In many Digital Signal Processing (DSP) applications such as Viterbi decoder and Fast Fourier Transform (FFT), Static Random Access Memory (SRAM) based embedded memory consumes significant portion of area and power. These DSP units are dominated by sequential memory access where SRAM-based memory is inefficient in terms of area and power. We propose spintronic Domain Wall Memory (DWM) based embedded memories for DSP building blocks e.g., survivor-path memories in Viterbi decoder and First-In-First-Out (FIFO) register files in FFT processor that exploit the unique serial access mechanism, non-volatility and small footprint of the memory for area and power saving. Simulations using 65nm technology show that the DWM based Viterbi decoder achieves 66.4 % area and 59.6 % power savings over the conventional SRAM-based implementation. For 8K point FFT processor, the DWM based design shows 60.6 % area and 60.3 % power savings.