A simple and unified proof of dyadic shift invariance and the extension to cyclic shift invariance

A new transform known as conjugate symmetric sequency-ordered complex Hadamard transform (CS-SCHT) is presented in this paper. The transform matrix of this transform possesses sequency ordering and the spectrum obtained by the CS-SCHT is conjugate symmetric. Some of its important properties are discussed and analyzed. Sequency defined in the CS-SCHT is interpreted as compared to frequency in the discrete Fourier transform. The exponential form of the CS-SCHT is derived, and the proof of the dyadic shift invariant property of the CS-SCHT is also given. The fast and efficient algorithm to compute the CS-SCHT is developed using the sparse matrix factorization method and its computational load is examined as compared to that of the SCHT. The applications of the CS-SCHT in spectrum estimation and image compression are discussed. The simulation results reveal that the CS-SCHT is promising to be employed in such applications.

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“…Let h(p, k) be any element of a CS-SCHT transformation matrix. Then the transformation is said to be dyadic shift invariant (DSI) as [20]…”

Section: Properties Of the Cs-schtmentioning

confidence: 99%

“…The proof is completed here. It is noted that the power spectrum of a realvalued input signal obtained through the DSI transformation is dyadic shift invariant [20]. Hence, the CS-SCHT power spectrum is also dyadic shift invariant.…”

Section: Properties Of the Cs-schtmentioning

confidence: 99%

Conjugate Symmetric Sequency-Ordered Complex Hadamard Transform

Aung

Rahardja

2009

IEEE Trans. Signal Process.

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“…Let h(p, k) be any element of a CS-SCHT transformation matrix. Then the transformation is said to be dyadic shift invariant (DSI) as it satisfies [67] h is the bit-reversed converted decimal number. Therefore, it has only one bit of 1 in its binary expression and the rest are 0 (see Table 7.1 for an example).…”

Section: Property 6: Dyadic Shift Invariant Power Spectrummentioning

confidence: 99%

“…The proof is completed here. It is noted that the power spectrum of a real-valued input signal obtained through the DSI transformation is dyadic shift invariant [67]. Hence, the CS-SCHT power spectrum is also dyadic shift invariant.…”

Section: Property 6: Dyadic Shift Invariant Power Spectrummentioning

confidence: 99%

Sequency-ordered complex hadamard transforms and their applications to communications and signal processing

Aung¹

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Computationally efficient wavelet decomposition/reconstruction for embedded systems

Trelewicz

Yeary²,

Griswold³

Proceedings of 2002 IEEE 10th Digital Signal Processing Workshop, 2002 and the 2nd Signal Processing Education Workshop.

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A simple and unified proof of dyadic shift invariance and the extension to cyclic shift invariance

Abstract: . ibstruct-In this paper, a simple and unified proof of the dg idic shift invariance and the extension to cyclic shift invariance an' presented. First, the concept of the dyadic shift invariance (DSI) and cyclic shift invariant (

Cited by 5 publications

References 7 publications

Conjugate Symmetric Sequency-Ordered Complex Hadamard Transform

Conjugate Symmetric Sequency-Ordered Complex Hadamard Transform

Sequency-ordered complex hadamard transforms and their applications to communications and signal processing

Computationally efficient wavelet decomposition/reconstruction for embedded systems

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