Current medical practice of long-term chronic respiratory diseases treatment lacks a convenient method of empowering the patients and caregivers to continuously quantitatively track the intensity of respiratory symptoms. Such is "asthmatic wheezing", occurring in respiratory sounds. We envision a mobile, personalized asthma monitoring system comprising of a wearable, energy-constrained acoustic sensor and smartphone. In this article we address the energy-burden of acquisition and streaming of acoustic respiratory signal, and lessen it by applying the concept of compressed sensing (CS). First we analyse the adherence of normal and pathologic respiratory sounds frequency representations (DFT, DCT) to the sparse signal model. Given the pseudo-random non-uniform subsampling encoder implemented on MSP430 microcontroller, we review tradeoffs of accuracy and execution time of different CS algorithms, suitable for realtime respiratory spectrum recovery on smartphone. Working CS respiratory spectrum acquisition prototype is demonstrated, and evaluated. Prototype enables for real-time reconstruction of spectra dominated by approximately 8 frequency components with more than 80% accuracy, on Android smartphone using OMP algorithm, from only 25% signal samples (w.r.t. Nyquist rate) acquired and streamed by sensor at 8 kbit/s. Index Terms-M-health, asthmatic wheezing, compressive sensing, non-uniform sampling, orthogonal matching pursuit.1530-437X (c)