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Related Concept Videos

Basic Discrete Time Signals01:16

Basic Discrete Time Signals

The unit step sequence is defined as 1 for zero and positive values of the integer n. This sequence can be graphically displayed using a set of eight sample points, showing a step function starting from n=0 and remaining constant thereafter.
The unit impulse or sample sequence is mathematically expressed as zero for all n values except at n=0, where it is one. The unit impulse sequence, denoted by δ(n), is the first difference of the unit step sequence, while the unit step sequence u(n) is the...
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.
The computational efficiency of the FFT becomes...
Convolution Properties I01:20

Convolution Properties I

Convolution computations can be simplified by utilizing their inherent properties.
The commutative property reveals that the input and the impulse response of an LTI (Linear Time-Invariant) system can be interchanged without affecting the output:
Maxam-Gilbert Sequencing01:05

Maxam-Gilbert Sequencing

In the same year as the discovery of the Sanger sequencing method, another group of scientists, Allan Maxam and Walter Gilbert, demonstrated their chemical-cleavage method for DNA sequencing. The Maxam-Gilbert method relies on using different chemicals that can cleave the DNA sequence at specific sites, the separation of resulting DNA fragments of variable size using electrophoresis, and deciphering the DNA sequence from the resulting gel bands.
Challenges of the Maxam-Gilbert Method
The...
Properties of DTFT I01:24

Properties of DTFT I

In signal processing, Discrete-Time Fourier Transforms (DTFTs) play a critical role in analyzing discrete-time signals in the frequency domain. Various properties of the DTFTs such as linearity, time-shifting, frequency-shifting, time reversal, conjugation, and time scaling help understand and manipulate these signals for different applications.
The linearity property of DTFTs is fundamental. If two discrete-time signals are multiplied by constants a and b respectively, and then combined to...
Vector Representation of Complex Numbers01:16

Vector Representation of Complex Numbers

Complex numbers, represented in Cartesian coordinates, can also be visualized as vectors. These vectors can be expressed in polar form, emphasizing their magnitude and angle. When a complex number is input into a function, the output is another complex number, highlighting the function's zero point from which the vector representation can originate.
Consider a function defined as the product of the complex factors in the numerator divided by the product of the complex factors in the denominator.

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Related Experiment Videos

Fast Algorithms for the Computation of Sliding Sequency-Ordered Complex Hadamard Transform.

Jiasong Wu1, Huazhong Shu, Lu Wang

  • 1LTSI, Laboratoire Traitement du Signal et de l'Image INSERM : U642 Université de Rennes I Campus de Beaulieu, 263 Avenue du Général Leclerc - CS 74205 - 35042 Rennes Cedex,FR.

IEEE Transactions on Signal Processing : a Publication of the IEEE Signal Processing Society
|September 13, 2011
PubMed
Summary
This summary is machine-generated.

New fast algorithms for sliding window complex Hadamard transforms offer significant computational efficiency. These methods outperform existing block-based and sliding FFT/DFT approaches for signal processing applications.

Related Experiment Videos

Area of Science:

  • Digital Signal Processing
  • Algorithm Development
  • Transform Analysis

Background:

  • The sequency-ordered complex Hadamard transform (SCHT) is crucial for various signal processing tasks.
  • Existing methods for computing sliding window SCHT can be computationally intensive.
  • Efficient algorithms are needed to reduce complexity in real-time applications.

Purpose of the Study:

  • To develop novel, fast algorithms for computing forward and inverse SCHT in a sliding window.
  • To enhance computational efficiency compared to existing transform domain methods.
  • To explore the application of these algorithms in transform domain adaptive filtering.

Main Methods:

  • Decomposition of inverse SCHT (ISCHT) into smaller transforms.
  • Recursive computation of window values using ISCHT and modified ISCHT (MISCHT).
  • Transposition of signal flow graphs for forward SCHT computation.

Main Results:

  • Proposed algorithms achieve O(N) arithmetic operations, significantly improving efficiency.
  • Algorithms offer a balance between computational and implementation complexity.
  • Demonstrated effectiveness of sliding ISCHT in transform domain adaptive filtering (TDAF).

Conclusions:

  • The developed algorithms provide a computationally efficient solution for sliding window SCHT.
  • These fast algorithms are superior to block-based and sliding FFT/DFT methods.
  • The sliding ISCHT is a viable and efficient tool for TDAF applications.