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A modified frequency-domain block adaptive quantizer (BAQ) is proposed for simultaneous sample-rate reduction and compression. Owing to practical hardware accelerators of fast Fourier transform (FFT) having sizes usually in powers of some simple primes, the influence on frequency-domain data compression caused by the trailing portion that follows echo signals to the FFT accelerator is first discussed. Then, both sample-rate reduction and compression are considered in frequency domain. Instead of zero padding, cyclic extension is employed for reserving the spectrum property of echo signals. Hamming windowing is applied on the cyclic extension for suppressing the sidelobe leakage. Furthermore, the distorted and noisy trailing portion can be discarded when the decompressed signal is transformed back to the time domain. From simulation results, the proposed approach achieves better signal-to-quantization noise ratio (SQNR) and smaller compressed data quantity than the conventional time-domain BAQ with anti-aliasing filter and conventional frequency-domain BAQ when sample-rate reduction is required.