RealTime Analog TimeFrequency Signal Analysis The shorttime Fourier transform (STFT), or spectrogram (SP), is a very powerful joint timefrequency signal analysis tool of importance for a wide range of applications, including information processing and communications based on radiofrequency (RF), terahertz or optical waves etc. Depending on the signal complexity and speed, an SP analysis may require significant, eventually unpractical, computational resources. This represents a crucial limitation for application of SPbased signal processing to the wide range of problems that involve highspeed (broadband) temporal waveforms. We report on a universal approach to obtain the STFT of an arbitrary continuous waveform purely in real time, avoiding computationally intensive fast Fourier transforms. This approach performs a direct mapping of the waveform STFT along the time axis, directly in the analog physical wave domain, using a simple and efficient scheme based on temporal sampling and dispersive delay. We present here a detailed theoretical study of the timemapped STFT scheme, including a formal derivation of its main design conditions and tradeoffs. Numerical simulations of a realistic photonic platform are also presented that validate the proposed principle and predicted performance for application on highspeed (e.g., RF or optical) waveforms.

Spectrum Activity Estimation by Partitionblind Block Partitioned Tensor Decomposition We consider a scenario where signals that can be modeled as finite sums of linearly modulated signals that are nonorthogonal in both time and frequency are observed by a sensor. Under this model, when an antidiagonal slice of the trispectum of the sum of these signals is computed for multiple segments in time and stacked into a frontal symmetric block partitioned tensor (FSBPT) whose factor matrices characterize the received power spectrum and transmission activities of the signals. We propose a new alternating soft thresholding decomposition strategy that is tailored to FSBPTs and, unlike existing BPT decomposition algorithms, simultaneously estimates the factor partitions which is necessary since in our signal model the partitioning is not known a priori. We demonstrate the algorithmxe2x80x99s performance via Monte Carlo simulations. We find that our proposed nonblind algorithm is able to estimate the tensor partitions and moderately accurately estimate the factor matrices under a range of factor matrix column collinearity values.