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\[\newcommand{\IC}{{\mathbb{C}}} % set of complex numbers \newcommand{\IN}{{\mathbb{N}}} % set of natural numbers \newcommand{\IR}{{\mathbb{R}}} % set of real numbers \newcommand{\IZ}{{\mathbb{Z}}} % set of integers \newcommand{\jj}{{\mathbb{j}}} % imaginary unit \newcommand{\e}{\operatorname{e}} % Euler's number \newcommand{\dd}{\operatorname{d}} % infinitesimal operator \newcommand{\abs}[1]{\left|#1\right|} % absolute value \newcommand{\conj}[1]{\overline{#1}} % complex conjugate \newcommand{\conjT}[1]{\overline{#1^T}} % transposed complex conjugate \newcommand{\inv}[1]{\left(#1\right)^{\!-1}} % inverse \newcommand{\rect}{\operatorname{rect}} % rect or boxcar function \newcommand{\sinc}{\operatorname{sinc}} % sinc(t) := sin(pi*t) / (pi*t) % overwrite macros: \renewcommand{\Re}{\operatorname{Re}} % real part of a complex number \renewcommand{\Im}{\operatorname{Im}} % imaginary part of a complex number % Since the physics package is not loaded, we define the macros ourselves: \newcommand{\vb}[1]{\mathbf{#1}} % vectors are bold \newcommand{\mat}[1]{\mathrm{#1}} % matrices are upright % % Abbreviations of matrices and vectors : \newcommand{\mF}{\mat{F}} % matrix with DFT coefficients \newcommand{\mI}{\mat{I}} % unity matrix\]