform eq. (3) with the **convolution and downsampling** eq:\n",
        "\n",
        " $$\\large\n",
        " \\begin{equation}\n",
        " y^{\\downarrow N}_{n_0}(m)= \\sum _ {n=0 }^ {L-1} x(mN+n_0-n) h_k(n)\n",
        " \\end{equation}\n",
        " $$\n",
        "\n",
        "We see that here the index n for our signal x has the **reverse order** /reverse sign as in eq. (3).\n",
        "\n",
        "But since we are interested in the equivalent impulse response, we simply **reverse the index order** in the transform equation (3) (we use the index substitution $n\\rightarrow N−1−n'$ ).\n",
        "\n",
        "We still obtain the same sum, because the sum ordering doesn't change the result.\n",
        "\n",
        "$$\\large\n",
        "y^{\\downarrow N}_{N-1}(m)= y_k(m) = \\sum _ {n'=0 }^ {N-1} x(mN+N-1-n') \\cdot e^{-j \\frac{2\\pi} {N} \\cdot (N-1-n') \\cdot k}\n",
        "$$\n",
        "\n",
        "Compare this with our convolution sum in (4) from last time, it looks like the convolution sum, with the phase index of $n_0=N-1$ and with filter length equal to the block lenght, $L=N$.\n",
        "\n",
        "This indicates that $y_k(m)$ contains **phase N-1** of the **downsampled subband signal**. Throught this comparison we obtain the **equivalent impulse response** of our DFT as:\n",
        "\n",
        "$$\\large\n",
        "h_k(n) = e^{-j \\dfrac{2\\pi}{N} \\cdot (N-1-n) \\cdot k} = T_{N-1-n,k}\n",
        "$$\n",
        "\n",
        "This is now the equivalent analysis impulse response of our DFT, interpreted as analysis filter bank! Observe that it can also be interpreted as a **rectangular window** of length N **with modulation** of this exponential term!\n",
        "\n",
        "**In Conclusion:** The **DFT** can also be seen as a **special kind of filter bank.** Each DFT coefficent can be seen as a sample of one of the downsampled subbands.\n",
        "**Each column of our transform matrix T represents the impulse response of one subband filter, but in reversed order** (we can read the impulse response out of the transform matrix starting from the bottom and going up)."
      ]
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      "source": [
        "## Equivalent Synthesis Filter Bank"
      ]
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        "%%html\n",
        "<center>\n",
        "<iframe width=\"560\" height=\"315\" src=\"https://www.youtube.com/embed/JXsMpUa8r20\" frameborder=\"0\" allow=\"accelerometer; encrypted-media; gyroscope; picture-in-picture\" allowfullscreen></iframe>\n",
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      "source": [
        "<center>\n",
        "    <img src=\"https://github.com/TUIlmenauAMS/MRSP_Tutorials/blob/master/images/msp_10_01_synthesis.JPG?raw=1\" width=500>\n",
        "</center>"
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      "source": [
        "We still need the find the equivalent synthesis filters, if we apply the inverse transform for the perfect reconstruction of our signal (we get perfect reconstruction, i.e. the original signal, if the transform **T** is invertible).\n",
        "\n",
        "For the mathematical formulation of the inverse transform, we can again write the reconstructed signal $\\hat{x}$ as a sequence of blocks,\n",
        "\n",
        "$$\\large\n",
        "\\hat{x} (m)=[\\hat{x}(mN),\\hat{x}(mN+1), ..., \\hat{x}(mN+N-1)]\n",
        "$$\n",
        "\n",
        "We obtain the reconstructed signal by simply multiplying the blocks of subband samples $y(m)$ with the inverse transform matrix,\n",
        "\n",
        "$$\\large\n",
        "\\begin{equation}\n",
        "\\hat{x} (m) = y(m) \\cdot T^{-1} \\quad (5)\n",
        "\\end{equation}\n",
        "$$\n",
        "\n",
        "The elements of this inverse DFT matrix are:\n",
        "\n",
        "$$\\large\n",
        "\\left( T^{-1}\\right)_{k,n} = \\dfrac{1}{N} \\cdot e^{j \\frac{2\\pi} { N} \\cdot k \\cdot n}\n",
        "$$\n",
        "\n",
        "Eq. (5) can now also be written as (using row times column):\n",
        "\n",
        "$$\\large\n",
        "\\begin{equation}\n",
        "\\hat{x}(mN+n) = \\sum_{k=0}^{N-1} y_k(m) \\cdot \\dfrac{1}{N} \\cdot e^{j \\frac{2\\pi} { N} \\cdot k \\cdot n} \\quad (6)\n",
        "\\end{equation}\n",
        "$$\n",
        "with n=0,...,N-1.\n",
        "\n",
        "To see the resulting impulse response of the equivalent synthesis filter bank, we need the equations for upsampling and filtering in the synthesis filter bank."
