In recent years, target recognition technology for synthetic aperture radar (SAR) images has witnessed significant advancements, particularly with the development of convolutional neural networks (CNNs). However, acquiring SAR images requires significant resources, both in terms of time and cost. Moreover, due to the inherent properties of radar sensors, SAR images are often marred by speckle noise, a form of high-frequency noise. To address this issue, we introduce a Generative Adversarial Network (GAN) with a dual discriminator and high-frequency pass filter, named DH-GAN, specifically designed for generating simulated images. DH-GAN produces images that emulate the high-frequency characteristics of real SAR images. Through power spectral density (PSD) analysis and experiments, we demonstrate the validity of the DH-GAN approach. The experimental results show that not only do the SAR image generated using DH-GAN closely resemble the high-frequency component of real SAR images, but the proficiency of CNNs in target recognition, when trained with these simulated images, is also notably enhanced.