{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Analysing Lapped Transforms\n", "\n", "[Nils Werner](https://www.audiolabs-erlangen.de/fau/assistant/werner) and [Bernd Edler](https://www.audiolabs-erlangen.de/fau/professor/edler)\n", "\n", "[International Audio Laboratories Erlangen](https://www.audiolabs-erlangen.de/)" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "import numpy as np\n", "import scipy as sp\n", "import scipy.signal as ss\n", "import scipy.linalg\n", "import skimage.util\n", "import matplotlib.pyplot as plt\n", "import itertools\n", "\n", "from utils import *" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Modified Discrete Cosine Transform\n", "\n", "In this notebook, we will specifically investigate the [MDCT](https://en.wikipedia.org/wiki/Modified_discrete_cosine_transform), which is defined as\n", "\n", "$$\n", "X_k = \\sum_{n=0}^{2N-1} h(n) x_n \\cos \\left[\\frac{\\pi}{N} \\left(n+\\frac{1}{2}-\\frac{N}{2}\\right) \\left(k+\\frac{1}{2}\\right) \\right] \\qquad k \\in 0, \\dots, N-1\n", "$$\n", "\n", "however, looking at this definition, almost none of the unique attributes of the transform are readily visible, i.e.\n", "\n", " - how is this transform related to DCT-IV?\n", " - why is this transform orthogonal?\n", " - why is the choice of window function $h(n)$ important for perfect reconstruction?\n", " - how and when can we exchange $h(n)$?\n", "\n", "### Polyphase Matrices\n", "\n", "If instead we use the polyphase matrix notation as introduced in [2]\n", "\n", "$$\n", "\\mathbf{D} = {\\left(\\cos\\left[\\frac{\\pi}{N}\\left(n + \\frac{1}{2}\\right)\\left(k + \\frac{1}{2}\\right)\\right]\\right)}_{\\substack{n=0,\\dots,N-1 \\\\ k=0,\\dots,N-1}} \\in \\mathbb{R}^{N \\times N}\n", "$$\n", "\n", "$$\n", "\\newcommand\\iddots{\\mathinner{\n", " \\raise1pt{.}\n", " \\raise3pt{.}\n", " \\raise5pt{.}\n", "}}\n", "\\mathbf{F}(z) = \\begin{bmatrix}\n", "& & h\\left(\\frac{1}{2} N - 1\\right)z^{-1} & h\\left(\\frac{1}{2} N\\right)z^{-1} \\\\\n", "& \\iddots & & & \\ddots \\\\\n", "h\\left(0\\right)z^{-1} & & & & & h\\left(N - 1\\right)z^{-1} \\\\\n", "h\\left(N\\right) & & & & & -h\\left(2N - 1\\right) \\\\\n", "& \\ddots & & & \\iddots \\\\\n", "& & h\\left(\\frac{3}{2} N - 1\\right) & -h\\left(\\frac{3}{2} N\\right) \\\\\n", "\\end{bmatrix} \\in \\mathbb{R}{(z)}^{N \\times N}\n", "$$\n", "\n", "transform operations become matrix products (and thus notation becomes simpler)\n", "\n", "$$\n", "\\vec{X}(z) = \\mathbf{D} \\; \\mathbf{F}(z) \\; \\vec{x}(z)\n", "$$\n", "\n", "and we can start to see some of the properties emerge:\n", "\n", " - We can see that the MDCT is actually some pre-permutation between two frames (expressed in $z$-Domain, where $z^{-1}$ references the previous frame), followed by a DCT-IV.\n", " - We see that only if $h(n)$ fulfills some certain conditions (the Princen-Bradley-condition), $\\mathbf{F}(z)$ is orthogonal.\n", " - We can see that (disregarding causality or delay) both $\\mathbf{D}$ and $\\mathbf{F}(z)$ are orthogonal, which means\n", "\n", "$$\n", "\\vec{x}(z) = \\mathbf{F}(z)^{T} \\; \\mathbf{D}^{T} \\; \\vec{X}(z)\n", "$$\n", "\n", "However, these matrices are still a little bit difficult to understand, and are **not suitable for usage in NumPy**." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Representing Polyphase Matrices in NumPy\n", "\n", "We will demonstrate how we can reformulate the previous matrices into blockdiagonal matrices that allow us to inspect the transform using NumPy.