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SEL4223 Digital Signal Processing Spectrum representation of discrete-time signals Musa MohdMokji Fourier transformation family Periodic Signal Aperiodic Signal Continuous Fourier Transform (FT) frequency - X Ω ,X(F) Continuous- time signal Discrete Fourier Series (FS) frequency - Discrete-time Fourier Transform Continuous - (DTFT) frequency X ω ,X(f) Discrete-time signal Discrete-time Fourier Discrete Fourier Transform (DFT) Discrete Series (DTFS) Fast Fourier Transform (FFT) frequency X[k] Fourier Series • Fourier series is the foundation to all of the Fourier transformation family • The name Fourier Series is actually refers to a representation of periodic signal in terms of sine and cosine signal where sine and cosine signals are known to be a single frequency signal. • In other words, Fourier Series decomposes periodic signal into a series of single frequency signals. Fourier Series (cont.) • Frequency response of the Fourier Series is called ‘Fourier Series Coefficient’. Fourier series,x t ! Fourier Series Coefficient,a% (time−domain) (frequency−domain)
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