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 paper, 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 (discrete Fourier transform and discrete cosine transform) 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 real-time 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 eight frequency components with more than 80% accuracy, on Android smartphone using Orthogonal Matching Pursuit algorithm, from only 25% signal samples (with respect to Nyquist rate) acquired and streamed by sensor at 8 kb/s.