RBFF

General

Lecture 6: Sampling And Aliasing

Di: Amelia

Things to Remember Signal pmcessing Frequency domain vs. spatial domain Filters in the frequency domain Filters in the spatial domain = convolution Sampling and aliasing Image Introduction to Signal Processing – Sampling, Reconstruction, and Aliasing Motivation from Week 1 Lecture Nyquist’s Sampling Theorem states that we must sample at twice the frequency of the highest-varying component of our image to avoid aliasing and consequently reducing spatial artifacts.

CS184/284A: Lecture 3: Sampling and Aliasing

Lecture Lecture slides on the Sampling Theorem in PowerPoint format. Fall 2024 Part 1: mixed-signal systems Fall 2024 Part 2: Notepad. Analog-to-digital converters Notepad. Effect of sample rate on aliasing Smoothing (lowpass filtering) Effect of smoothing on aliasing Things to Remember Signal processing Frequency domain vs. spatial domain Filters in the frequency domain Filters in the spatial domain = convolution Sampling and aliasing Image

• Separate by removing high frequencies from the original signal (low pass pre-filtering) • Separate by increasing the sampling density • If we can’t separate the copies, we will have overlapping

6.801 / 6.866 Machine Version, Lecture Notes

Nyquist Limit / Shannon’s Sampling Theorem • If we insufficiently sample the signal, it may be mistaken for something simpler during reconstruction (that’s aliasing!) Image from Robert L. Sampling ( unless otherwise stated slides are taken or adopted from Video Lecture and Questions for Aliasing or Effect of Under Sampling – Generation of Aliasing – Effect and Solution of Aliasing Video Lecture – Crash Course for GATE Instrumentation

Determine samples/period, the resulting recovered signal ,and aliased frequencies if present Determine the number of samples/ period 60 Hz 0.01 s = 0.6 samples/pa-iod Below Nyquist

LECTURE OBJECTIVES SAMPLING can cause ALIASING Sampling Theorem Sampling Rate > 2(Highest Frequency) Spectrum for digital signals, x[n] Normalized Frequency

Introduction to Signal Processing – Sampling, Reconstruction, and Aliasing Motivation from Week 1 Lecture hat are the sampling issues and how to deal with them ? Texture magnification: a pixel in texture image (‚texel‘) maps to an area larger than one pixel in image Texture minification: a pixel in

  • Digital Signal Processing Lecture 5
  • Lecture 6: Sampling Theorem
  • MIT 6.450 Principles of Digital Communications I

DIP Lecture 7: The 2D Discrete Fourier Transform Watch on Lecture 8: Frequency Domain Filtering; Sampling and Aliasing

MIT 6.450 Principles of Digital Communications I

Aliasing Jaggies Demo What is a point sample (aka sample)? An evaluation At an infinitesimal point (2-D) Or along a ray (3-D) What is evaluated Work 1 Inclusion (2-D) or intersection Introduction to Signal Processing – Sampling, Reconstruction, and Aliasing Motivation from Week 1 Lecture

UNIT I LINEAR FILTERS Lecture 8Hrs Introduction to Computer Vision, Linear Filters and Convolution, Shift Invariant Linear Systems, Spatial Frequency and Fourier Transforms, Inadequate Johnson All content How many samples are enough to avoid aliasing? How many samples needed to represent a given signal without loss? What signals can be reconstructed without loss for a

Work # 1. Sampling Theorem and Aliasing Theory basics The idea of the sampling theorem is the following: otherwise speci the continuous real signal with the spectrum limited by the frequency range 0 < f < fm

  • Sampling and Anti-Aliasing
  • Sampling, Resampling, and Warping
  • Foundations of Digital Signal Processing
  • Sampling and Reconstruction: DSP Lecture
  • 6.801 / 6.866 Machine Version, Lecture Notes

This lecture includes demonstrations of sampling and aliasing with a sinusoidal signal, sinusoidal response of digital filters, dependence of frequency response on sampling period, and the Lecture Slides Lecture 1: The Goals of Rendering Lecture 2: Ray Tracing I: Basic Algorithm, Ray-Surface Intersection Lecture 3: Ray Tracing II: Acceleration Techniques Lecture 4: The Light

It is important to understand that in sampling and reconstruction with an ideal lowpass filter, the reconstructed output will not be equal to the original input in the presence of aliasing, but Lecture 23: Aliasing in Frequency: the Sampling Theorem Mark Hasegawa-Johnson All content CC-SA 4.0 unless otherwise speci ed. How does sampling affect the information contained in a signal? We would like to sample in a way that preserves information, which may not seem possible. Therefore, the same samples To

Sampling and Anti-Aliasing

This lecture includes demonstrations of sampling and aliasing with a sinusoidal signal, sinusoidal response of digital filters, dependence of frequency response on sampling period, and the What if we “missed” things between the samples? Simple example: undersampling a sine wave unsurprising result: information is lost surprising result: indistinguishable from lower frequency

ECE406/506 Real-Time Digital Signal Processing Lecture 3 – Sampling and Reconstruction Electrical Engineering and Computer Science University of Tennessee, Knoxville Increasing the sampling rate moves each copy of the spectra further apart, potentially reducing the overlap and thus aliasing Resulting samples must be resampled (filtered) to image

Sampling, Aliasing, and Quantization Now that we have the basic background material covered, let’s start talking about DSP. The starting point we need to understand is sampling and its

Work # 1. Sampling theorem and aliasing Objective: Acquiring of elementary skills of work with MATLAB package; examination of the sampling theorem and aliasing effect. The fact that a signal is bandlimited is a very powerful constraint. Sampling Examples Aliasing and the Minimum Sampling Rate When the sampling rate is too low, the spectral replicas Lecture 8: Sampling Theorem Mark Hasegawa-Johnson All content CC-SA 4.0 unless otherwise speci ed.