      ]
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    {
      "cell_type": "markdown",
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      "source": [
        "In the synthesis filter bank, the subband signals $y_k(m)$ are **upsampled** first, and we obtain the upsampled signal $y_{0,k}^{\\uparrow N}(n)$ with phase 0 and time index *n* because we are at the higher sampling rate.\n",
        "\n",
        "The following filtering is the convolution with the synthesis subband impulse responses $g_k(n)$ , hence we get the\n",
        "output of the k'th filter as:\n",
        "\n",
        "$$\\large\n",
        "\\begin{equation}\n",
        "x_k(n) = y_{0,k}^{\\uparrow N}(n) * g_k(n) = \\sum_{n'=0}^{L-1} y_{0,k}^{\\uparrow N} (n-n')\\cdot g_k(n') \\quad (7)\n",
        "\\end{equation}\n",
        "$$\n",
        "where L is the length of the synthesis filter. We assume that L is a multiple of N, which we can always obtain by appending zeros if necessary.\n",
        "\n",
        "Observe that most samples of $y_{0, k}^{\\uparrow N}(n)$ are zero. To rewrite (7) such that we only process the non-zero samples, we again use the block wise processing, by substituting $ n \\rightarrow mN+n$  and $n'\\rightarrow m' N+n'$ (using block indices m and m' and in block or phase indices n and n') to obtain:\n",
        "\n",
        "$$\\large\n",
        "\\hat{x}(mN+n) = \\sum_{m'=0}^{\\frac{L}{N-1}} \\sum_{n'=0}^{N-1} y_{0, k}^{\\uparrow N} (mN + n - m'N-n') \\cdot g_k(m'N+n')\n",
        "$$\n",
        "with n=0,...,N-1.\n",
        "\n",
        "Here we can see that we get the non-zero elements of $y_{0, k}^{\\uparrow N}(n)$ if its argument is integer multiples of N, and we get this if we have n=n '. Because of this, the inner sum only consists of one summand (because the sum over n' disappears),\n",
        "\n",
        "$$\\large\n",
        "\\hat{x}(mN+n) = \\sum_{m'=0}^{\\frac{L}{N-1}} y_{0,k}^{\\uparrow N} ((m-m')N)\\cdot g_k(m'N+n)\n",
        "$$\n",
        "\n",
        "For the reconstructed signal, we simply **add up** all the N **subbands**,\n",
        "\n",
        "$$\\large\n",
        "\\hat{x}(mN+n) = \\sum_{k=0}^{N-1} \\sum_{m'=0}^{\\frac{L}{N-1}}  y_{0, k}^{\\uparrow N} ((m-m')N)\\cdot g_k(m'N+n)\n",
        "$$\n",
        "\n",
        "Here we can now replace $y_{0,k}^{\\uparrow N}(mN)$ by $y_k{m}$, since we now address only the non-zero elements,\n",
        "\n",
        "$$\\large\n",
        "\\begin{equation}\n",
        "\\hat{x}(mN+n) = \\sum_{k=0}^{N-1} \\sum_{m'=0}^{\\frac{L}{N-1}}  y_k(m-m') \\cdot g_k(m'N+n) \\quad (8)\n",
        "\\end{equation}\n",
        "$$\n",
        "\n",
        "This is now our reconstructed signal, where the first sum is over the subbands, and the second sum is over the blocks."