\n", "\n", "Note that the definitions of `dct4`, `mdct`, `freq` and `env` are all in `utils.py`. Look at that file for their definitions.\n", "\n", "## Single Frame\n", "\n", "In this section, we will investigate how the MDCT will analyse a single signal frame.\n", "\n", "Note that any lapped transform always requires more than one frame to synthesize the output signal ($\\mathbf{F}(z)^{T}$ always has at least one $z^{-n}$ term with nonzero $n$), this means this single-frame analysis is only useful for learning about basic transform properties. It cannot be used to actually transform signals, or to analyze how two frames interact when being transformed (which is exactly the motivation for this publication [1]).\n", "\n", "### MDCT Folding Behaviour\n", "\n", "Since the MDCT is directly related to the [DCT-IV](https://en.wikipedia.org/wiki/Discrete_cosine_transform#DCT-IV), we can immediately get the folding behaviour of the MDCT by multiplying it with the inverse DCT-IV." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "<Figure size 1296x201.6 with 3 Axes>" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "D = dct4(16)\n", "M = mdct(16) * ss.cosine(32)\n", "P = D.T @ M\n", "\n", "\n", "f, (a, b, c) = plt.subplots(1, 3, figsize=(18, 2.8))\n", "a.imshow(D)\n", "a.set_title(\"DCT-IV $\\mathbf{D}$\")\n", "b.imshow(M)\n", "b.set_title(\"Windowed MDCT $\\mathbf{M}$\")\n", "c.imshow(P)\n", "c.set_title(\"Folding Matrix $\\mathbf{F} = \\mathbf{D}^{-1}\\mathbf{M}$\")\n", "\n", "b.annotate('$z^{-1}$', xy=(6, 8), color='black', backgroundcolor=(1, 1, 1, 0.7), fontsize='xx-large')\n", "b.annotate('$z^{0}$', xy=(23, 8), color='black', backgroundcolor=(1, 1, 1, 0.7), fontsize='xx-large')\n", "\n", "c.annotate('even symmetry', xy=(4, 3), xytext=(5, 9), color='white', arrowprops={'facecolor': 'white', 'shrink': 0.05})\n", "c.annotate('', xy=(11, 3), xytext=(6, 8), arrowprops={'facecolor': 'white', 'shrink': 0.05})\n", "\n", "c.annotate('odd symmetry', xy=(20, 12), xytext=(22, 7), color='white', arrowprops={'facecolor': 'white', 'shrink': 0.05})\n", "c.annotate('', xy=(28, 12), xytext=(23, 8), arrowprops={'facecolor': 'white', 'shrink': 0.05})\n", "\n", "c.annotate('$z^{-1}$', xy=(6, 13), color='white', fontsize='xx-large')\n", "c.annotate('$z^{0}$', xy=(23, 4), color='white', fontsize='xx-large')\n", "\n", "None" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The result is a sparse matrix that immediately reveals the nature of the time domain aliasing introduced by MDCT:\n", "\n", " - The first and last quarter is folded ontop the second and third quarter, respectively\n", " - The first half has an even symmetry (equal sign)\n", " - The second half has an odd symmetry (different sign)\n", "\n", "However, these matrices are **not square**, so no inverse exists and we cannot synthesize a time-domain signal from this.\n", "\n", "## Multiple Frames\n", "\n", "To better understand how two frames interact when transformed using MDCT, we can extend our transform matrices to process more than frame at once:\n", "\n", "A matrix that transforms multiple frames individually is just a blockdiagonal matrix with the individual transforms on the main diagonal. We can very easily construct a block diagonal transform using multiple DCT-IV (Figure 1), then create folding matrix that folds adjacent frames (Figure 2), and create a multiple frame MDCT matrix by multiplying the two matrices (Frame 3).