M4: Quantization of Continues Amplitude Signals

Quantization Error

The error introduced in representing the continuous–valued signal by a finite set of discrete value levels.

Minimum Step Size (Resolution)

Distance between two successive quantization level.

QUANTIZATION ERROR ( eq[n]):

Signal to Quantization Noise Ratio (SQNR)

(How clear a digital signal is compared to the error/noise from converting analog to digital)

Signal to quantization noise ratio of signal power to noise power.

SQNR Formula:

Digital-to-Analog Converter

__________ used to convert the digital signal back to analog.

digital control system

Digital computer is used to __________.

Impulse Train

Digital data initially converted into an __________ with specific spectrum.

Low-Pass Filter

(it allows low frequencies to pass and blocks high frequencies)

Removes frequency above half the sampling rate (Nyquist frequencies) to reconstruct the analog signal.

Zeroth-order Hold

It use instead of an impulse train.

Spectrum of Zeroth-Order Hold

__________ is equal to the spectrum of the impulse train multiplied by the SinC function.

Analog Filter

To recover the original analog signal.
- Remove the frequency above the Nyquist Rate.
- Compensate for the SinC distortion by amplifying frequencies with the reciprocal of sinC (1/sinC).

36%

An amplification of about _____ at half sampling frequencies.

• Graphical

• Tabular

• Functional

• Sequential (finite or infinite)

4 ways in representing signal:

Quantization

_____ is the process of approximating a continuous range of values (or a very large set of possible discrete values) by a relatively-small set of discrete symbols or integer values.

Analog electronic filters

__________ are used to satisfy the sampling theorem.

Antialias Filter

(A filter that removes high frequencies before the signal is sampled.
Purpose: Prevent aliased or wrong frequencies from entering the digital system.)

The electronic filter placed before an ADC is called an _________. It is used to remove frequency components above one-half of the sampling rate that would alias during the sampling.

Reconstruction Filter

(A filter that smooths the signal after it is converted back to analog.
Purpose: Remove unwanted high frequencies and make the output signal clean and smooth.)

The electronic filter placed after a DAC is called a __________. It also eliminates frequencies above the Nyquist rate, and may include a correction for the zeroth-order hold.

Bessel Filter

• Also known as Thompson Filter

• Best step response

• Worst roll-off rate but can be improved by adding more poles

Butterworth Filter

• Has the flattest passband

• Better roll-off rate w/o allowing ripple

• Good step response

Chebyshev Filter

• Has the sharpest roll-off rate

• Has 6% ripple in the passband

• Has ringing and possibility of overshoot

• It cannot eliminate HF noise

• Bessel

• Butterworth

• Chebyshev

3 Types of Analog Filters: