Chapter 8(Digital signal spectrum).ppt

Chapter 8Digital Signal Spectrum Digital signal spectrum Signal f(t) Example8.4 (P295)：Find the amplitude and phase spectrum of the square wave signal shown below. The period N=8. Periodic digital signal Solution： ?????? period N = 8, the Fourier coefficients : Periodic digital signal Calculations results: 0.000 0 0.000 0 4 0.392 7 0.135 3 5 0.000 0 0.000 0 6 -0.392 7 0.135 3 3 0.000 0 0.000 0 2 1.178 1 0.326 6 7 -1.178 8 0.326 6 1 0.000 0 0.500 0 0 ?k | ck |/8 k Periodic digital signal * * The definition of the digital signal spectrum How to use the DTFT to calculate the non-periodic signal spectrum Introduce the Discrete Fourier Series (DFS) Shows how to calculate spectra for periodic signal using the DFS Introduces the fundamental frequency and harmonic frequency Spectrum F(Ω) Continuous non-periodic Discrete non-periodic Continuous periodic FS DTFT DFS FT Continuous periodic Continuous non-periodic Discrete periodic Discrete periodic Discrete periodic Signal Spectrum FT DTFT DFS 8.1 Digital signal spectrum In the frequency domain, every digital signal has a typical characteristic. For example: the sine wave contains only a single frequency, white noise contains all frequency components.Smooth changes in the signal comes from its low frequency components, the steep edges and sharp change from its high-frequency components. A square wave, contains the low-frequency component to produce a smooth change, as well as high-frequency components that form a steep edge. Digital signal spectrum Digital signal spectrum The spectrum of the signal has two parts. Magnitude spectrum is related to the size or amplitude of each frequency component. Phase spectrum gives the phase relationships between different frequency components. Digital signal spectrum All the digital signals have spectra, but different tools must be used to compute them. non-periodic digital signal: DTFT periodic digital signal: DFS Digital signal spectrum 8.2 Non-periodic digital signals Non-period