Semantic communication can effectively improve the efficiency of data transmission by extracting the deeper meanings of information, addressing the issue of the rapidly increasing data transmission volumes in the communication industry. Semantic compression is one of the key technologies that determine the performance of semantic communication system. This study investigates semantic compression methods within the semantic communication system and constructs a frequency domain compressed semantic communication system tailored for image classification tasks, and compares it with the compression method based on feature map weights. Experimental results demonstrate that the two semantic compression methods can significantly reduce data transmission volumes while maintaining high classification accuracy. Under the compression ratio of 60% and SNR greater than 0, the difference of classification accuracy before and after semantic compression is within 5%, and the proposed frequency-domain compression method has better anti-noise performance. When SNR is less than 0, the frequency domain compression method has higher classification accuracy.