Signal processing and Information theory are two disparate fields used for characterizing signals for various scientific and engineering applications. Spectral/Fourier analysis, a technique employed in signal processing, helps estimation of power at different frequency components present in the signal. Characterizing a time-series based on its average amount of information (Shannon entropy) is useful for estimating its complexity and compressibility (eg., for communication applications). Information theory doesn't deal with spectral content while signal processing doesn't directly consider the information content or compressibility of the signal. In this work, we attempt to bring the fields of signal processing and information theory together by using a lossless data compression algorithm to estimate the amount of information or `compressibility' of time series at different scales. To this end, we employ the Effort-to-Compress (ETC) algorithm to obtain what we call as a Compression Spectrum. This new tool for signal analysis is demonstrated on synthetically generated periodic signals, a sinusoid, chaotic signals (weak and strong chaos) and uniform random noise. The Compression Spectrum is applied on heart interbeat intervals (RR) obtained from real-world normal young and elderly subjects. The compression spectrum of healthy young RR tachograms in the log-log scale shows behaviour similar to $1/f$ noise whereas the healthy old RR tachograms show a different behaviour. We envisage exciting possibilities and future applications of the Compression Spectrum.

翻译：信号处理与信息论是描述信号特征的两大不同领域，广泛应用于各类科学与工程场景。谱分析/傅里叶分析作为信号处理的核心技术，可估算信号中不同频率分量的功率。基于信号平均信息量（香农熵）对时间序列进行表征，有助于评估其复杂性与可压缩性（例如通信应用领域）。信息论不涉及频谱内容，而信号处理也未直接考虑信号的信息含量或可压缩性。本研究尝试通过无损数据压缩算法，将信号处理与信息论两个领域相融合，以估算时间序列在不同尺度下的信息量或“可压缩性”。为此，我们采用“压缩努力度”（ETC）算法，构建出所谓的“压缩谱”。这一新型信号分析工具已在合成生成周期信号（正弦波）、混沌信号（弱混沌与强混沌）及均匀随机噪声中得以验证。我们将压缩谱应用于实际采集的年轻健康受试者与老年健康受试者的心搏间期（RR）数据。在双对数坐标下，健康年轻人RR心动图的压缩谱展现出类似$1/f$噪声的特征，而健康老年人的RR心动图则呈现出不同行为。我们预期压缩谱将激发更多富有前景的研究方向与未来应用。