      ]
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      "source": [
        "At this point, we can compare this filter bank eq. (8) with the synthesis transform eq. (6).\n",
        "\n",
        "$$\\large\n",
        "\\hat{x}(mN+n) = \\sum_{k=0}^{N-1} y_k(m) \\cdot \\dfrac{1}{N} \\cdot e^{j \\frac{2\\pi} { N} \\cdot k \\cdot n} \\quad (6)\n",
        "$$\n",
        "\n",
        "First we see that the transform eq. (6) has no sum over the blocks, meaning the filters only have length <u>L=N</u>, hence the inner sum disappears with <u>m'=0</u>. With this, (8) becomes:\n",
        "\n",
        "$$\\large\n",
        "\\hat{x}(mN+n) = \\sum_{k=0}^{N-1} y_k(m) \\cdot g_k(n)\n",
        "$$\n",
        "\n",
        "Compare this with the transform equation (6), we can see now that the equivalent impulse responses are:\n",
        "\n",
        "$$\\large\n",
        "g_k(n) = \\dfrac{1}{N} \\cdot e^{j \\frac{2\\pi} { N} \\cdot k \\cdot n} = \\left( T^{-1} \\right)_{k,n}\n",
        "$$\n",
        "\n",
        "Looking at our transform matrix, we see that this impulse responses correspond to each row of the inverse transform matrix, non-reversed.\n",
        "\n",
        "**In Conclusion:** the **impulse responses of our subbands are the rows of the synthesis transform matrix,** here **not time reversed!** (We can read out the impulse responses of the synthesis filter bank from left to right in each column of the transform matrix).\n",
        "\n",
        "Observe: Each time we got our result by comparing the convolution sum of our equivalent filter bank with the transform sum."
      ]
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      "source": [
        "## Python Example"
      ]
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        "id": "F38CjcV4vgh7"
      },
      "source": [
        "Take a DFT of size N=4 . Its transform matrix T can be obtained with"
      ]
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        "%%html\n",
        "<center>\n",
        "<iframe width=\"560\" height=\"315\" src=\"https://www.youtube.com/embed/--B_ms6Sph4\" frameborder=\"0\" allow=\"accelerometer; encrypted-media; gyroscope; picture-in-picture\" allowfullscreen></iframe>\n",
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      "execution_count": 1,
      "metadata": {
        "id": "xs8UbFievgh9"
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      "outputs": [],
      "source": [
        "from numpy import fft, eye"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 5,
      "metadata": {
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        "colab": {
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          "text": [
            "eye=\n",
            " [[1. 0. 0. 0.]\n",
            " [0. 1. 0. 0.]\n",
            " [0. 0. 1. 0.]\n",
            " [0. 0. 0. 1.]]\n",
            "T=\n",
            " [[ 1.+0.j  1.+0.j  1.+0.j  1.+0.j]\n",
            " [ 1.+0.j  0.-1.j -1.+0.j  0.+1.j]\n",
            " [ 1.+0.j -1.+0.j  1.+0.j -1.+0.j]\n",
            " [ 1.+0.j  0.+1.j -1.+0.j  0.-1.j]]\n"
          ]
        }
      ],
      "source": [
        "print(\"eye=\\n\",eye(4))\n",
        "T=fft.fft(eye(4))\n",
        "print(\"T=\\n\",T)"
      ]
    },
    {
      "cell_type": "markdown",
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      },
      "source": [
        "Observe that we have complex values in the transform, and hence obtain complex valued filters. To evaluate complex valued filters, we need the full circle in the frequency domain, from 0 to $2\\pi$.\n",
        "\n",
        "If we want to obtain the frequency response of subband k=1 of this DFT filter bank, we take the second column, time-reverse it, and plot the frequency response with freqz."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 6,
      "metadata": {
        "id": "3-HFVJgKvgh_"
      },
      "outputs": [],
      "source": [
        "import scipy.signal as sp\n",
        "import matplotlib.pyplot as plt\n",
        "import numpy as np"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 7,
      "metadata": {
        "id": "F-zrqt7GvgiA",
        "outputId": "679d9d89-a770-432b-82fb-5142673aa9e5",
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          "base_uri": "https://localhost:8080/",
          "height": 718
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      "outputs": [
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            "text/plain": [
              "<Figure size 1000x800 with 1 Axes>"
