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发布时间：2022-06-13 发布人：admin 分类：说明书 资料大小：2.27M 资料格式：pdf 举报 版权申诉
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    11: Multirate Systems
    Multirate Systems
    Building blocks
    Resampling Cascades
    Noble Identities
    Noble Identities Proof
    Upsampled z-transform
    Downsampled z-transform
    Downsampled Spectrum
    Power Spectral Density
    Perfect Reconstruction
    Commutators
    Summary
    MATLAB routines
    11: Multirate Systems • Multirate Systems • Building blocks • Resampling Cascades • Noble Identities • Noble Identities Proof • Upsampled z-transform • Downsampled z-transform • Downsampled Spectrum • Power Spectral Density • Perfect Reconstruction • Commutators • Summary • MATLAB routines 11: Multirate Systems DSP and Digital Filters (2016-9045) Multirate: 11 – 1 / 14
    Multirate Systems Multirate systems include more than one sample rate 11: Multirate Systems • Multirate Systems • Building blocks • Resampling Cascades • Noble Identities • Noble Identities Proof • Upsampled z-transform • Downsampled z-transform • Downsampled Spectrum • Power Spectral Density • Perfect Reconstruction • Commutators • Summary • MATLAB routines DSP and Digital Filters (2016-9045) Multirate: 11 – 2 / 14
    Multirate Systems Multirate systems include more than one sample rate Why bother?: • May need to change the sample rate e.g. Audio sample rates include 32, 44.1, 48, 96 kHz 11: Multirate Systems • Multirate Systems • Building blocks • Resampling Cascades • Noble Identities • Noble Identities Proof • Upsampled z-transform • Downsampled z-transform • Downsampled Spectrum • Power Spectral Density • Perfect Reconstruction • Commutators • Summary • MATLAB routines DSP and Digital Filters (2016-9045) Multirate: 11 – 2 / 14
    Multirate Systems 11: Multirate Systems • Multirate Systems • Building blocks • Resampling Cascades • Noble Identities • Noble Identities Proof • Upsampled z-transform • Downsampled z-transform • Downsampled Spectrum • Power Spectral Density • Perfect Reconstruction • Commutators • Summary • MATLAB routines Multirate systems include more than one sample rate Why bother?: • May need to change the sample rate e.g. Audio sample rates include 32, 44.1, 48, 96 kHz • Can relax analog or digital filter requirements e.g. Audio DAC increases sample rate so that the reconstruction filter can have a more gradual cutoff DSP and Digital Filters (2016-9045) Multirate: 11 – 2 / 14
    Multirate Systems 11: Multirate Systems • Multirate Systems • Building blocks • Resampling Cascades • Noble Identities • Noble Identities Proof • Upsampled z-transform • Downsampled z-transform • Downsampled Spectrum • Power Spectral Density • Perfect Reconstruction • Commutators • Summary • MATLAB routines Multirate systems include more than one sample rate Why bother?: • May need to change the sample rate e.g. Audio sample rates include 32, 44.1, 48, 96 kHz • Can relax analog or digital filter requirements e.g. Audio DAC increases sample rate so that the reconstruction filter can have a more gradual cutoff • Reduce computational complexity FIR filter length ∝ fs Lower fs ⇒ shorter filter + fewer samples ⇒computation ∝ f 2 s ∆f where ∆f is width of transition band DSP and Digital Filters (2016-9045) Multirate: 11 – 2 / 14
    Building blocks Downsample y[m] = x[Km] 11: Multirate Systems • Multirate Systems • Building blocks • Resampling Cascades • Noble Identities • Noble Identities Proof • Upsampled z-transform • Downsampled z-transform • Downsampled Spectrum • Power Spectral Density • Perfect Reconstruction • Commutators • Summary • MATLAB routines DSP and Digital Filters (2016-9045) Multirate: 11 – 3 / 14
    Building blocks Downsample y[m] = x[Km] Upsample v[n] =(u n 0 K K | n else 11: Multirate Systems • Multirate Systems • Building blocks • Resampling Cascades • Noble Identities • Noble Identities Proof • Upsampled z-transform • Downsampled z-transform • Downsampled Spectrum • Power Spectral Density • Perfect Reconstruction • Commutators • Summary • MATLAB routines DSP and Digital Filters (2016-9045) Multirate: 11 – 3 / 14
    11: Multirate Systems • Multirate Systems • Building blocks • Resampling Cascades • Noble Identities • Noble Identities Proof • Upsampled z-transform • Downsampled z-transform • Downsampled Spectrum • Power Spectral Density • Perfect Reconstruction • Commutators • Summary • MATLAB routines Building blocks Downsample y[m] = x[Km] Upsample Example: v[n] =(u n 0 K K | n else Downsample by 3 then upsample by 4 w[n] 0 DSP and Digital Filters (2016-9045) Multirate: 11 – 3 / 14
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