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Review of Discrete-Time Signal Processing. Sampling. CT. DT. Zero-Order Hold (ZOH). Sampling. Impulse train. Sampling. δ (t-nT). Spectrum of Sampled Signal ( Ω s >2 Ω N ). The spectrum of the sampled signal is periodic in Ω s =2 π /T. Spectrum of Sampled Signal ( Ω s <2 Ω N ).

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Review of discrete time signal processing

Review of Discrete-TimeSignal Processing


Sampling
Sampling

CT

DT



Sampling1
Sampling

Impulse train


Sampling2
Sampling

δ(t-nT)


Spectrum of sampled signal s 2 n
Spectrum of Sampled Signal (Ωs>2ΩN)

The spectrum of the sampled signal is periodic in Ωs=2π/T.


Spectrum of sampled signal s 2 n1
Spectrum of Sampled Signal (Ωs<2ΩN)

  • Aliasing (folding) results in irreversible signal distortion.

  • Can only be avoided by using sufficiently high sample rate, or band-

    limit the input signal with a coarse, continuous-time filter – AAF.


Reconstruction filter nyquist
Reconstruction Filter (Nyquist)

Reconstruction filter = “smoothing” filter = “interpolation” filter


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