For $J$-level wavelet encoding, assume that the gradient strength along $x$-axis is $Gx$, the FOV along $x$-axis is $X$ centimeters, and the highest resolution is $N$. According to Eqs. (1)-(3), we combine one set of scaling functions {$\phi \u2212J,k(x)$, $k=0,1,\u2026,N2\u2212J\u22121$} and $J$ sets of wavelets {$\psi \u2212j,k(x)$, $j=1,\u2026J$; $k=0,1,\u2026,N2\u2212J\u22121$} required to shape the excitation profiles. Therefore, ($J+1$) RF pulse profiles $\Phi \u2212J,k$ and {$\Psi \u2212j,k$, $j=1,\u2026,J$} are required to generate $k$-spaces $V\u2212J$ and {$W\u2212j$, $j=1,\u2026J$}, where $\Phi \u2212J,k$ and {$\Psi \u2212j,k$, $j=1,\u2026,J$} are Fourier transforms of $\phi \u2212J,k(x)$ and {$\psi \u2212j,k(x)$, $j=1,\u2026,J$}, respectively. The excited location along $x$-axis is determined by the center carrier frequency of the RF pulse. In order to cover the entire FOV, the fundamental size $\Delta x$ of translation step is $X/N$. According to the Bloch equation, there is a linear mapping of the resonant frequency $\omega x$ of the spins and the spatial location $x$, i.e., $\omega x=\gamma Gxx$, and the fundamental frequency step $\Delta \omega x=\gamma Gx\Delta x$, where $\gamma $ is gyromagnetic ratio (approximately $42.58\u2009\u2009MHz/T$ for hydrogen). For small-flip-angle excitation, the carrier frequencies of each pulse in {$\Phi \u2212J,k$} and {$\Psi \u2212j,k$} are offset by {$k\xb72J\Delta \omega x$} and {$k\xb72j\Delta \omega x$} correspondingly to excite each of the locations {$k\xb72J\Delta x$} and {$k\xb72j\Delta x$}. The duration time $\Delta t$ of pulse {$\Phi \u2212J,k$} is computed by $\Delta t=1/(2J\Delta \omega x)$ and used to compute the half-power width of {$\Phi \u2212J,k$}. For example, in 4-level wavelet encoding (e.g., $J=4$), $Gx=1\u2009\u2009G/cm$, $X=25.6\u2009\u2009cm$, and $N=256$. Five types of pulse profiles, labeled RF-V4, RF-W4, RF-W3, RF-W2 and RF-W1, are required to produce these RF pulses $\Phi \u22124,k$ and {$\Psi \u2212j,k$, $j=1,\u2026,4$}. The fundamental frequency step $\Delta \omega x$ is 426 Hz, and the duration time $\Delta t$ of pulse RF-V4 is approximately 0.15 ms, as shown in Fig. 3. After reconstruction of MR images in the spatial domain, the imaging resolution of 1 mm can be achieved.