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\n"
          },
          "metadata": {}
        }
      ],
      "source": [
        "W,H=sp.freqz(np.flipud(T[:,1]),whole=True)\n",
        "H[H == 0] = np.finfo(float).eps\n",
        "\n",
        "plt.figure(figsize=(10,8))\n",
        "plt.plot(W, 20*np.log10(abs(H)))\n",
        "plt.axis([0,6.28, -20,15])\n",
        "plt.xlabel('Normalized Frequency')\n",
        "plt.ylabel('dB')\n",
        "plt.title('Magnitude Response for DFT suband k=1');\n",
        "plt.grid()"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "CypMdOFwvgiG"
      },
      "source": [
        "**Observe:** We have a bad stopband attenuation (less than 20dB).\n",
        "Also **observe:** The frequency axis is going from **0 to $2\\pi$** (instead of just pi). This is because we have a **complex** impulse response. The normalized frequency $2\\pi$ is the sampling frequency.\n",
        "\n",
        "Since we have a $2\\pi$ periodic frequency, this is identical to frequency 0, and the **frequencies from $\\pi$ to $2\\pi$** can also be seen as the **negative frequencies from $-\\pi$ to 0.** This shows that this filter has a **pass band at the positive frequencies, but not at the negative frequencies.**\n",
        "\n",
        "The equivalent passband at the negative frequencies is obtained from subband k=3,"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 8,
      "metadata": {
        "id": "GaRgiI1NvgiJ",
        "outputId": "692f309c-f690-4f3b-e9ca-8462afc34370",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 718
        }
      },
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 1000x800 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ],
      "source": [
        "W,H=sp.freqz(np.flipud(T[:,3]),whole=True)\n",
        "H[H == 0] = np.finfo(float).eps\n",
        "\n",
        "plt.figure(figsize=(10,8))\n",
        "plt.plot(W, 20*np.log10(abs(H)))\n",
        "plt.axis([0,6.28, -20,15])\n",
        "plt.xlabel('Normalized Frequency')\n",
        "plt.ylabel('dB')\n",
        "plt.title('Magnitude Response for DFT suband k=3');\n",
        "plt.grid()"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "wU4rg7TWvgiK"
      },
      "source": [
        "**Observe:** This looks like the frequency mirrored version of the filter for k=1. This also shows how to separate positive and negative frequencies.\n",
        "\n",
        "The **low pass is at k=0**, and the **high pass appears at k=2.** Observe that here the high pass appears in the middle, because of this symmetry between positive and negative frequencies."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "3eyr0IpQvgiK"
      },
      "source": [
        "## Example Transform as Filter Bank:"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Y5K_GhEQvgiM"
      },
      "source": [
        "Now we show in an example that the **transform is** indeed a special case of **a critically sampled filter bank** with the above computed filters.\n",
        "\n",
        "Take the example signal of length 8:"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "hide_input": true,
        "id": "aPpYIspqvgiM",
        "outputId": "d68288ab-fbaa-4ef3-e046-a92ad5ac476f"
      },
      "outputs": [
        {
          "data": {
            "text/html": [
              "<center>\n",
              "<iframe width=\"560\" height=\"315\" src=\"https://www.youtube.com/embed/znEpH7ebWac\" frameborder=\"0\" allow=\"accelerometer; encrypted-media; gyroscope; picture-in-picture\" allowfullscreen></iframe>\n",
              "</center>\n"
            ],
            "text/plain": [
              "<IPython.core.display.HTML object>"
            ]
          },
          "metadata": {},
          "output_type": "display_data"
        }
      ],
      "source": [
        "%%html\n",
        "<center>\n",
        "<iframe width=\"560\" height=\"315\" src=\"https://www.youtube.com/embed/znEpH7ebWac\" frameborder=\"0\" allow=\"accelerometer; encrypted-media; gyroscope; picture-in-picture\" allowfullscreen></iframe>\n",
        "</center>"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 9,
      "metadata": {
        "id": "co2-nO6TvgiN",
        "outputId": "35bffae4-c40a-4f74-e184-94e2fea7506c",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([ 0.00000000e+00,  7.07106781e-01,  1.00000000e+00,  7.07106781e-01,\n",
              "        1.22464680e-16, -7.07106781e-01, -1.00000000e+00, -7.07106781e-01])"
            ]
          },
          "metadata": {},
          "execution_count": 9
