This chapter delves into the principles of multiresolution analysis in signal processing, focusing on the decomposition of signals into time-frequency representations using filter banks. It begins with a practical introduction to spectrograms as a tool for uniform filter bank frequency decomposition. It explores nonuniform decomposition through the discrete wavelet transform (DWT), enabling improved time-frequency localization. A detailed examination of frequency-domain notation and conventions sets the groundwork for understanding various frequency transforms, including the discrete-time Fourier transform (DTFT), discrete Fourier transform (DFT), discrete cosine transform (DCT), z-transform, and the short-time Fourier transform (STFT). These transforms are analyzed in terms of their resolution, periodicity, and implementation. Python examples reinforce key concepts, demonstrating aliasing effects, spectrogram analysis, and filter design. The chapter highlights the trade-offs between time and frequency resolution, particularly in STFT and wavelet methods. Emphasis is placed on the importance of understanding the transform properties for designing efficient and accurate multirate systems, forming a foundation for advanced techniques in later chapters.