Assistance from the Analog Components

October 23, 2019

Sampling

Introduction to Sampling

Perfect Reconstruction from Samples

Examples of Waveform Sampling

Waveform Analysis Using Sampling

Distortion Introduced by Sampling

Frequency Domain Consequences of Sampling

Introduction

Definitions

DTFT of a Sampled Sequence

Fourier Transform of a Sampled Sequence

Sampling at the Nyquist Rate

Oversampling

Undersampling and Aliasing

Reconstruction Via Interpolation

Introduction to Interpolation

Waveform Approximation Using Lagrange Polynomial Interpolation

Perfect Waveform Reconstruction Using Sinc Interpolation

Interpolation in the Frequency Domain

Assistance from the Analog Components

Quantization noise and over-sampling

Quantization and Noise

Signal-to-Quantization Noise Ratio (SQNR)

Increasing SQNR by Increasing Bits Per Sample

Increasing SQNR by Increasing the Sample Rate

Differential Quantization / Delta Modulation

Differential Quantization and Delta Modulation

Noise Shaping / Delta-Sigma Modulation

Introduction

Delta-Sigma Encoding

Quiz: Sampling & Reconstruction

Back to: Sampling & Reconstruction

Two questions may arise when using the sampling theorem:

How is the signal band-limited?
How can x(t) be reconstructed using the sinc functions?

Fortunately, we can perform both operations using analog electronics. Band-limiting is performed using an anti-aliasing filter and reconstruction is performed using a reconstruction filter.

x(t) to anti-aliasing filter to ADC to DSP to DAC to reconstruction filter to y(t)