        }
      ],
      "source": [
        "x=np.sin(2*np.pi/8*1*np.arange(8))\n",
        "x"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "V4CMpsDJvgiO"
      },
      "source": [
        "and its decomposition into blocks of length 4:"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 10,
      "metadata": {
        "id": "B-ZQScHVvgiP",
        "outputId": "7901214d-d0d4-42c4-a2f4-2f9a36aa7c6b",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[ 0.00000000e+00,  7.07106781e-01,  1.00000000e+00,\n",
              "         7.07106781e-01],\n",
              "       [ 1.22464680e-16, -7.07106781e-01, -1.00000000e+00,\n",
              "        -7.07106781e-01]])"
            ]
          },
          "metadata": {},
          "execution_count": 10
        }
      ],
      "source": [
        "xm=np.zeros((2,4))\n",
        "xm[0,:]=x[0:4]\n",
        "xm[1,:]=x[4:8]\n",
        "xm"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "UUj1uNxrvgiR"
      },
      "source": [
        "Again we obtain our DFT **transform matrix** as"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 11,
      "metadata": {
        "id": "ptOmKNdYvgiS",
        "outputId": "faffd0d4-4c60-439f-8094-462461e519a4",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[ 1.+0.j,  1.+0.j,  1.+0.j,  1.+0.j],\n",
              "       [ 1.+0.j,  0.-1.j, -1.+0.j,  0.+1.j],\n",
              "       [ 1.+0.j, -1.+0.j,  1.+0.j, -1.+0.j],\n",
              "       [ 1.+0.j,  0.+1.j, -1.+0.j,  0.-1.j]])"
            ]
          },
          "metadata": {},
          "execution_count": 11
        }
      ],
      "source": [
        "T=fft.fft(eye(4))\n",
        "T"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "5JqihP9xvgiT"
      },
      "source": [
        "We obtain the **transformed blocks** with"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 12,
      "metadata": {
        "id": "9EYylS81vgiT",
        "outputId": "9da1c5f1-1b1a-4872-f69c-120817bc932f",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[ 2.41421356+0.00000000e+00j, -1.        +1.11022302e-16j,\n",
              "        -0.41421356+0.00000000e+00j, -1.        -1.11022302e-16j],\n",
              "       [-2.41421356+0.00000000e+00j,  1.        -2.22044605e-16j,\n",
              "         0.41421356+0.00000000e+00j,  1.        +2.22044605e-16j]])"
            ]
          },
          "metadata": {},
          "execution_count": 12
        }
      ],
      "source": [
        "yt=np.dot(xm,T)\n",
        "yt"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "c4UXA3cRvgia"
      },
      "source": [
        "Here, **each row** contains the **spectrum** of each corresponding block.\n",
        "\n",
        "Now we process the input signal x through a **critically sampled filter bank** with the **equivalent filter impulse responses,** the transform matrix columns, flipped up-down, and down-sampled with the last phase of the blocks, $n_0=N−1=3$ (as it appeared in our derivation of the equivalent impulse responses),"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 13,
      "metadata": {
        "id": "FGpHWCN5vgib",
        "outputId": "c9055905-a23d-46bb-9551-2501b295004b",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[ 2.41421356+0.00000000e+00j, -1.        +1.11022302e-16j,\n",
              "        -0.41421356+0.00000000e+00j, -1.        -1.11022302e-16j],\n",
              "       [-2.41421356+0.00000000e+00j,  1.        -2.22044605e-16j,\n",
              "         0.41421356+0.00000000e+00j,  1.        +2.22044605e-16j]])"
            ]
          },
          "metadata": {},
          "execution_count": 13
        }
      ],
      "source": [
        "y=np.zeros((2,4))*1j\n",
        "for k in range(4):\n",
        "    y[:,k]=sp.lfilter(np.flipud(T[:,k]),1,x)[3::4] #first index: n_0=N-1=3, last index: downsampling factor N=4\n",
        "y"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "6E-dApwhvgic"
      },
      "source": [
        "Compare with the transform output yt.\n",
        "\n",
        "We can see that yt from the **transform** and y from the critically sampled **filter bank** are indeed the **same!**\n",
        "\n",
        "**In conclusion:** We see that a **transform** is a **special case** of a **filter bank.** The tool of reading out the impulse responses from a transform matrix allows us to **analyze the resulting filters**, and to judge if they fulfill our requirements."
      ]
    }
  ],
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