\n", "\n", "In theory, for an infinite signal, this matrix would be infinitely large of course." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "<Figure size 1296x864 with 3 Axes>" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "D = dct4(16)\n", "M = mdct(16) * ss.cosine(32)\n", "P = D.T @ M\n", "\n", "D8 = scipy.linalg.block_diag(*[D] * 8)\n", "tmp = make_twoframe(P, trim=True)\n", "P8 = scipy.linalg.block_diag(np.eye(8), *[tmp] * 7, np.eye(8))\n", "M8 = D8 @ P8\n", "\n", "fig, (a, b, c) = plt.subplots(1, 3, figsize=(18, 12))\n", "a.imshow(D8)\n", "a.set_title(\"Multi-Block DCT-IV $\\mathbf{D}_8$\")\n", "b.imshow(P8)\n", "b.set_title(\"Multi-Block Folding $\\mathbf{P}_8$\")\n", "c.imshow(M8)\n", "c.set_title(\"Multi-Block MDCT $\\mathbf{M}_8 = \\mathbf{D}_8 \\mathbf{P}_8$\")\n", "\n", "a.annotate('One matrix per frame', xy=(40, 40), xytext=(48, 28), color='white', arrowprops={'facecolor': 'white', 'shrink': 0.05})\n", "b.annotate('Folding between two \\n adjacent frames', xy=(48, 48), xytext=(58, 28), color='white', arrowprops={'facecolor': 'white', 'shrink': 0.05})\n", "\n", "None" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Two Frames\n", "\n", "To get a closer look into how two frames interact when transformed using MDCT, we can limit our transform matrices to process two frames at once.\n", "\n", "Basically we are extracting two DCT-IV matrices, and the folding matrix that affects the two.\n", "\n", "It will later turn out that these matrices can also be used to transform an actual real-world signal." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [ { "data": { "image/png": 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"text/plain": [ "<Figure size 1296x864 with 6 Axes>" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "D = dct4(16)\n", "M = mdct(16) * ss.cosine(32)\n", "P = D.T @ M\n", "\n", "D2 = scipy.linalg.block_diag(D, D)\n", "P2 = make_twoframe(P)\n", "M2 = D2 @ P2\n", "\n", "\n", "fig, ((a, b, c), (d, e, f)) = plt.subplots(2, 3, figsize=(18, 12))\n", "a.imshow(D2)\n", "a.set_title(\"Two-Block DCT-IV $\\mathbf{D}_2$\")\n", "b.imshow(P2)\n", "b.set_title(\"Two-Block Folding $\\mathbf{P}_2$\")\n", "c.imshow(M2)\n", "c.set_title(\"Two-Block MDCT $\\mathbf{M}_2 = \\mathbf{D}_2 \\mathbf{P}_2$\")\n", "d.imshow(freq(M2))\n", "d.set_title(\"Frequency Response\")\n", "e.imshow(env(M2))\n", "e.set_title(\"Impulse Response Envelope\")\n", "f.set_visible(False)\n", "\n", "a.annotate('no overlap', xy=(18, 6), xytext=(22, 2), color='white', arrowprops={'facecolor': 'white', 'shrink': 0.05})\n", "a.annotate('no overlap', xy=(12, 22), xytext=(1, 26), color='white', arrowprops={'facecolor': 'white', 'shrink': 0.05})\n", "c.annotate('overlap', xy=(18, 6), xytext=(22, 2), color='white', arrowprops={'facecolor': 'white', 'shrink': 0.05})\n", "c.annotate('overlap', xy=(12, 22), xytext=(1, 26), color='white', arrowprops={'facecolor': 'white', 'shrink': 0.05})\n", "\n", "d.annotate('uniform frequency response', xy=(12, 6), xytext=(16, 2), color='white', arrowprops={'facecolor': 'white', 'shrink': 0.05})\n", "e.annotate('uniform impulse response', xy=(8, 6), xytext=(12, 2), color='white', arrowprops={'facecolor': 'white', 'shrink': 0.05})\n", "\n", "None" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "In the last two plots we can easily observe two critical properties of the transform:\n", " \n", " 1. Each filter in each frame has a distinct frequency response center, and they're all of same width\n", " 1. The impulse responses in each frame are roughly in the same position, and they're all of same width\n", " \n", "In other words: This filterbank is **uniform**." