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INF4420 Discrete time signals Dag T. Wisland Spring 2014 Outline Impulse sampling z Transform Frequency response Stability Spring 2014 Discrete time signals 2 Introduction More practical to do processing on sampled

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INF4420

Discrete time signals

Dag T. Wisland Spring 2014

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Spring 2014 Discrete time signals 2

Outline

Impulse sampling
z‐Transform
Frequency response
Stability

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Introduction

More practical to do processing on sampled

signals in many cases

Sampled + quantized signals = digital
Inputs and outputs are not sampled
How does sampling affect the signals?
Tools for analyzing sampled signals and systems

(“discrete Laplace transform”, the z‐transform)

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Introduction

We have already seen sample and hold circuits
We can also realize integrators, filters, etc. as

sampled analog systems—switched capacitor

techniques. Discrete time, continuous amplitude.
Digital processing is efficient and robust, usually

preferred where applicable. Sampling also applies to digital.

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Introduction

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Introduction

Sample a continuous time input signal at

uniformely spaced time points.

Output is a discrete sequence of values (in

theory).

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Introduction

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Sampling

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Laplace transform: Fourier transform:

Input signal

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Sampling

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Sampling

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Sampling

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Sampling

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Sampling

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Sampling

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Sampling

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Frequency response

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Frequency response

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Frequency response

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Frequency response

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Frequency response

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Frequency response

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Sampling rate conversion

Changing the sampling rate after sampling
We come back to this when discussing
versampled converters
Oversampling = sampling faster than the Nyquist

frequency would indicate

Upsampling is increasing the sampling rate

(number of samples per unit of time)

Downsampling is decreasing the sampling rate

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Downsampling

Keep every n‐th sample. Downsample too much: Aliasing

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Upsampling

Insert n zero valued samples between each original sample, and low‐pass filter. Requires gain to maintain the signal level.

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Discrete time filters

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Discrete time filters

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Stability

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IIR filters

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FIR filters

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Bilinear transform

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Sample and hold

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Sample and hold

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Sample and hold

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Sample and hold

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Sampled signal spectrum

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References

Gregorian and Temes, Analog MOS Integrated Circuits for Signal Processing, Wiley, 1986

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