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Signal Processing and Communications

(MCT 4338)

Department of Mechatronics Engineering

International Islamic University Malaysia

Sampling and Interpolation

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Outline

• Sampling theorem

• Ideal and practical interpolation

• Aliasing

• Non-ideal interpolation

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Sampling Theorem

fs

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Fourier Transform of III(t)

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Fourier Transform of Sampled Signal

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Sampled Signal and Fourier Transform

Figure 6.1 Sampled signal and its Fourier spectra.

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Outline

• Sampling theorem

• Ideal and practical interpolation

• Aliasing

• Non-ideal interpolation

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Reconstruction from Uniform Samples

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Ideal Interpolation

Figure 6.2 Ideal interpolation.

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Practical Interpolation (1)

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Practical Interpolation (2)

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Practical Interpolation (3)

Figure 6.5 Practical signal reconstruction.

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Practical Interpolation (4)

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Outline

• Sampling theorem

• Ideal and practical interpolation

• Aliasing

• Non-ideal interpolation

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Aliasing Effect

If we sample too slowly, the shifted spectrums overlap.

High frequency components are “folded” back into the

spectrum. This should be avoided.

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Anti-aliasing Filter

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(a) Non-band limited signal spectrum and its sampled spectrum G( f ).

(b) Equivalent low-pass signal spectrum Ga( f ) constructed from uniform samples of g(t) at sampling rate 2B.

Maximum Information Rate

A maximum of 2B independent pieces of information per second can be transmitted,

error free, over a noiseless channel of bandwidth B Hz

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Outline

• Sampling theorem

• Ideal and practical interpolation

• Aliasing

• Non-ideal interpolation

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Non-ideal Practical Sampling (1)

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Non-ideal Practical Sampling (2)

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Non-ideal Practical Sampling (3)