Typical methods for signal analysis utilize the Fourier Transform based algorithms to estimate the spectral response of a signal. This current practice suffers from poor frequency resolution when estimating non stationary signals. This paper describes some alternative methods based on time frequency distributions from a Cohen class point of view. Four distribution cases are evaluated: Wigner Ville, Choi Williams, Bessel and Born Jordan. Continuous and discrete distributions are presented for each case. Simplified discretised expressions for the implementation of distributions are formulated, these leading to a reduction of the computations realized when comparing to original definitions. Also, two parallel approaches (intrinsic parallelism and data parallelism) for the computation of the distributions are proposed, implemented and assessed by using a parallel DSP based system. Finally, a further simplification by truncating the simplified expressions is proposed; this truncation is restricted by the error in spectral estimations. Results are applied to the development of a real time spectrum analyzer for Doppler blood flow instrumentation.