The Goertzel algorithm is one of the turns in digital signal processing that efficiently detects specific frequency components of a signal. In contrast to methods such as the Fast Fourier Transform, which examines all the frequencies, the Goertzel algorithm is applied to the selection of single frequencies or a few of them for analysis hence, in situations where resources are limited, this method becomes very useful. This abstract considers the operational principles of the algorithm, which basically contains two major phases: processing and evaluation. During the processing phase, the algorithm works as a kind of digital filter, ringing on the target frequency at the same time, the evaluation phase calculates the magnitude of this frequency component. Because of computational efficiency and simplicity, the Goertzel algorithm is applied perfectly in real-time systems, especially in systems with limited processing power. An especially notable application of the Goertzel algorithm in Dual-Tone Multi-Frequency decoding is that it will precisely detect the pairs of frequencies a telephone keypad generates and enables applications such as automated call routing. This abstract evidence the relevance and applicability of the Goertzel algorithm in DSP, with specific applications where the detection of certain, pre-defined targeted frequencies has to be made with very minimal computational overhead.