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Invertibility\n", "\n", "One crucial attribute of the MDCT is orthogonality and perfect reconstruction. Using the matrices we have created so far, we can also verify this property. For a few selected windows (rectangular, Kaiser-Bessel-derived, or cosine), this matrix is orthogonal, and for an incompatible window (i.e. Hann), it is not." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "<Figure size 1296x864 with 6 Axes>" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "iM = mdct(16) * ss.hann(32)\n", "iP = D.T @ iM\n", "\n", "iP2 = make_twoframe(iP)\n", "iM2 = D2 @ iP2\n", "\n", "\n", "fig, ((a, b, c), (d, e, f)) = plt.subplots(2, 3, figsize=(18, 12))\n", "a.imshow(P2)\n", "a.set_title(\"Two-Block Folding $\\mathbf{P}_2$, Cosine Window\")\n", "b.imshow(P2.T)\n", "b.set_title(\"Inverse Two-Block Folding $\\mathbf{P}_2^{-1}$, Cosine Window\")\n", "c.imshow(P2.T @ P2)\n", "c.set_title(\"Cancelled Two-Block Folding $\\mathbf{P}^{-1}_2 \\mathbf{P}_2$, Cosine Window\")\n", "\n", "d.imshow(iP2)\n", "d.set_title(\"Two-Block Folding $\\mathbf{P}_2$, Hann Window\")\n", "e.imshow(iP2.T)\n", "e.set_title(\"Inverse Two-Block Folding $\\mathbf{P}_2^{-1}$, Hann Window\")\n", "f.imshow(iP2.T @ iP2)\n", "f.set_title(\"Cancelled Two-Block Folding $\\mathbf{P}^{-1}_2 \\mathbf{P}_2$, Hann Window\")\n", "\n", "a.annotate('overlap/aliasing', xy=(19, 12), xytext=(21, 8), color='white', arrowprops={'facecolor': 'white', 'shrink': 0.05})\n", "a.annotate('overlap/aliasing', xy=(12, 19), xytext=(1, 24), color='white', arrowprops={'facecolor': 'white', 'shrink': 0.05})\n", "\n", "b.annotate('aliasing cancelling', xy=(19, 12), xytext=(21, 8), color='white', arrowprops={'facecolor': 'white', 'shrink': 0.05})\n", "b.annotate('aliasing cancelling', xy=(12, 19), xytext=(1, 24), color='white', arrowprops={'facecolor': 'white', 'shrink': 0.05})\n", "\n", "c.annotate('identity matrix', xy=(16, 16), xytext=(5, 20), color='white', arrowprops={'facecolor': 'white', 'shrink': 0.05})\n", "f.annotate('residual error', xy=(16, 16), xytext=(5, 20), color='white', arrowprops={'facecolor': 'white', 'shrink': 0.05})\n", "\n", "\n", "None" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Nonuniform Transforms\n", "\n", "Cascaded filterbanks to generate non-uniform orthogonal transforms [4,5] can be easily implemented and analysed, too. In this framework, Subband Merging is yet another matrix with transforms on the main diagonal.\n", "\n", "Because we are inspecting more than one frame at once, we can, in theory, also design and investigate lapped or aliasing-reduced subband merging as introduced in [6]. For simplicity sake these will be skipped here, however." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [ { "data": { "image/png": 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"text/plain": [ "<Figure size 1296x864 with 6 Axes>" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "mfs = np.array([8, 4, 4])\n", "S = scipy.linalg.block_diag(*([dct4(m) for m in mfs] * 2))\n", "\n", "\n", "fig, ((a, b, c), (d, e, f)) = plt.subplots(2, 3, figsize=(18, 12))\n", "a.imshow(M2)\n", "a.set_title(\"Two-Block MDCT $\\mathbf{M}_2$\")\n", "b.imshow(S)\n", "b.set_title(\"Subband Merging Matrix $\\mathbf{S}$\")\n", "c.imshow(S @ M2)\n", "c.set_title(\"Cascaded Transform $\\mathbf{S} \\mathbf{M}_2$\")\n", "d.imshow(freq(S @ M2))\n", "d.set_title(\"Merged Frequency Response\")\n", "e.imshow(env(S @ M2))\n", "e.set_title(\"Merged Impulse Response Envelope\")\n", "f.set_visible(False)\n", "\n", "b.annotate('applied to first frame', xy=(6, 6), xytext=(10, 2), color='white', arrowprops={'facecolor': 'white', 'shrink': 0.05})\n", "b.annotate('applied to second frame', xy=(22, 22), xytext=(2, 26), color='white', arrowprops={'facecolor': 'white', 'shrink': 0.05})\n", "\n", "c.annotate('aliasing', xy=(18, 6), xytext=(22, 2), color='white', arrowprops={'facecolor': 'white', 'shrink': 0.05})\n", "c.annotate('aliasing', xy=(12, 18), xytext=(1, 22), color='white', arrowprops={'facecolor': 'white', 'shrink': 0.05})\n", "\n", "d.annotate('non-uniform \\nfrequency response', xy=(8, 3), xytext=(20, 3), color='white', arrowprops={'facecolor': 'white', 'shrink': 0.05})\n", "d.annotate('', xy=(20, 10), xytext=(20, 3), arrowprops={'facecolor': 'white', 'shrink': 0.05})\n", "\n", "e.annotate('non-uniform \\nimpulse response', xy=(8, 3), xytext=(20, 3), color='white', arrowprops={'facecolor': 'white', 'shrink': 0.05})\n", "e.annotate('', xy=(8, 10), xytext=(20, 3), arrowprops={'facecolor': 'white', 'shrink': 0.05})\n", "\n", "None" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "In the last two plots we can observe two new properties of the transform:\n", " \n", " 1. In each frame, more than one filter share about the same frequency response center, the're much wider, and they're of different widths (proportional to the merge factor in this band)\n", " 1. In each frame, the impulse responses are now in new positions, the're much more narrow, and they're of different widths (proportional to the merge factor in this band)\n", " \n", "In other words: This transform is **non-uniform**\n", "\n", "What we can also see in subplots 3 and 4 is a significant amount of **aliasing**. The method introduced in [3] can be used to cancel this aliasing. Again, this method can be implemented as a square polyphase matrix." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# References\n", "\n", " 1. Werner, Nils and Edler, Bernd, \"[Experimenting with Lapped Transforms in Numerical Computation Libraries using Polyphase Matrices and Strided Memory Views](http://www.aes.org/e-lib/browse.cfm?elib=20381)\". Audio Engineering Society Convention 146, 2019\n", " 1. Schuller, G. D. T. and Smith, M. J. T., \"[New framework for modulated perfect reconstruction filter banks](https://ieeexplore.ieee.org/document/533715)\". IEEE Transactions on Signal Processing, 44(8), pp. 1941–1954, 1996, ISSN 1053-587X, doi:10.1109/78.533715.\n", " 1. Werner, Nils and Edler, Bernd, \"[Nonuniform Orthogonal Filterbanks Based on MDCT Analysis/Synthesis and Time-Domain Aliasing Reduction](ieeexplore.ieee.org/document/7870593/)\". IEEE Signal Processing Letters, 24(5): 589–593, 2017.\n", " 1. H. S. Malvar, \"[Biorthogonal and nonuniform lapped transforms for transform coding with reduced blocking and ringing artifacts](https://ieeexplore.ieee.org/document/668555)\", IEEE Transactions on Signal Processing, Bd. 46, Nr. 4, S. 1043–1053, Apr. 1998.\n", " 1. O. A. Niamut und R. Heusdens, \"[Subband merging in cosine-modulated filter banks](https://ieeexplore.ieee.org/document/1186767)\", IEEE Signal Processing Letters, Bd. 10, Nr. 4, S. 111–114, Apr. 2003." ] } ], "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", "version": "3.7.2" } }, "nbformat": 4, "nbformat_minor": 2 }