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Related Concept Videos

Upsampling01:22

Upsampling

Managing signal sampling rates is essential in digital signal processing to maintain signal integrity. A decimated signal, characterized by a reduced frequency range due to its lower sampling rate, can be upsampled by inserting zeros between each sample. This upsampling process expands the original spectrum and introduces repeated spectral replicas at intervals dictated by the new Nyquist frequency. To refine this zero-inserted sequence, it is passed through a lowpass filter with a cutoff...
Sampling Theorem01:15

Sampling Theorem

In signal processing, the analysis of continuous-time signals, denoted as x(t), often involves sampling techniques to convert these signals into discrete-time signals. This process is essential for digital representation and manipulation. A critical component in sampling is the train of impulses, characterized by the sampling interval and the sampling frequency. The relationship between these parameters and the original signal's properties dictates the success of the sampling process.
Aliasing01:18

Aliasing

Accurate signal sampling and reconstruction are crucial in various signal-processing applications. A time-domain signal's spectrum can be revealed using its Fourier transform. When this signal is sampled at a specific frequency, it results in multiple scaled replicas of the original spectrum in the frequency domain. The spacing of these replicas is determined by the sampling frequency.
If the sampling frequency is below the Nyquist rate, these replicas overlap, preventing the original signal...
Bandpass Sampling01:17

Bandpass Sampling

In signal processing, bandpass sampling is an effective technique for sampling signals that have most of their energy concentrated within a narrow frequency band. This type of signal is known as a bandpass signal. The key principle of bandpass sampling involves sampling the signal at a rate that is greater than twice the signal's bandwidth to prevent aliasing.
A bandpass signal has a spectrum with a lower frequency limit, denoted as ω1, and an upper frequency limit, denoted as ω2. The spectrum...
Downsampling01:20

Downsampling

When considering a sampled sequence with zero values between sampling instants, one can replace it by taking every N-th value of the sequence. At these integer multiples of N, the original and sampled sequences coincide. This process, known as decimation, involves extracting every N-th sample from a sequence, thereby creating a more efficient sequence.
The Fourier transform of the decimated sequence reveals a combination of scaled and shifted versions of the original spectrum. This...
Linear Approximation in Frequency Domain01:26

Linear Approximation in Frequency Domain

Linear systems are characterized by two main properties: superposition and homogeneity. Superposition allows the response to multiple inputs to be the sum of the responses to each individual input. Homogeneity ensures that scaling an input by a scalar results in the response being scaled by the same scalar.
In contrast, nonlinear systems do not inherently possess these properties. However, for small deviations around an operating point, a nonlinear system can often be approximated as linear.

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Related Experiment Video

Updated: Jul 7, 2026

Time Multiplexing Super Resolving Technique for Imaging from a Moving Platform
06:25

Time Multiplexing Super Resolving Technique for Imaging from a Moving Platform

Published on: February 12, 2014

Generalization of spatially variant apodization to noninteger Nyquist sampling rates.

B H Smith1

  • 1ERIM Int. Inc., Ann Arbor, MI 48113-4008, USA. bhsmith@erimint.com

IEEE Transactions on Image Processing : a Publication of the IEEE Signal Processing Society
|February 8, 2008
PubMed
Summary

Spatially variant apodization (SVA) was reformulated for synthetic aperture radar (SAR) imagery, reducing sidelobe energy without losing resolution. This method effectively eliminates artifacts in SAR images.

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Area of Science:

  • Radar Imaging
  • Signal Processing

Background:

  • Synthetic Aperture Radar (SAR) imagery often suffers from sidelobe artifacts.
  • Existing apodization techniques may not be optimal for arbitrary sampling rates.

Purpose of the Study:

  • To reformulate Spatially Variant Apodization (SVA) for SAR imagery with arbitrary sampling rates.
  • To develop a method for reducing sidelobe energy without compromising image resolution.

Main Methods:

  • Implemented SVA as a spatially varying three-point finite impulse response filter.
  • Developed filter parameter constraints based on physical concepts.
  • Varied filter parameters to reduce sidelobe energy.

Main Results:

  • Achieved significant reduction in sidelobe energy.
  • Maintained effective resolution without loss.
  • Produced output comparable to the integer Nyquist version of SVA.
  • Effectively eliminated sidelobe artifacts.

Conclusions:

  • The reformulated SVA effectively suppresses sidelobe artifacts in SAR imagery.
  • The method is suitable for SAR data with arbitrary sampling rates.
  • This approach offers a robust solution for enhancing SAR image quality.