Learnable Linear Phase FIR Filter Designs Using a Generative Adversarial Network

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This paper proposes a new design technique to make trainable / learnable linear phase FIR (Finite Impulse Response) filters using a GAN (generative adversarial network). Instead of random noise for conventional GANs, the new FIR filter design uses an ideal LPF in time domain (i.e., sinc function) as an input to the GAN. With the ideal LPF in time, a learnable window function is trained by the GAN to make a close frequency response to a desired filter. The GAN includes also a symmetric extension to satisfy a linear phase constraint. The proposed design for learnable linear phase FIR filters is accomplished by two competing objects, generator and discriminator, in the GAN. It will be shown in this paper that the new technique can be applied to design various FIR filters such as LPFs (low pass filters), HPFs (high pass filters), BPFs (band pass filters), and BSFs (band stop filters) for any given arbitrary cutoff frequencies. Obtained window by training the GAN shows periodic deep valleys/ hills in a similar window shape for traditional FIR filter designs. Comparing with conventional approximate solutions to design such FIR filters, the proposed technique leads to a data-driven learnable filter design. The proposed filter design can be embedded to other DNNs requiring learnable filters and be jointly trained/ adjusted with other DNN parameters given by diverse loss or objective functions depending on applications.