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This paper presents implementation of Discrete Fourier Transform and Orthogonal Discrete Wavelet Transform in Python computer programming language. The Fourier Transform is a fundamental signal processing tool whereas the Wavelet Transform is a powerful and advanced signal processing tool. Both have applications in numerous scientific and engineering disciplines. Our implementation aims to develop a deeper understanding of these transformations by presenting detailed coding steps to generate the frequency-domain and wavelet-domain outputs for selected example time-domain input signals. The results generated from developed program code are compared using built-in functions with similar matches have shown the successful implementation.