  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.
