This paper presents a novel approach for signal reconstruction using Spiking Neural Networks (SNN) based on the principles of Cognitive Informatics and Cognitive Computing. The proposed SNN leverages the Discrete Fourier Transform (DFT) to represent and reconstruct arbitrary time series signals. By employing N spiking neurons, the SNN captures the frequency components of the input signal, with each neuron assigned a unique frequency. The relationship between the magnitude and phase of the spiking neurons and the DFT coefficients is explored, enabling the reconstruction of the original signal. Additionally, the paper discusses the encoding of impulse delays and the phase differences between adjacent frequency components. This research contributes to the field of signal processing and provides insights into the application of SNN for cognitive signal analysis and reconstruction.