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Related Concept Videos

Discrete-time Fourier transform01:26

Discrete-time Fourier transform

The Discrete-Time Fourier Transform (DTFT) is an essential mathematical tool for analyzing discrete-time signals, converting them from the time domain to the frequency domain. This transformation allows for examining the frequency components of discrete signals, providing insights into their spectral characteristics. In the DTFT, the continuous integral used in the continuous-time Fourier transform is replaced by a summation to accommodate the discrete nature of the signal.
One of the notable...
Discrete Fourier Transform01:15

Discrete Fourier Transform

The Discrete Fourier Transform (DFT) is a fundamental tool in signal processing, extending the discrete-time Fourier transform by evaluating discrete signals at uniformly spaced frequency intervals. This transformation converts a finite sequence of time-domain samples into frequency components, each representing complex sinusoids ordered by frequency. The DFT translates these sequences into the frequency domain, effectively indicating the magnitude and phase of each frequency component present...
Properties of the z-Transform I01:17

Properties of the z-Transform I

The z-transform is a fundamental tool in digital signal processing, enabling the analysis of discrete-time systems through its various properties. It is an invaluable tool for analyzing discrete-time systems, offering a range of properties that simplify complex signal manipulations. One fundamental property is linearity. For any two discrete-time signals, the z-transform of their linear combination equals the same linear combination of their individual z-transforms. This property is essential...
Discrete-Time Fourier Series01:20

Discrete-Time Fourier Series

The Discrete-Time Fourier Series (DTFS) is a fundamental concept in signal processing, serving as the discrete-time counterpart to the continuous-time Fourier series. It allows for the representation and analysis of discrete-time periodic signals in terms of their frequency components. Unlike its continuous counterpart, which utilizes integrals, the calculation of DTFS expansion coefficients involves summations due to the discrete nature of the signal.
For a discrete-time periodic signal x[n]...
Fast Fourier Transform01:10

Fast Fourier Transform

The Fast Fourier Transform (FFT) is a computational algorithm designed to compute the Discrete Fourier Transform (DFT) efficiently. By breaking down the calculations into smaller, manageable sections, the FFT significantly reduces the computational complexity involved. Direct computation of an N-point DFT requires N2 complex multiplications, whereas the FFT algorithm needs only (N/2)log⁡2N multiplications, offering a much faster performance.
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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.
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Precision-aware self-quantizing hardware architectures for the discrete wavelet transform.

Dong-U Lee1, Lok-Won Kim, John D Villasenor

  • 1Mojix Inc., Los Angeles, CA 90025, USA. dongu@mojix.com

IEEE Transactions on Image Processing : a Publication of the IEEE Signal Processing Society
|August 10, 2011
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Summary
This summary is machine-generated.

This study introduces optimized bit-parallel (BP) and digit-serial (DS) discrete wavelet transform (DWT) designs. These methods enable customizable precision and energy-efficient implementations for applications like JPEG 2000.

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Area of Science:

  • Digital Signal Processing
  • VLSI Design
  • Image Compression

Background:

  • The Discrete Wavelet Transform (DWT) is crucial for signal and image processing, particularly in compression standards like JPEG 2000.
  • Energy efficiency and computational accuracy are critical for deploying DWT in resource-constrained environments.
  • Existing DWT implementations often require separate quantization steps, adding complexity.

Purpose of the Study:

  • To present novel precision-optimized bit-parallel (BP) and digit-serial (DS) implementations of the DWT.
  • To analyze the impact of DWT depth on computational accuracy and hardware resource utilization.
  • To develop energy-minimal DWT designs suitable for mobile and embedded systems.

Main Methods:

  • Design and implementation of both BP and DS architectures for DWT.
  • Integration of coefficient quantization directly into the DWT computation process.
  • Evaluation of design performance (area, speed, power) using 90-nm CMOS technology.

Main Results:

  • BP designs offer higher speed, while DS designs achieve better area efficiency, especially at higher precision and DWT levels.
  • The integrated quantization eliminates the need for a separate downstream step, simplifying application pipelines.
  • A flexible DWT processor supporting run-time configurable parameters was also developed.

Conclusions:

  • Precision-optimized BP and DS DWT designs provide trade-offs between speed and hardware resources.
  • These designs enhance the applicability of DWT algorithms on energy-constrained platforms.
  • The presented flexible DWT processor offers adaptability for various application requirements.