Time-frequency analysis plays a crucial role in various fields, including signal processing and feature extraction. In this article, we propose an alternative and innovative method for time-frequency analysis using a biologically inspired spiking neural network (SNN), encompassing both specific spike-continuous-time-neuron (SCTN) based neural architecture and an adaptive learning rule. We aim to efficiently detect frequencies embedded in a given signal for the purpose of feature extraction. To achieve this, we suggest using an SN-based network functioning as a resonator for the detection of specific frequencies. We developed a modified supervised Spike-Timing-Dependent Plasticity (STDP) learning rule to effectively adjust the network parameters. Unlike traditional methods for time-frequency analysis, our approach obviates the need for segmenting the signal into several frames, resulting in a streamlined and more effective frequency analysis process. Simulation results demonstrate the efficiency of the proposed method, showcasing its ability to detect frequencies and  generate a Spikegram akin to the Fast Fourier Transform (FFT) based spectrogram. The proposed approach is applied to analyzing EEG signals demonstrating an accurate correlation to the equivalent FFT transform.