Design of Low-Complexity IFRM-UMFB Architecture for Wideband Digital Receivers

Abstract

Modulated filter bank with low complexity is the key to realize the engineering applications for speech signal processing, multicarrier communication, and wideband digital receivers. The frequency response masking (FRM) technology is an effective method to design finite impulse response filters with narrow transition band (NTB). In this paper, an interpolation FRM unified modulated filter bank (IFRM-UMFB) architecture with NTB is proposed to reduce the computational complexity of the modulated filter bank architecture. The IFRM approach increases the transition band of two masking filters by the interpolation of N and reduces the computational complexity of two masking filters compared with classic FRM approach. The proposed IFRM-UMFB architecture with NTB is suitable for different odd-stacked or even-stacked, maximally decimated or non-maximally decimated structures. The proposed IFRM-UMFB architecture with NTB is verified to be correct through simulation. The complexity comparison result shows that the proposed IFRM-UMFB architecture offers multipliers reduction of 77.4% over the directly design approach and 26.5% over the classic FRM approach. Moreover, the proposed IFRM-UMFB architecture with NTB also can be directly applied to wideband digital receivers with high sampling rate.

The constraint condition in Fig. 4

In Fig. 4, the range of $\omega _p$ and $\omega _s$ is as follows

$$\begin{aligned} \frac{2m\pi }{L}<\omega _p<\omega _s <\frac{(2m+1)\pi }{L} \end{aligned}$$

(15)

where m is an integer.

$$\begin{aligned} \omega _p= & {} \frac{\omega _{ap} }{L}+\frac{2m\pi }{L} \end{aligned}$$

(16)

$$\begin{aligned} \omega _s= & {} \frac{\omega _{as} }{L}+\frac{2m\pi }{L} \end{aligned}$$

(17)

The passband and stopband edges of the prototype filter $H_a(z)$ can be written as

$$\begin{aligned} \omega _{ap}= & {} L\omega _p -2m\pi \end{aligned}$$

(18)

$$\begin{aligned} \omega _{as}= & {} L\omega _s -2m\pi \end{aligned}$$

(19)

The passband and stopband edges of the masking filters $H_{Ma}(z)$ and $H_{Mc}(z)$ can be given by

$$\begin{aligned} \omega _{Map}= & {} \frac{2m\pi +\omega _{ap} }{L}N \end{aligned}$$

(20)

$$\begin{aligned} \omega _{Mas}= & {} \frac{2(m+1)\pi -\omega _{as} }{L}N \end{aligned}$$

(21)

$$\begin{aligned} \omega _{Mcp}= & {} \frac{2m\pi -\omega _{ap} }{L}N \end{aligned}$$

(22)

$$\begin{aligned} \omega _{Mcs}= & {} \frac{2m\pi +\omega _{as} }{L}N \end{aligned}$$

(23)

It is noted that the stopband edges of the masking filters $H_{Ma}(z)$ and $H_{Mc}(z)$ are as follows

$$\begin{aligned} \omega _{Mas}= & {} \frac{2(m+1)\pi -\omega _{as} }{L}N<\pi \end{aligned}$$

(24)

$$\begin{aligned} \omega _{Mcs}= & {} \frac{2m\pi +\omega _{as}}{L}N<\pi \end{aligned}$$

(25)

Because N is interpolation factor of the masking filters and $N\ge 1$, we can obtain the range of N as follows

$$\begin{aligned} 1\le N\le \frac{\pi }{\omega _s }-1 \end{aligned}$$

(26)

The passband edge of the filter G(z) is the same to the passband edge of the overall filter H(z). The stopband edge of the filter G(z) is as follows

$$\begin{aligned} \omega _{Gs} \le \frac{2\pi }{N}-\frac{2m\pi +\omega _{as}}{L} \end{aligned}$$

(27)

To reduce the order of the filter G(z), the stopband edge of the filter G(z) should select its maximum value. Therefore, the passband and stopband edges of the filter G(z) can be given by

$$\begin{aligned} \omega _{Gp}= & {} \frac{2m\pi }{L}+\frac{\omega _{ap} }{L}=\frac{\omega _{Map}}{N}=\omega _p \end{aligned}$$

(28)

$$\begin{aligned} \omega _{Gs}= & {} \frac{2\pi }{N}-\frac{2m\pi +\omega _{as}}{L} \end{aligned}$$

(29)