Spectral analysis of nonstationary biological processes such as heart rate variability (HRV) and EEG poses a unique challenge: localized, accurate and interpretable descriptions of both frequency and time are required. By reframing this question in a reduced rank regression setting, we propose a novel approach that produces a low-dimensional and empirical basis that is localized in bands of time and frequency. To estimate this frequency-time basis, we apply penalized reduced rank regression with singular value decomposition to the localized discrete Fourier transform. An adaptive sparse fused lasso penalty is applied to the left and right singular vectors, resulting in low-dimensional measures that are interpretable as localized bands in time and frequency. Asymptotic properties of this method are derived, and it is shown to provide a consistent estimator of the time-varying spectrum. Simulation studies are used to evaluate its performance and its utility in practice in illustrated through the analysis of HRV during sleep.